%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:03:08 PM UTC 2026
% Result : Theorem 12.06s 12.09s
% Output : Proof 12.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_d_subst,type,
d_subst: $tType ).
thf(ty_d_term,type,
d_term: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_induction2lem,type,
induction2lem: $o ).
thf(ty_pushprop_lem1v2_lthm,type,
pushprop_lem1v2_lthm: $o ).
thf(ty_hoasapinj2_gthm,type,
hoasapinj2_gthm: $o ).
thf(ty_apnotvar,type,
apnotvar: $o ).
thf(ty_hoasinduction_lem3aaa,type,
hoasinduction_lem3aaa: $o ).
thf(ty_id,type,
id: subst ).
thf(ty_hoasinduction_lem1_lthm,type,
hoasinduction_lem1_lthm: $o ).
thf(ty_hoasinduction_lem2,type,
hoasinduction_lem2: $o ).
thf(ty_pushprop_lthm,type,
pushprop_lthm: $o ).
thf(ty_axabs,type,
axabs: $o ).
thf(ty_hoasinduction,type,
hoasinduction: $o ).
thf(ty_comp,type,
comp: subst > subst > subst ).
thf(ty_hoaslamnotap_lthm,type,
hoaslamnotap_lthm: $o ).
thf(ty_eigen__159,type,
eigen__159: term ).
thf(ty_axidl,type,
axidl: $o ).
thf(ty_pushprop_lem1_lthm,type,
pushprop_lem1_lthm: $o ).
thf(ty_hoasinduction_lem0_lthm,type,
hoasinduction_lem0_lthm: $o ).
thf(ty_hoasinduction_lem1,type,
hoasinduction_lem1: $o ).
thf(ty_hoaslaminj_gthm,type,
hoaslaminj_gthm: $o ).
thf(ty_pushprop_lem0_lthm,type,
pushprop_lem0_lthm: $o ).
thf(ty_hoasinduction_no_psi_cond_lthm,type,
hoasinduction_no_psi_cond_lthm: $o ).
thf(ty_hoasinduction_lem3aa_lthm,type,
hoasinduction_lem3aa_lthm: $o ).
thf(ty_axassoc,type,
axassoc: $o ).
thf(ty_hoaslaminj_lthm,type,
hoaslaminj_lthm: $o ).
thf(ty_hoasinduction_lem2_gthm,type,
hoasinduction_lem2_gthm: $o ).
thf(ty_pushprop_lem2v2_gthm,type,
pushprop_lem2v2_gthm: $o ).
thf(ty_pushprop,type,
pushprop: $o ).
thf(ty_lam,type,
lam: term > term ).
thf(ty_hoaslamnotvar,type,
hoaslamnotvar: $o ).
thf(ty_hoasapnotvar_lthm,type,
hoasapnotvar_lthm: $o ).
thf(ty_hoasapnotvar,type,
hoasapnotvar: $o ).
thf(ty_hoasinduction_gthm,type,
hoasinduction_gthm: $o ).
thf(ty_axvarcons,type,
axvarcons: $o ).
thf(ty_hoasinduction_lem2v2,type,
hoasinduction_lem2v2: $o ).
thf(ty_hoasinduction_lem3v2_gthm,type,
hoasinduction_lem3v2_gthm: $o ).
thf(ty_induction,type,
induction: $o ).
thf(ty_axvarshift,type,
axvarshift: $o ).
thf(ty_hoasapinj1_lthm,type,
hoasapinj1_lthm: $o ).
thf(ty_d2term,type,
d2term: d_term > term ).
thf(ty_axapp,type,
axapp: $o ).
thf(ty_eigen__136,type,
eigen__136: term ).
thf(ty_axscons,type,
axscons: $o ).
thf(ty_axvarid,type,
axvarid: $o ).
thf(ty_hoaslam,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(ty_hoaslaminj,type,
hoaslaminj: $o ).
thf(ty_induction2,type,
induction2: $o ).
thf(ty_hoaslamnotap_gthm,type,
hoaslamnotap_gthm: $o ).
thf(ty_hoasinduction_lem3v2a_lthm,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(ty_eigen__147,type,
eigen__147: term > $o ).
thf(ty_eigen__125,type,
eigen__125: term ).
thf(ty_pushprop_lem3v2,type,
pushprop_lem3v2: $o ).
thf(ty_hoasinduction_p_and_p_prime,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(ty_hoasinduction_lem3,type,
hoasinduction_lem3: $o ).
thf(ty_pushprop_lem2v2,type,
pushprop_lem2v2: $o ).
thf(ty_eigen__158,type,
eigen__158: subst > term > subst > $o ).
thf(ty_induction2lem_lthm,type,
induction2lem_lthm: $o ).
thf(ty_eigen__169,type,
eigen__169: term ).
thf(ty_hoasinduction_lem3v2,type,
hoasinduction_lem3v2: $o ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_hoaslamnotvar_gthm,type,
hoaslamnotvar_gthm: $o ).
thf(ty_hoasinduction_lem3b_gthm,type,
hoasinduction_lem3b_gthm: $o ).
thf(ty_substmonoid_gthm,type,
substmonoid_gthm: $o ).
thf(ty_termmset_gthm,type,
termmset_gthm: $o ).
thf(ty_axshiftcons,type,
axshiftcons: $o ).
thf(ty_eigen__1,type,
eigen__1: term > $o ).
thf(ty_apinj2,type,
apinj2: $o ).
thf(ty_termmset_lthm,type,
termmset_lthm: $o ).
thf(ty_hoasinduction_lem1v2,type,
hoasinduction_lem1v2: $o ).
thf(ty_hoasapinj1_gthm,type,
hoasapinj1_gthm: $o ).
thf(ty_hoasap,type,
hoasap: subst > term > subst > term > term ).
thf(ty_hoasinduction_lthm,type,
hoasinduction_lthm: $o ).
thf(ty_hoasinduction_lem3b_lthm,type,
hoasinduction_lem3b_lthm: $o ).
thf(ty_pushprop_lem2v2_lthm,type,
pushprop_lem2v2_lthm: $o ).
thf(ty_eigen__148,type,
eigen__148: term ).
thf(ty_pushprop_lem1_gthm,type,
pushprop_lem1_gthm: $o ).
thf(ty_axclos,type,
axclos: $o ).
thf(ty_eigen__4,type,
eigen__4: term ).
thf(ty_push,type,
push: term > subst > subst ).
thf(ty_var,type,
var: term > $o ).
thf(ty_ulamvar1,type,
ulamvar1: $o ).
thf(ty_hoasinduction_lem3_gthm,type,
hoasinduction_lem3_gthm: $o ).
thf(ty_hoasinduction_no_psi_cond,type,
hoasinduction_no_psi_cond: $o ).
thf(ty_hoasinduction_lem3b,type,
hoasinduction_lem3b: $o ).
thf(ty_hoasinduction_lem2_lthm,type,
hoasinduction_lem2_lthm: $o ).
thf(ty_pushprop_p_and_p_prime,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(ty_pushprop_lem1v2_gthm,type,
pushprop_lem1v2_gthm: $o ).
thf(ty_apinj1,type,
apinj1: $o ).
thf(ty_eigen__114,type,
eigen__114: subst > term > subst > $o ).
thf(ty_eigen__0,type,
eigen__0: term > $o ).
thf(ty_induction2lem_gthm,type,
induction2lem_gthm: $o ).
thf(ty_hoasinduction_lem2v2_gthm,type,
hoasinduction_lem2v2_gthm: $o ).
thf(ty_hoasinduction_lem3v2_f,type,
hoasinduction_lem3v2_f: $o ).
thf(ty_induction2_lthm,type,
induction2_lthm: $o ).
thf(ty_hoaslamnotap,type,
hoaslamnotap: $o ).
thf(ty_shinj,type,
shinj: $o ).
thf(ty_hoasapnotvar_gthm,type,
hoasapnotvar_gthm: $o ).
thf(ty_one,type,
one: term ).
thf(ty_eigen__3,type,
eigen__3: subst ).
thf(ty_hoasinduction_lem3v2a,type,
hoasinduction_lem3v2a: $o ).
thf(ty_hoasapinj2,type,
hoasapinj2: $o ).
thf(ty_axidr,type,
axidr: $o ).
thf(ty_d2subst,type,
d2subst: d_subst > subst ).
thf(ty_pushprop_lem0,type,
pushprop_lem0: $o ).
thf(ty_termmset,type,
termmset: $o ).
thf(ty_hoasinduction_lthm_3,type,
hoasinduction_lthm_3: $o ).
thf(ty_pushprop_lem1,type,
pushprop_lem1: $o ).
thf(ty_hoasinduction_lem0,type,
hoasinduction_lem0: $o ).
thf(ty_hoasinduction_lem3a_lthm,type,
hoasinduction_lem3a_lthm: $o ).
thf(ty_substmonoid_lthm,type,
substmonoid_lthm: $o ).
thf(ty_eigen__115,type,
eigen__115: term ).
thf(ty_sh,type,
sh: subst ).
thf(ty_hoasapinj2_lthm,type,
hoasapinj2_lthm: $o ).
thf(ty_substmonoid,type,
substmonoid: $o ).
thf(ty_pushprop_lem1v2,type,
pushprop_lem1v2: $o ).
thf(ty_hoasinduction_lem3v2_f_lthm,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(ty_hoasinduction_lem3v2_lthm,type,
hoasinduction_lem3v2_lthm: $o ).
thf(ty_hoasinduction_lem3aa,type,
hoasinduction_lem3aa: $o ).
thf(ty_laminj,type,
laminj: $o ).
thf(ty_lamnotap,type,
lamnotap: $o ).
thf(ty_eigen__2,type,
eigen__2: term ).
thf(ty_pushprop_lem0_gthm,type,
pushprop_lem0_gthm: $o ).
thf(ty_pushprop_gthm,type,
pushprop_gthm: $o ).
thf(ty_eigen__146,type,
eigen__146: subst > term > subst > $o ).
thf(ty_eigen__135,type,
eigen__135: subst > term > subst > $o ).
thf(ty_axmap,type,
axmap: $o ).
thf(ty_ulamvarsh,type,
ulamvarsh: $o ).
thf(ty_lamnotvar,type,
lamnotvar: $o ).
thf(ty_induction2_gthm,type,
induction2_gthm: $o ).
thf(ty_pushprop_lthm_orig,type,
pushprop_lthm_orig: $o ).
thf(ty_hoasinduction_lem3a_gthm,type,
hoasinduction_lem3a_gthm: $o ).
thf(ty_hoasinduction_lem3a,type,
hoasinduction_lem3a: $o ).
thf(ty_ap,type,
ap: term > term > term ).
thf(ty_hoaslamnotvar_lthm,type,
hoaslamnotvar_lthm: $o ).
thf(ty_ulamvarind,type,
ulamvarind: $o ).
thf(ty_hoasapinj1,type,
hoasapinj1: $o ).
thf(ty_d_id,type,
d_id: d_subst ).
thf(ty_hoasinduction_lem1_gthm,type,
hoasinduction_lem1_gthm: $o ).
thf(ty_pushprop_lem3v2_lthm,type,
pushprop_lem3v2_lthm: $o ).
thf(ty_hoasinduction_lem3_lthm,type,
hoasinduction_lem3_lthm: $o ).
thf(ty_hoasvar,type,
hoasvar: subst > term > subst > $o ).
thf(ty_d_one,type,
d_one: d_term ).
thf(ty_hoasinduction_lem1v2_gthm,type,
hoasinduction_lem1v2_gthm: $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( pushprop_p_and_p_prime @ eigen__2 @ eigen__3 )
= ( ^ [X1: term > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ ( sub @ X3 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: subst] :
( ( pushprop_p_and_p_prime @ eigen__2 @ X1 )
= ( ^ [X2: term > $o,X3: term > $o] :
! [X4: term] :
( ( X3 @ X4 )
= ( X2 @ ( sub @ X4 @ ( push @ eigen__2 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: subst] :
( X1
= ( comp @ id @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ( pushprop_p_and_p_prime
!= ( ^ [X1: term,X2: subst,X3: term > $o,X4: term > $o] :
! [X5: term] :
( ( X4 @ X5 )
= ( X3 @ ( sub @ X5 @ ( push @ X1 @ X2 ) ) ) ) ) ) )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2
!= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) )
=> ( X2 @ one ) ) ) ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f
!= ( ! [X1: term] :
~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( sub @ X1 @ ( push @ X3 @ X4 ) )
= ( X2 @ X4 @ X3 ) ) ) ) )
=> ~ axvarshift )
=> ( hoasapinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm
!= ( ! [X1: term] :
~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( sub @ X1 @ ( push @ X3 @ X4 ) )
= ( X2 @ X4 @ X3 ) ) ) ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( ! [X1: subst > term > subst > $o] :
~ ! [X2: term > $o] :
~ ! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) )
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ $false ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) )
=> ( X2 @ one ) ) ) ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0
!= ( ! [X1: subst > term > subst > $o] :
~ ! [X2: term > $o] :
~ ! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm
!= ( ! [X1: term] :
~ ! [X2: subst > term > term] :
( ( X2 @ sh @ one )
!= ( sub @ X1 @ ( push @ one @ sh ) ) ) ) ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr
!= ( ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) ) ) ) )
=> ( pushprop_lem1
!= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst,X5: term] :
( ( X1 @ X3 )
=> ( X2 @ ( sub @ X3 @ ( push @ X5 @ X4 ) ) ) ) ) ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0
!= ( ! [X1: term > $o,X2: term,X3: subst] :
~ ! [X4: term > $o] :
~ ! [X5: term] :
( ( X4 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ) ) ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( ! [X1: term] :
~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( sub @ X1 @ ( push @ X3 @ X4 ) )
= ( X2 @ X4 @ X3 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm
!= ( ! [X1: subst > term > subst > $o] :
~ ! [X2: term > $o] :
~ ! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) )
=> ~ ( sP4
=> ~ ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) ) ) ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b
!= ( ! [X1: term] :
~ ! [X2: subst > term > term] :
( ( X2 @ sh @ one )
!= ( sub @ X1 @ ( push @ one @ sh ) ) ) ) ) )
=> ( substmonoid
!= ( ~ ( sP4
=> ~ ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) ) ) ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm )
=> ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
=> ( hoaslamnotap
!= ( ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ) )
=> ~ substmonoid_gthm )
=> ~ ulamvarsh )
=> ( induction2
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ~ pushprop_lem3v2 )
=> ~ pushprop_lem2v2_gthm )
=> ( pushprop_lem1_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst,X5: term] :
( ( X1 @ X3 )
=> ( X2 @ ( sub @ X3 @ ( push @ X5 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 @ ( sub @ eigen__4 @ ( push @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP5
=> ( hoasinduction_lem3v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( axshiftcons
!= ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( termmset
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) ) ) ) )
=> ( pushprop_lem0_lthm
!= ( ! [X1: term > $o,X2: term,X3: subst] :
~ ! [X4: term > $o] :
~ ! [X5: term] :
( ( X4 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ) ) ) )
=> ~ hoasapnotvar_lthm )
=> ( hoasinduction_lem3v2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: term > $o,X2: term,X3: subst,X4: term] :
( ( var @ X2 )
=> ( X1 @ ( sub @ X2 @ ( push @ X4 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: term] :
~ ! [X2: subst > term > term] :
( ( X2 @ sh @ one )
!= ( sub @ X1 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: subst > term > subst > $o] :
~ ! [X2: term > $o] :
~ ! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP4
=> ~ ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst,X5: term] :
( ( X1 @ X3 )
=> ( X2 @ ( sub @ X3 @ ( push @ X5 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ~ sP5
=> ( hoasinduction_lem3v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( axshiftcons
!= ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP7
=> ( axvarid
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ( pushprop_p_and_p_prime
!= ( ^ [X1: term,X2: subst,X3: term > $o,X4: term > $o] :
! [X5: term] :
( ( X4 @ X5 )
= ( X3 @ ( sub @ X5 @ ( push @ X1 @ X2 ) ) ) ) ) ) )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2
!= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) )
=> ( X2 @ one ) ) ) ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f
!= ( ! [X1: term] :
~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( sub @ X1 @ ( push @ X3 @ X4 ) )
= ( X2 @ X4 @ X3 ) ) ) ) )
=> ~ axvarshift )
=> ( hoasapinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm
!= ( ! [X1: term] :
~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( sub @ X1 @ ( push @ X3 @ X4 ) )
= ( X2 @ X4 @ X3 ) ) ) ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ $false ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) )
=> ( X2 @ one ) ) ) ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr
!= ( ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) ) ) ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0
!= ( ! [X1: term > $o,X2: term,X3: subst] :
~ ! [X4: term > $o] :
~ ! [X5: term] :
( ( X4 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ) ) ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( ! [X1: term] :
~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( sub @ X1 @ ( push @ X3 @ X4 ) )
= ( X2 @ X4 @ X3 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) )
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm )
=> ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
=> ( hoaslamnotap
!= ( ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ) )
=> ~ substmonoid_gthm )
=> ~ ulamvarsh )
=> ( induction2
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ~ pushprop_lem3v2 )
=> ~ pushprop_lem2v2_gthm ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: subst] :
( X1
= ( comp @ X1 @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( var @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: term,X2: subst,X3: term] :
( ( var @ X1 )
=> ( eigen__0 @ ( sub @ X1 @ ( push @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) )
=> ( X2 @ one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: term] :
( ( eigen__1 @ X1 )
= ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: term] :
~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( sub @ X1 @ ( push @ X3 @ X4 ) )
= ( X2 @ X4 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP14
=> ( hoasinduction_lthm_3
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: term > $o] :
( ( pushprop_p_and_p_prime @ eigen__2 @ eigen__3 @ eigen__0 @ X1 )
= ( ! [X2: term] :
( ( X1 @ X2 )
= ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: subst,X2: term] :
( sP18
=> ( eigen__0 @ ( sub @ eigen__4 @ ( push @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X3 = X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP5
=> ( hoasinduction_lem3v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( ~ sP13
=> ( termmset
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) ) ) ) )
=> ( pushprop_lem0_lthm
!= ( ! [X1: term > $o,X2: term,X3: subst] :
~ ! [X4: term > $o] :
~ ! [X5: term] :
( ( X4 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP28
=> ~ hoasapnotvar_lthm ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( pushprop_p_and_p_prime @ eigen__2 )
= ( ^ [X1: subst,X2: term > $o,X3: term > $o] :
! [X4: term] :
( ( X3 @ X4 )
= ( X2 @ ( sub @ X4 @ ( push @ eigen__2 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP18
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP13
=> ( termmset
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> $false ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) )
=> ( X2 @ one ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP18
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( pushprop_p_and_p_prime
= ( ^ [X1: term,X2: subst,X3: term > $o,X4: term > $o] :
! [X5: term] :
( ( X4 @ X5 )
= ( X3 @ ( sub @ X5 @ ( push @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: term] :
( sP18
=> ( eigen__0 @ ( sub @ eigen__4 @ ( push @ X1 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> sP26 ) ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0
!= ( ! [X1: term > $o,X2: term,X3: subst] :
~ ! [X4: term > $o] :
~ ! [X5: term] :
( ( X4 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ) ) ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm )
=> ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
=> ( hoaslamnotap
!= ( ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ) )
=> ~ substmonoid_gthm )
=> ~ ulamvarsh )
=> ( induction2
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ~ pushprop_lem3v2 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP16 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: term > $o,X2: term,X3: subst] :
~ ! [X4: term > $o] :
~ ! [X5: term] :
( ( X4 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: term > $o] :
( ( pushprop_p_and_p_prime @ eigen__2 @ eigen__3 @ X1 )
= ( ^ [X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ ( sub @ X3 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( pushprop_p_and_p_prime @ eigen__2 @ eigen__3 @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( pushprop_p_and_p_prime @ eigen__2 @ eigen__3 @ eigen__0 )
= ( ^ [X1: term > $o] :
! [X2: term] :
( ( X1 @ X2 )
= ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: term] :
( ( pushprop_p_and_p_prime @ X1 )
= ( ^ [X2: subst,X3: term > $o,X4: term > $o] :
! [X5: term] :
( ( X4 @ X5 )
= ( X3 @ ( sub @ X5 @ ( push @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> pushprop_lem3v2 ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP44 = sP21 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(pushprop_lem3v2,conjecture,
( sP47
= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ X5 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
( sP47
!= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ X5 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[pushprop_lem3v2]) ).
thf(h1,assumption,
sP47,
introduced(assumption,[]) ).
thf(h2,assumption,
! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ X5 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP47,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ X5 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: term > $o,X2: term,X3: subst] :
( ( pushprop_p_and_p_prime @ X2 @ X3 @ eigen__0 @ X1 )
=> ( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: term] :
( ( var @ X4 )
=> ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: term,X2: subst] :
( ( pushprop_p_and_p_prime @ X1 @ X2 @ eigen__0 @ eigen__1 )
=> ( sP1
=> ! [X3: term] :
( ( var @ X3 )
=> ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: subst] :
( ( pushprop_p_and_p_prime @ eigen__2 @ X1 @ eigen__0 @ eigen__1 )
=> ( sP1
=> ! [X2: term] :
( ( var @ X2 )
=> ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP44
=> ( sP1
=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP44,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP1
=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP31,
introduced(assumption,[]) ).
thf(h14,assumption,
sP18,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h17,assumption,
( hoasinduction_lthm_3
= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h19,assumption,
( axvarid
= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h21,assumption,
( hoasinduction_lem3v2_lthm
= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h23,assumption,
hoasapnotvar_lthm,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(h25,assumption,
pushprop_lem0_lthm = sP41,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h27,assumption,
( termmset
= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h29,assumption,
( axshiftcons
= ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h31,assumption,
( hoasinduction_lem3v2
= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h33,assumption,
( pushprop_lem1_lthm
= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> sP12 ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ sP38,
introduced(assumption,[]) ).
thf(h35,assumption,
pushprop_lem2v2_gthm,
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm )
=> ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
=> ( hoaslamnotap
!= ( ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ) )
=> ~ substmonoid_gthm )
=> ~ ulamvarsh )
=> ( induction2
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm )
=> ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
=> ( hoaslamnotap
!= ( ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ) )
=> ~ substmonoid_gthm )
=> ~ ulamvarsh ),
introduced(assumption,[]) ).
thf(h38,assumption,
( induction2
= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm )
=> ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
=> ( hoaslamnotap
!= ( ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ) )
=> ~ substmonoid_gthm ),
introduced(assumption,[]) ).
thf(h40,assumption,
ulamvarsh,
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm )
=> ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
=> ( hoaslamnotap
!= ( ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
substmonoid_gthm,
introduced(assumption,[]) ).
thf(h43,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm )
=> ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
( hoaslamnotap
= ( ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm )
=> ~ pushprop_lem2v2_lthm ),
introduced(assumption,[]) ).
thf(h46,assumption,
~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ induction2_gthm ),
introduced(assumption,[]) ).
thf(h48,assumption,
pushprop_lem2v2_lthm,
introduced(assumption,[]) ).
thf(h49,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm )
=> ( hoasinduction_no_psi_cond
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h50,assumption,
induction2_gthm,
introduced(assumption,[]) ).
thf(h51,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ~ hoasinduction_lem1_gthm ),
introduced(assumption,[]) ).
thf(h52,assumption,
( hoasinduction_no_psi_cond
= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h53,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar )
=> ( hoasinduction_lem3a
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h54,assumption,
hoasinduction_lem1_gthm,
introduced(assumption,[]) ).
thf(h55,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) )
=> ~ lamnotvar ),
introduced(assumption,[]) ).
thf(h56,assumption,
( hoasinduction_lem3a
= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h57,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) )
=> ( substmonoid != ( ~ sP11 ) ) ),
introduced(assumption,[]) ).
thf(h58,assumption,
lamnotvar,
introduced(assumption,[]) ).
thf(h59,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm )
=> ( hoasinduction_lem3b != sP9 ) ),
introduced(assumption,[]) ).
thf(h60,assumption,
( substmonoid = ( ~ sP11 ) ),
introduced(assumption,[]) ).
thf(h61,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm )
=> ~ hoasinduction_lem2_gthm ),
introduced(assumption,[]) ).
thf(h62,assumption,
hoasinduction_lem3b = sP9,
introduced(assumption,[]) ).
thf(h63,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop )
=> ~ hoasinduction_lem3_gthm ),
introduced(assumption,[]) ).
thf(h64,assumption,
hoasinduction_lem2_gthm,
introduced(assumption,[]) ).
thf(h65,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) )
=> ~ pushprop ),
introduced(assumption,[]) ).
thf(h66,assumption,
hoasinduction_lem3_gthm,
introduced(assumption,[]) ).
thf(h67,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) )
=> ( substmonoid_lthm
!= ( sP4
=> ( sP17
=> ~ sP11 ) ) ) ),
introduced(assumption,[]) ).
thf(h68,assumption,
pushprop,
introduced(assumption,[]) ).
thf(h69,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) )
=> ( hoasinduction_lem0_lthm != sP10 ) ),
introduced(assumption,[]) ).
thf(h70,assumption,
( substmonoid_lthm
= ( sP4
=> ( sP17
=> ~ sP11 ) ) ),
introduced(assumption,[]) ).
thf(h71,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm )
=> ( induction2_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h72,assumption,
hoasinduction_lem0_lthm = sP10,
introduced(assumption,[]) ).
thf(h73,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) )
=> ~ hoaslaminj_gthm ),
introduced(assumption,[]) ).
thf(h74,assumption,
( induction2_lthm
= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h75,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar )
=> ( axidl != sP4 ) ),
introduced(assumption,[]) ).
thf(h76,assumption,
hoaslaminj_gthm,
introduced(assumption,[]) ).
thf(h77,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm )
=> ~ hoaslamnotvar ),
introduced(assumption,[]) ).
thf(h78,assumption,
axidl = sP4,
introduced(assumption,[]) ).
thf(h79,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap )
=> ~ hoasapinj1_gthm ),
introduced(assumption,[]) ).
thf(h80,assumption,
hoaslamnotvar,
introduced(assumption,[]) ).
thf(h81,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm )
=> lamnotap ),
introduced(assumption,[]) ).
thf(h82,assumption,
hoasapinj1_gthm,
introduced(assumption,[]) ).
thf(h83,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm )
=> ~ hoasinduction_lem1_lthm ),
introduced(assumption,[]) ).
thf(h84,assumption,
~ lamnotap,
introduced(assumption,[]) ).
thf(h85,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm )
=> ~ hoasapinj2_gthm ),
introduced(assumption,[]) ).
thf(h86,assumption,
hoasinduction_lem1_lthm,
introduced(assumption,[]) ).
thf(h87,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) )
=> ~ hoasinduction_lem2_lthm ),
introduced(assumption,[]) ).
thf(h88,assumption,
hoasapinj2_gthm,
introduced(assumption,[]) ).
thf(h89,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs )
=> ( hoasinduction_lem3v2a_lthm
!= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h90,assumption,
hoasinduction_lem2_lthm,
introduced(assumption,[]) ).
thf(h91,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm )
=> ~ axabs ),
introduced(assumption,[]) ).
thf(h92,assumption,
( hoasinduction_lem3v2a_lthm
= ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h93,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) )
=> ~ pushprop_gthm ),
introduced(assumption,[]) ).
thf(h94,assumption,
axabs,
introduced(assumption,[]) ).
thf(h95,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ( pushprop_lem0 != sP41 ) ),
introduced(assumption,[]) ).
thf(h96,assumption,
pushprop_gthm,
introduced(assumption,[]) ).
thf(h97,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasinduction_lem3_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h98,assumption,
pushprop_lem0 = sP41,
introduced(assumption,[]) ).
thf(h99,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) )
=> ( laminj
!= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h100,assumption,
( hoasinduction_lem3_lthm
= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h101,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) )
=> ( pushprop_lem1 != sP12 ) ),
introduced(assumption,[]) ).
thf(h102,assumption,
( laminj
= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h103,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm )
=> ( axidr != sP17 ) ),
introduced(assumption,[]) ).
thf(h104,assumption,
pushprop_lem1 = sP12,
introduced(assumption,[]) ).
thf(h105,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) )
=> ~ hoasinduction_lem2v2_gthm ),
introduced(assumption,[]) ).
thf(h106,assumption,
axidr = sP17,
introduced(assumption,[]) ).
thf(h107,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) )
=> ( axscons
!= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h108,assumption,
hoasinduction_lem2v2_gthm,
introduced(assumption,[]) ).
thf(h109,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) )
=> ( axvarcons
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h110,assumption,
( axscons
= ( ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h111,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) )
=> ( hoaslaminj_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h112,assumption,
( axvarcons
= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h113,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) )
=> ( hoasapinj1_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h114,assumption,
( hoaslaminj_lthm
= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h115,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) )
=> ( hoasinduction_lem3v2a
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h116,assumption,
( hoasapinj1_lthm
= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h117,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ( hoasapinj2_lthm != sP43 ) ),
introduced(assumption,[]) ).
thf(h118,assumption,
( hoasinduction_lem3v2a
= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h119,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( apinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h120,assumption,
hoasapinj2_lthm = sP43,
introduced(assumption,[]) ).
thf(h121,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm )
=> ( apinj2
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h122,assumption,
( apinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h123,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) )
=> ~ pushprop_lthm ),
introduced(assumption,[]) ).
thf(h124,assumption,
( apinj2
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h125,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc )
=> ( hoasinduction_lem2v2
!= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h126,assumption,
pushprop_lthm,
introduced(assumption,[]) ).
thf(h127,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos )
=> ~ axassoc ),
introduced(assumption,[]) ).
thf(h128,assumption,
( hoasinduction_lem2v2
= ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h129,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm )
=> ~ axclos ),
introduced(assumption,[]) ).
thf(h130,assumption,
axassoc,
introduced(assumption,[]) ).
thf(h131,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 )
=> ~ hoasinduction_lem3a_gthm ),
introduced(assumption,[]) ).
thf(h132,assumption,
axclos,
introduced(assumption,[]) ).
thf(h133,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm )
=> ~ pushprop_lem2v2 ),
introduced(assumption,[]) ).
thf(h134,assumption,
hoasinduction_lem3a_gthm,
introduced(assumption,[]) ).
thf(h135,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm )
=> ~ hoasinduction_lem3b_gthm ),
introduced(assumption,[]) ).
thf(h136,assumption,
pushprop_lem2v2,
introduced(assumption,[]) ).
thf(h137,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm )
=> ~ hoaslamnotvar_gthm ),
introduced(assumption,[]) ).
thf(h138,assumption,
hoasinduction_lem3b_gthm,
introduced(assumption,[]) ).
thf(h139,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm )
=> ~ hoaslamnotap_gthm ),
introduced(assumption,[]) ).
thf(h140,assumption,
hoaslamnotvar_gthm,
introduced(assumption,[]) ).
thf(h141,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) )
=> ~ pushprop_lem1v2_gthm ),
introduced(assumption,[]) ).
thf(h142,assumption,
hoaslamnotap_gthm,
introduced(assumption,[]) ).
thf(h143,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm )
=> ( hoasinduction_lem3aa != sP40 ) ),
introduced(assumption,[]) ).
thf(h144,assumption,
pushprop_lem1v2_gthm,
introduced(assumption,[]) ).
thf(h145,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) )
=> ~ termmset_gthm ),
introduced(assumption,[]) ).
thf(h146,assumption,
hoasinduction_lem3aa = sP40,
introduced(assumption,[]) ).
thf(h147,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) )
=> ( hoasinduction_lem3a_lthm
!= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h148,assumption,
termmset_gthm,
introduced(assumption,[]) ).
thf(h149,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind )
=> ( induction
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h150,assumption,
( hoasinduction_lem3a_lthm
= ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h151,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) )
=> ~ ulamvarind ),
introduced(assumption,[]) ).
thf(h152,assumption,
( induction
= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h153,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm )
=> ( hoasinduction_lem3b_lthm != sP9 ) ),
introduced(assumption,[]) ).
thf(h154,assumption,
ulamvarind,
introduced(assumption,[]) ).
thf(h155,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm )
=> ~ pushprop_lem3v2_lthm ),
introduced(assumption,[]) ).
thf(h156,assumption,
hoasinduction_lem3b_lthm = sP9,
introduced(assumption,[]) ).
thf(h157,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp )
=> ~ hoaslamnotvar_lthm ),
introduced(assumption,[]) ).
thf(h158,assumption,
pushprop_lem3v2_lthm,
introduced(assumption,[]) ).
thf(h159,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm )
=> ~ axapp ),
introduced(assumption,[]) ).
thf(h160,assumption,
hoaslamnotvar_lthm,
introduced(assumption,[]) ).
thf(h161,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) )
=> ~ hoasinduction_gthm ),
introduced(assumption,[]) ).
thf(h162,assumption,
axapp,
introduced(assumption,[]) ).
thf(h163,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) )
=> ( hoasinduction
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h164,assumption,
hoasinduction_gthm,
introduced(assumption,[]) ).
thf(h165,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar )
=> ( hoasinduction_lem0 != sP10 ) ),
introduced(assumption,[]) ).
thf(h166,assumption,
( hoasinduction
= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h167,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) )
=> ~ hoasapnotvar ),
introduced(assumption,[]) ).
thf(h168,assumption,
hoasinduction_lem0 = sP10,
introduced(assumption,[]) ).
thf(h169,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm )
=> ( pushprop_lem1v2_lthm != sP20 ) ),
introduced(assumption,[]) ).
thf(h170,assumption,
hoasapnotvar,
introduced(assumption,[]) ).
thf(h171,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 )
=> ~ hoaslamnotap_lthm ),
introduced(assumption,[]) ).
thf(h172,assumption,
pushprop_lem1v2_lthm = sP20,
introduced(assumption,[]) ).
thf(h173,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) )
=> ~ hoasinduction_lem1 ),
introduced(assumption,[]) ).
thf(h174,assumption,
hoaslamnotap_lthm,
introduced(assumption,[]) ).
thf(h175,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) )
=> ( termmset_lthm != ( ~ sP33 ) ) ),
introduced(assumption,[]) ).
thf(h176,assumption,
hoasinduction_lem1,
introduced(assumption,[]) ).
thf(h177,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) )
=> ( hoasinduction_lem2
!= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h178,assumption,
( termmset_lthm = ( ~ sP33 ) ),
introduced(assumption,[]) ).
thf(h179,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) )
=> ( hoasinduction_lem3
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h180,assumption,
( hoasinduction_lem2
= ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h181,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm )
=> ( hoasinduction_lem3aa_lthm != sP40 ) ),
introduced(assumption,[]) ).
thf(h182,assumption,
( hoasinduction_lem3
= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h183,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ~ induction2lem_gthm ),
introduced(assumption,[]) ).
thf(h184,assumption,
hoasinduction_lem3aa_lthm = sP40,
introduced(assumption,[]) ).
thf(h185,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) )
=> ( hoasinduction_lem3aaa
!= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h186,assumption,
induction2lem_gthm,
introduced(assumption,[]) ).
thf(h187,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) )
=> ( hoaslaminj
!= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h188,assumption,
( hoasinduction_lem3aaa
= ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h189,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) )
=> ( hoasinduction_no_psi_cond_lthm
!= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h190,assumption,
( hoaslaminj
= ( ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h191,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) )
=> ( hoasinduction_lthm
!= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h192,assumption,
( hoasinduction_no_psi_cond_lthm
= ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h193,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig )
=> ( hoasinduction_lem3v2_f_lthm != sP22 ) ),
introduced(assumption,[]) ).
thf(h194,assumption,
( hoasinduction_lthm
= ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h195,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar )
=> ~ pushprop_lthm_orig ),
introduced(assumption,[]) ).
thf(h196,assumption,
hoasinduction_lem3v2_f_lthm = sP22,
introduced(assumption,[]) ).
thf(h197,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm )
=> ~ apnotvar ),
introduced(assumption,[]) ).
thf(h198,assumption,
pushprop_lthm_orig,
introduced(assumption,[]) ).
thf(h199,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) )
=> ~ hoasinduction_lem3v2_gthm ),
introduced(assumption,[]) ).
thf(h200,assumption,
apnotvar,
introduced(assumption,[]) ).
thf(h201,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 )
=> ( induction2lem_lthm
!= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h202,assumption,
hoasinduction_lem3v2_gthm,
introduced(assumption,[]) ).
thf(h203,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) )
=> ulamvar1 ),
introduced(assumption,[]) ).
thf(h204,assumption,
( induction2lem_lthm
= ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h205,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm )
=> ( hoasapinj1
!= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h206,assumption,
~ ulamvar1,
introduced(assumption,[]) ).
thf(h207,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) )
=> ~ hoasapnotvar_gthm ),
introduced(assumption,[]) ).
thf(h208,assumption,
( hoasapinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h209,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift )
=> ( hoasapinj2 != sP26 ) ),
introduced(assumption,[]) ).
thf(h210,assumption,
hoasapnotvar_gthm,
introduced(assumption,[]) ).
thf(h211,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) )
=> ~ axvarshift ),
introduced(assumption,[]) ).
thf(h212,assumption,
hoasapinj2 = sP26,
introduced(assumption,[]) ).
thf(h213,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) )
=> ( hoasinduction_lem3v2_f != sP22 ) ),
introduced(assumption,[]) ).
thf(h214,assumption,
axvarshift,
introduced(assumption,[]) ).
thf(h215,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm )
=> ( induction2lem
!= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h216,assumption,
hoasinduction_lem3v2_f = sP22,
introduced(assumption,[]) ).
thf(h217,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 )
=> ~ hoasinduction_lem1v2_gthm ),
introduced(assumption,[]) ).
thf(h218,assumption,
( induction2lem
= ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h219,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) )
=> ~ hoasinduction_lem1v2 ),
introduced(assumption,[]) ).
thf(h220,assumption,
hoasinduction_lem1v2_gthm,
introduced(assumption,[]) ).
thf(h221,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm )
=> ( shinj
!= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h222,assumption,
hoasinduction_lem1v2,
introduced(assumption,[]) ).
thf(h223,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap )
=> ~ pushprop_lem0_gthm ),
introduced(assumption,[]) ).
thf(h224,assumption,
( shinj
= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h225,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm )
=> ~ axmap ),
introduced(assumption,[]) ).
thf(h226,assumption,
pushprop_lem0_gthm,
introduced(assumption,[]) ).
thf(h227,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) )
=> ~ pushprop_lem1_gthm ),
introduced(assumption,[]) ).
thf(h228,assumption,
axmap,
introduced(assumption,[]) ).
thf(h229,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) )
=> ( pushprop_lem1v2 != sP34 ) ),
introduced(assumption,[]) ).
thf(h230,assumption,
pushprop_lem1_gthm,
introduced(assumption,[]) ).
thf(h231,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 )
=> ( var @ ( d2term @ d_one ) ) ),
introduced(assumption,[]) ).
thf(h232,assumption,
pushprop_lem1v2 = sP34,
introduced(assumption,[]) ).
thf(h233,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) )
=> ~ sP36 ),
introduced(assumption,[]) ).
thf(h234,assumption,
~ ( var @ ( d2term @ d_one ) ),
introduced(assumption,[]) ).
thf(h235,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) )
=> ( hoasinduction_p_and_p_prime
!= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h236,assumption,
sP36,
introduced(assumption,[]) ).
thf(h237,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( hoaslam
!= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ) ),
introduced(assumption,[]) ).
thf(h238,assumption,
( hoasinduction_p_and_p_prime
= ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
! [X3: term] :
( ( X2 @ X3 )
= ( X1 @ id @ X3 @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h239,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) ),
introduced(assumption,[]) ).
thf(h240,assumption,
( hoaslam
= ( ^ [X1: subst,X2: subst > term > term] : ( d2term @ d_one ) ) ),
introduced(assumption,[]) ).
thf(h241,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) )
=> ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) ),
introduced(assumption,[]) ).
thf(h242,assumption,
( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
= ( d2term @ d_one ) ),
introduced(assumption,[]) ).
thf(h243,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) )
=> ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2subst @ d_id ) ) ),
introduced(assumption,[]) ).
thf(h244,assumption,
( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
= ( d2subst @ d_id ) ),
introduced(assumption,[]) ).
thf(h245,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) )
=> ( sh
!= ( d2subst @ d_id ) ) ),
introduced(assumption,[]) ).
thf(h246,assumption,
( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= ( d2subst @ d_id ) ),
introduced(assumption,[]) ).
thf(h247,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) )
=> ( id
!= ( d2subst @ d_id ) ) ),
introduced(assumption,[]) ).
thf(h248,assumption,
( sh
= ( d2subst @ d_id ) ),
introduced(assumption,[]) ).
thf(h249,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= ( d2term @ d_one ) ) ),
introduced(assumption,[]) ).
thf(h250,assumption,
( id
= ( d2subst @ d_id ) ),
introduced(assumption,[]) ).
thf(h251,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) )
=> ( ( lam @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) ),
introduced(assumption,[]) ).
thf(h252,assumption,
( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= ( d2term @ d_one ) ),
introduced(assumption,[]) ).
thf(h253,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) )
=> ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
!= ( d2term @ d_one ) ) ),
introduced(assumption,[]) ).
thf(h254,assumption,
( ( lam @ ( d2term @ d_one ) )
= ( d2term @ d_one ) ),
introduced(assumption,[]) ).
thf(h255,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( one
!= ( d2term @ d_one ) ) ),
introduced(assumption,[]) ).
thf(h256,assumption,
( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
= ( d2term @ d_one ) ),
introduced(assumption,[]) ).
thf(h257,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) )
=> ~ ! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h258,assumption,
( one
= ( d2term @ d_one ) ),
introduced(assumption,[]) ).
thf(h259,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) )
=> ~ ! [X1: d_subst] : ( X1 = d_id ) ),
introduced(assumption,[]) ).
thf(h260,assumption,
! [X1: d_subst,X2: d_subst] :
( ( ( d2subst @ X1 )
= ( d2subst @ X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h261,assumption,
~ ( ~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h262,assumption,
! [X1: d_subst] : ( X1 = d_id ),
introduced(assumption,[]) ).
thf(h263,assumption,
~ ( ~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) )
=> ~ ! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h264,assumption,
! [X1: subst] :
~ ! [X2: d_subst] :
( X1
!= ( d2subst @ X2 ) ),
introduced(assumption,[]) ).
thf(h265,assumption,
~ ( ! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) )
=> ~ ! [X1: d_term] : ( X1 = d_one ) ),
introduced(assumption,[]) ).
thf(h266,assumption,
! [X1: d_term,X2: d_term] :
( ( ( d2term @ X1 )
= ( d2term @ X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h267,assumption,
! [X1: term] :
~ ! [X2: d_term] :
( X1
!= ( d2term @ X2 ) ),
introduced(assumption,[]) ).
thf(h268,assumption,
! [X1: d_term] : ( X1 = d_one ),
introduced(assumption,[]) ).
thf(h269,assumption,
pushprop_lem1v2,
introduced(assumption,[]) ).
thf(h270,assumption,
sP34,
introduced(assumption,[]) ).
thf(h271,assumption,
~ pushprop_lem1v2,
introduced(assumption,[]) ).
thf(h272,assumption,
~ sP34,
introduced(assumption,[]) ).
thf(h273,assumption,
shinj,
introduced(assumption,[]) ).
thf(h274,assumption,
! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h275,assumption,
~ shinj,
introduced(assumption,[]) ).
thf(h276,assumption,
~ ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h277,assumption,
induction2lem,
introduced(assumption,[]) ).
thf(h278,assumption,
! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h279,assumption,
~ induction2lem,
introduced(assumption,[]) ).
thf(h280,assumption,
~ ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h281,assumption,
hoasinduction_lem3v2_f,
introduced(assumption,[]) ).
thf(h282,assumption,
sP22,
introduced(assumption,[]) ).
thf(h283,assumption,
~ hoasinduction_lem3v2_f,
introduced(assumption,[]) ).
thf(h284,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h285,assumption,
hoasapinj2,
introduced(assumption,[]) ).
thf(h286,assumption,
sP26,
introduced(assumption,[]) ).
thf(h287,assumption,
~ hoasapinj2,
introduced(assumption,[]) ).
thf(h288,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h289,assumption,
hoasapinj1,
introduced(assumption,[]) ).
thf(h290,assumption,
! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h291,assumption,
~ hoasapinj1,
introduced(assumption,[]) ).
thf(h292,assumption,
~ ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h293,assumption,
induction2lem_lthm,
introduced(assumption,[]) ).
thf(h294,assumption,
( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h295,assumption,
~ induction2lem_lthm,
introduced(assumption,[]) ).
thf(h296,assumption,
~ ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( sP17
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h297,assumption,
hoasinduction_lem3v2_f_lthm,
introduced(assumption,[]) ).
thf(h298,assumption,
~ hoasinduction_lem3v2_f_lthm,
introduced(assumption,[]) ).
thf(h299,assumption,
hoasinduction_lthm,
introduced(assumption,[]) ).
thf(h300,assumption,
( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h301,assumption,
~ hoasinduction_lthm,
introduced(assumption,[]) ).
thf(h302,assumption,
~ ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h303,assumption,
hoasinduction_no_psi_cond_lthm,
introduced(assumption,[]) ).
thf(h304,assumption,
( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h305,assumption,
~ hoasinduction_no_psi_cond_lthm,
introduced(assumption,[]) ).
thf(h306,assumption,
~ ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h307,assumption,
hoaslaminj,
introduced(assumption,[]) ).
thf(h308,assumption,
! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ),
introduced(assumption,[]) ).
thf(h309,assumption,
~ hoaslaminj,
introduced(assumption,[]) ).
thf(h310,assumption,
~ ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ),
introduced(assumption,[]) ).
thf(h311,assumption,
hoasinduction_lem3aaa,
introduced(assumption,[]) ).
thf(h312,assumption,
! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ),
introduced(assumption,[]) ).
thf(h313,assumption,
~ hoasinduction_lem3aaa,
introduced(assumption,[]) ).
thf(h314,assumption,
~ ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term,X4: term] :
( ~ ( ~ ( ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X3 @ id @ X5 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X3 @ X5 @ X6 ) @ X7 )
= ( sub @ ( sub @ X4 @ ( push @ X6 @ X5 ) ) @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( X3 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ X4 @ ( push @ ( sub @ X6 @ X7 ) @ ( comp @ X5 @ X7 ) ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ),
introduced(assumption,[]) ).
thf(h315,assumption,
hoasinduction_lem3aa_lthm,
introduced(assumption,[]) ).
thf(h316,assumption,
sP40,
introduced(assumption,[]) ).
thf(h317,assumption,
~ hoasinduction_lem3aa_lthm,
introduced(assumption,[]) ).
thf(h318,assumption,
~ sP40,
introduced(assumption,[]) ).
thf(h319,assumption,
hoasinduction_lem3,
introduced(assumption,[]) ).
thf(h320,assumption,
! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ),
introduced(assumption,[]) ).
thf(h321,assumption,
~ hoasinduction_lem3,
introduced(assumption,[]) ).
thf(h322,assumption,
~ ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ),
introduced(assumption,[]) ).
thf(h323,assumption,
hoasinduction_lem2,
introduced(assumption,[]) ).
thf(h324,assumption,
! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ),
introduced(assumption,[]) ).
thf(h325,assumption,
~ hoasinduction_lem2,
introduced(assumption,[]) ).
thf(h326,assumption,
~ ! [X1: subst > term > subst > $o,X2: term,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: term,X5: term] :
( ~ ( ( X1 @ id @ X4 @ id )
=> ~ ( X1 @ id @ X5 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X4 @ id ) @ X5 ) @ id ) ) )
=> ~ ( X1 @ id @ X2 @ id ) )
=> ~ ( X1 @ id @ X3 @ id ) )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ),
introduced(assumption,[]) ).
thf(h327,assumption,
termmset_lthm,
introduced(assumption,[]) ).
thf(h328,assumption,
~ sP33,
introduced(assumption,[]) ).
thf(h329,assumption,
~ termmset_lthm,
introduced(assumption,[]) ).
thf(h330,assumption,
sP33,
introduced(assumption,[]) ).
thf(h331,assumption,
pushprop_lem1v2_lthm,
introduced(assumption,[]) ).
thf(h332,assumption,
sP20,
introduced(assumption,[]) ).
thf(h333,assumption,
~ pushprop_lem1v2_lthm,
introduced(assumption,[]) ).
thf(h334,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h335,assumption,
hoasinduction_lem0,
introduced(assumption,[]) ).
thf(h336,assumption,
sP10,
introduced(assumption,[]) ).
thf(h337,assumption,
~ hoasinduction_lem0,
introduced(assumption,[]) ).
thf(h338,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h339,assumption,
hoasinduction,
introduced(assumption,[]) ).
thf(h340,assumption,
! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ),
introduced(assumption,[]) ).
thf(h341,assumption,
~ hoasinduction,
introduced(assumption,[]) ).
thf(h342,assumption,
~ ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ),
introduced(assumption,[]) ).
thf(h343,assumption,
hoasinduction_lem3b_lthm,
introduced(assumption,[]) ).
thf(h344,assumption,
sP9,
introduced(assumption,[]) ).
thf(h345,assumption,
~ hoasinduction_lem3b_lthm,
introduced(assumption,[]) ).
thf(h346,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h347,assumption,
induction,
introduced(assumption,[]) ).
thf(h348,assumption,
! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h349,assumption,
~ induction,
introduced(assumption,[]) ).
thf(h350,assumption,
~ ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h351,assumption,
hoasinduction_lem3a_lthm,
introduced(assumption,[]) ).
thf(h352,assumption,
( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h353,assumption,
~ hoasinduction_lem3a_lthm,
introduced(assumption,[]) ).
thf(h354,assumption,
~ ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h355,assumption,
hoasinduction_lem3aa,
introduced(assumption,[]) ).
thf(h356,assumption,
~ hoasinduction_lem3aa,
introduced(assumption,[]) ).
thf(h357,assumption,
hoasinduction_lem2v2,
introduced(assumption,[]) ).
thf(h358,assumption,
! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ),
introduced(assumption,[]) ).
thf(h359,assumption,
~ hoasinduction_lem2v2,
introduced(assumption,[]) ).
thf(h360,assumption,
~ ! [X1: subst > term > subst > $o,X2: term > $o,X3: term,X4: term] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) )
=> ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 ) )
=> ~ ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X1 @ ( comp @ X5 @ X8 ) @ ( sub @ X6 @ X8 ) @ X7 )
=> ( X1 @ X5 @ X6 @ ( comp @ X8 @ X7 ) ) ) )
=> ~ ! [X5: term,X6: term] :
( ~ ( ( X1 @ id @ X5 @ id )
=> ~ ( X1 @ id @ X6 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X5 @ id ) @ X6 ) @ id ) ) )
=> ~ ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ id @ X5 @ id ) ) )
=> ~ ( X2 @ X3 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ ( ap @ X3 @ X4 ) ) ),
introduced(assumption,[]) ).
thf(h361,assumption,
apinj2,
introduced(assumption,[]) ).
thf(h362,assumption,
! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ),
introduced(assumption,[]) ).
thf(h363,assumption,
~ apinj2,
introduced(assumption,[]) ).
thf(h364,assumption,
~ ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ),
introduced(assumption,[]) ).
thf(h365,assumption,
apinj1,
introduced(assumption,[]) ).
thf(h366,assumption,
! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h367,assumption,
~ apinj1,
introduced(assumption,[]) ).
thf(h368,assumption,
~ ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h369,assumption,
hoasapinj2_lthm,
introduced(assumption,[]) ).
thf(h370,assumption,
sP43,
introduced(assumption,[]) ).
thf(h371,assumption,
~ hoasapinj2_lthm,
introduced(assumption,[]) ).
thf(h372,assumption,
~ sP43,
introduced(assumption,[]) ).
thf(h373,assumption,
hoasinduction_lem3v2a,
introduced(assumption,[]) ).
thf(h374,assumption,
! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h375,assumption,
~ hoasinduction_lem3v2a,
introduced(assumption,[]) ).
thf(h376,assumption,
~ ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h377,assumption,
hoasapinj1_lthm,
introduced(assumption,[]) ).
thf(h378,assumption,
( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h379,assumption,
~ hoasapinj1_lthm,
introduced(assumption,[]) ).
thf(h380,assumption,
~ ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h381,assumption,
hoaslaminj_lthm,
introduced(assumption,[]) ).
thf(h382,assumption,
( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h383,assumption,
~ hoaslaminj_lthm,
introduced(assumption,[]) ).
thf(h384,assumption,
~ ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: subst > term > term,X2: subst > term > term,X3: subst,X4: term] :
( ~ ( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( lam @ ( X2 @ sh @ one ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= ( X2 @ X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h385,assumption,
axvarcons,
introduced(assumption,[]) ).
thf(h386,assumption,
! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h387,assumption,
~ axvarcons,
introduced(assumption,[]) ).
thf(h388,assumption,
~ ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h389,assumption,
axscons,
introduced(assumption,[]) ).
thf(h390,assumption,
! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h391,assumption,
~ axscons,
introduced(assumption,[]) ).
thf(h392,assumption,
~ ! [X1: subst] :
( X1
= ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h393,assumption,
axidr,
introduced(assumption,[]) ).
thf(h394,assumption,
sP17,
introduced(assumption,[]) ).
thf(h395,assumption,
~ axidr,
introduced(assumption,[]) ).
thf(h396,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h397,assumption,
pushprop_lem1,
introduced(assumption,[]) ).
thf(h398,assumption,
sP12,
introduced(assumption,[]) ).
thf(h399,assumption,
~ pushprop_lem1,
introduced(assumption,[]) ).
thf(h400,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h401,assumption,
laminj,
introduced(assumption,[]) ).
thf(h402,assumption,
! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h403,assumption,
~ laminj,
introduced(assumption,[]) ).
thf(h404,assumption,
~ ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h405,assumption,
hoasinduction_lem3_lthm,
introduced(assumption,[]) ).
thf(h406,assumption,
( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h407,assumption,
~ hoasinduction_lem3_lthm,
introduced(assumption,[]) ).
thf(h408,assumption,
~ ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( sP40
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h409,assumption,
pushprop_lem0,
introduced(assumption,[]) ).
thf(h410,assumption,
sP41,
introduced(assumption,[]) ).
thf(h411,assumption,
~ pushprop_lem0,
introduced(assumption,[]) ).
thf(h412,assumption,
~ sP41,
introduced(assumption,[]) ).
thf(h413,assumption,
hoasinduction_lem3v2a_lthm,
introduced(assumption,[]) ).
thf(h414,assumption,
( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h415,assumption,
~ hoasinduction_lem3v2a_lthm,
introduced(assumption,[]) ).
thf(h416,assumption,
~ ( sP22
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h417,assumption,
axidl,
introduced(assumption,[]) ).
thf(h418,assumption,
sP4,
introduced(assumption,[]) ).
thf(h419,assumption,
~ axidl,
introduced(assumption,[]) ).
thf(h420,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h421,assumption,
induction2_lthm,
introduced(assumption,[]) ).
thf(h422,assumption,
( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h423,assumption,
~ induction2_lthm,
introduced(assumption,[]) ).
thf(h424,assumption,
~ ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ~ ( ~ ( ! [X4: term,X5: term] :
( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X1 @ ( ap @ X4 @ X5 ) ) )
=> ~ ! [X4: term] :
( ! [X5: term] :
( ( X1 @ X5 )
=> ( X1 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) )
=> ~ ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h425,assumption,
hoasinduction_lem0_lthm,
introduced(assumption,[]) ).
thf(h426,assumption,
~ hoasinduction_lem0_lthm,
introduced(assumption,[]) ).
thf(h427,assumption,
substmonoid_lthm,
introduced(assumption,[]) ).
thf(h428,assumption,
( sP4
=> ( sP17
=> ~ sP11 ) ),
introduced(assumption,[]) ).
thf(h429,assumption,
~ substmonoid_lthm,
introduced(assumption,[]) ).
thf(h430,assumption,
~ ( sP4
=> ( sP17
=> ~ sP11 ) ),
introduced(assumption,[]) ).
thf(h431,assumption,
hoasinduction_lem3b,
introduced(assumption,[]) ).
thf(h432,assumption,
~ hoasinduction_lem3b,
introduced(assumption,[]) ).
thf(h433,assumption,
substmonoid,
introduced(assumption,[]) ).
thf(h434,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h435,assumption,
~ substmonoid,
introduced(assumption,[]) ).
thf(h436,assumption,
sP11,
introduced(assumption,[]) ).
thf(h437,assumption,
hoasinduction_lem3a,
introduced(assumption,[]) ).
thf(h438,assumption,
! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ),
introduced(assumption,[]) ).
thf(h439,assumption,
~ hoasinduction_lem3a,
introduced(assumption,[]) ).
thf(h440,assumption,
~ ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) )
=> ~ ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ),
introduced(assumption,[]) ).
thf(h441,assumption,
hoasinduction_no_psi_cond,
introduced(assumption,[]) ).
thf(h442,assumption,
! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ),
introduced(assumption,[]) ).
thf(h443,assumption,
~ hoasinduction_no_psi_cond,
introduced(assumption,[]) ).
thf(h444,assumption,
~ ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ),
introduced(assumption,[]) ).
thf(h445,assumption,
hoaslamnotap,
introduced(assumption,[]) ).
thf(h446,assumption,
! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h447,assumption,
~ hoaslamnotap,
introduced(assumption,[]) ).
thf(h448,assumption,
~ ! [X1: subst > term > term,X2: term,X3: term] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X1 @ X4 @ X5 ) @ X6 )
= ( X1 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h449,assumption,
induction2,
introduced(assumption,[]) ).
thf(h450,assumption,
! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h451,assumption,
~ induction2,
introduced(assumption,[]) ).
thf(h452,assumption,
~ ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h453,assumption,
pushprop_lem1_lthm,
introduced(assumption,[]) ).
thf(h454,assumption,
( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> sP12 ) ),
introduced(assumption,[]) ).
thf(h455,assumption,
~ pushprop_lem1_lthm,
introduced(assumption,[]) ).
thf(h456,assumption,
~ ( ! [X1: term,X2: subst] :
( X1
= ( sub @ one @ ( push @ X1 @ X2 ) ) )
=> ( ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) )
=> sP12 ) ),
introduced(assumption,[]) ).
thf(h457,assumption,
hoasinduction_lem3v2,
introduced(assumption,[]) ).
thf(h458,assumption,
! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h459,assumption,
~ hoasinduction_lem3v2,
introduced(assumption,[]) ).
thf(h460,assumption,
~ ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h461,assumption,
axshiftcons,
introduced(assumption,[]) ).
thf(h462,assumption,
! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h463,assumption,
~ axshiftcons,
introduced(assumption,[]) ).
thf(h464,assumption,
~ ! [X1: term,X2: subst] :
( X2
= ( comp @ sh @ ( push @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h465,assumption,
termmset,
introduced(assumption,[]) ).
thf(h466,assumption,
! [X1: term] :
( X1
= ( sub @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h467,assumption,
~ termmset,
introduced(assumption,[]) ).
thf(h468,assumption,
~ ! [X1: term] :
( X1
= ( sub @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h469,assumption,
pushprop_lem0_lthm,
introduced(assumption,[]) ).
thf(h470,assumption,
~ pushprop_lem0_lthm,
introduced(assumption,[]) ).
thf(h471,assumption,
hoasinduction_lem3v2_lthm,
introduced(assumption,[]) ).
thf(h472,assumption,
( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h473,assumption,
~ hoasinduction_lem3v2_lthm,
introduced(assumption,[]) ).
thf(h474,assumption,
~ ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) )
=> ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 ) )
=> ~ ! [X4: subst,X5: term,X6: subst,X7: subst] :
( ( X1 @ ( comp @ X4 @ X7 ) @ ( sub @ X5 @ X7 ) @ X6 )
=> ( X1 @ X4 @ X5 @ ( comp @ X7 @ X6 ) ) ) )
=> ~ ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h475,assumption,
axvarid,
introduced(assumption,[]) ).
thf(h476,assumption,
~ axvarid,
introduced(assumption,[]) ).
thf(h477,assumption,
hoasinduction_lthm_3,
introduced(assumption,[]) ).
thf(h478,assumption,
( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h479,assumption,
~ hoasinduction_lthm_3,
introduced(assumption,[]) ).
thf(h480,assumption,
~ ( sP10
=> ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h477,h478,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[1,2,3,4,5,6,h14,h15,h398]) ).
thf(h481,assumption,
~ ( ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( ap @ X3 @ X4 ) ) ) )
=> ~ ! [X3: term] :
( ! [X4: term] :
( ( X1 @ X4 )
=> ( X1 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X1 @ ( lam @ X3 ) ) ) )
=> ( X1 @ X2 ) )
=> ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h482,assumption,
~ ( ! [X1: term] :
( X1
= ( sub @ X1 @ id ) )
=> ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h483,assumption,
~ ( ! [X1: subst > term > subst > $o,X2: term > $o,X3: term] :
( ~ ( ~ ( ! [X4: subst > term > term] :
( ~ ( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X5 @ X6 ) @ X7 )
= ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) ) )
=> ~ ! [X5: term] :
( ( X1 @ id @ X5 @ id )
=> ( X1 @ id @ ( X4 @ id @ X5 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
= ( X1 @ id @ X4 @ id ) ) )
=> ~ ! [X4: term] :
( ( X2 @ X4 )
=> ( X2 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
=> ! [X1: subst > term > subst > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( X1 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( X1 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: term] :
( ( var @ ( sub @ X3 @ id ) )
=> ( X1 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term,X4: term] :
( ~ ( ( X1 @ id @ X3 @ id )
=> ~ ( X1 @ id @ X4 @ id ) )
=> ( X1 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( X1 @ id @ X4 @ id )
=> ( X1 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( X1 @ id @ X2 @ id ) ) ),
introduced(assumption,[]) ).
thf(h484,assumption,
~ ! [X1: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( eigen__114 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( eigen__114 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ~ ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( eigen__114 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( eigen__114 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) ) )
=> ~ ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( eigen__114 @ id @ X2 @ id ) ) )
=> ~ ! [X2: term,X3: term] :
( ~ ( ( eigen__114 @ id @ X2 @ id )
=> ~ ( eigen__114 @ id @ X3 @ id ) )
=> ( eigen__114 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ~ ! [X2: subst > term > term] :
( ~ ( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ~ ! [X3: term] :
( ( eigen__114 @ id @ X3 @ id )
=> ( eigen__114 @ id @ ( X2 @ id @ X3 ) @ id ) ) )
=> ( eigen__114 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ( eigen__114 @ id @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h485,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__114 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__114 @ id @ X1 @ id )
=> ~ ( eigen__114 @ id @ X2 @ id ) )
=> ( eigen__114 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__114 @ id @ X2 @ id )
=> ( eigen__114 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__114 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) )
=> ( eigen__114 @ id @ eigen__115 @ id ) ),
introduced(assumption,[]) ).
thf(h486,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__114 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__114 @ id @ X1 @ id )
=> ~ ( eigen__114 @ id @ X2 @ id ) )
=> ( eigen__114 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__114 @ id @ X2 @ id )
=> ( eigen__114 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__114 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h487,assumption,
~ ( eigen__114 @ id @ eigen__115 @ id ),
introduced(assumption,[]) ).
thf(h488,assumption,
~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__114 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__114 @ id @ X1 @ id )
=> ~ ( eigen__114 @ id @ X2 @ id ) )
=> ( eigen__114 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h489,assumption,
! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__114 @ id @ X2 @ id )
=> ( eigen__114 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__114 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ),
introduced(assumption,[]) ).
thf(h490,assumption,
~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__114 @ id @ X1 @ id ) ) ),
introduced(assumption,[]) ).
thf(h491,assumption,
! [X1: term,X2: term] :
( ~ ( ( eigen__114 @ id @ X1 @ id )
=> ~ ( eigen__114 @ id @ X2 @ id ) )
=> ( eigen__114 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ),
introduced(assumption,[]) ).
thf(h492,assumption,
~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h493,assumption,
! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__114 @ id @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h494,assumption,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) ),
introduced(assumption,[]) ).
thf(h495,assumption,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__114 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__114 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(8,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h494,h495,h492,h493,h490,h491,h488,h489,h486,h487,h485,h484,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[8,9,10,11,12,13,h14,h15,h398]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h492,h493,h490,h491,h488,h489,h486,h487,h485,h484,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h494,h495])],[h492,14,h494,h495]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h490,h491,h488,h489,h486,h487,h485,h484,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h492,h493])],[h490,15,h492,h493]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h488,h489,h486,h487,h485,h484,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h490,h491])],[h488,16,h490,h491]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h486,h487,h485,h484,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h488,h489])],[h486,17,h488,h489]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h485,h484,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h486,h487])],[h485,18,h486,h487]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h484,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h485]),tab_negall(eigenvar,eigen__115)],[h484,19,h485]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h484]),tab_negall(eigenvar,eigen__114)],[h342,20,h484]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h374,h342])],[h483,21,h374,h342]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h450,h482,h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h466,h483])],[h482,22,h466,h483]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h336,h481,h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h450,h482])],[h481,23,h450,h482]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h479,h480,h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h336,h481])],[h480,24,h336,h481]) ).
thf(26,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h475,h466,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h477,h478]),tab_bq(discharge,[h479,h480])],[h17,7,25,h477,h478,h479,h480]) ).
thf(h496,assumption,
( eigen__125
!= ( sub @ eigen__125 @ id ) ),
introduced(assumption,[]) ).
thf(27,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h477,h478,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[27,28,29,30,31,32,h14,h15,h398]) ).
thf(h497,assumption,
~ ! [X1: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( eigen__135 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( eigen__135 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ~ ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( eigen__135 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( eigen__135 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) ) )
=> ~ ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( eigen__135 @ id @ X2 @ id ) ) )
=> ~ ! [X2: term,X3: term] :
( ~ ( ( eigen__135 @ id @ X2 @ id )
=> ~ ( eigen__135 @ id @ X3 @ id ) )
=> ( eigen__135 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ~ ! [X2: subst > term > term] :
( ~ ( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ~ ! [X3: term] :
( ( eigen__135 @ id @ X3 @ id )
=> ( eigen__135 @ id @ ( X2 @ id @ X3 ) @ id ) ) )
=> ( eigen__135 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ( eigen__135 @ id @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h498,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__135 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__135 @ id @ X1 @ id )
=> ~ ( eigen__135 @ id @ X2 @ id ) )
=> ( eigen__135 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__135 @ id @ X2 @ id )
=> ( eigen__135 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__135 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) )
=> ( eigen__135 @ id @ eigen__136 @ id ) ),
introduced(assumption,[]) ).
thf(h499,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__135 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__135 @ id @ X1 @ id )
=> ~ ( eigen__135 @ id @ X2 @ id ) )
=> ( eigen__135 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__135 @ id @ X2 @ id )
=> ( eigen__135 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__135 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h500,assumption,
~ ( eigen__135 @ id @ eigen__136 @ id ),
introduced(assumption,[]) ).
thf(h501,assumption,
~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__135 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__135 @ id @ X1 @ id )
=> ~ ( eigen__135 @ id @ X2 @ id ) )
=> ( eigen__135 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h502,assumption,
! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__135 @ id @ X2 @ id )
=> ( eigen__135 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__135 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ),
introduced(assumption,[]) ).
thf(h503,assumption,
~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__135 @ id @ X1 @ id ) ) ),
introduced(assumption,[]) ).
thf(h504,assumption,
! [X1: term,X2: term] :
( ~ ( ( eigen__135 @ id @ X1 @ id )
=> ~ ( eigen__135 @ id @ X2 @ id ) )
=> ( eigen__135 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ),
introduced(assumption,[]) ).
thf(h505,assumption,
~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h506,assumption,
! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__135 @ id @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h507,assumption,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) ),
introduced(assumption,[]) ).
thf(h508,assumption,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__135 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__135 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(34,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h498,h497,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[34,35,36,37,38,39,h14,h15,h398]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h505,h506,h503,h504,h501,h502,h499,h500,h498,h497,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h507,h508])],[h505,40,h507,h508]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h503,h504,h501,h502,h499,h500,h498,h497,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h505,h506])],[h503,41,h505,h506]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h501,h502,h499,h500,h498,h497,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h503,h504])],[h501,42,h503,h504]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h499,h500,h498,h497,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h501,h502])],[h499,43,h501,h502]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h498,h497,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h499,h500])],[h498,44,h499,h500]) ).
thf(46,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h497,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h498]),tab_negall(eigenvar,eigen__136)],[h497,45,h498]) ).
thf(47,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h497]),tab_negall(eigenvar,eigen__135)],[h342,46,h497]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h466,h483,h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h374,h342])],[h483,47,h374,h342]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h450,h482,h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h466,h483])],[h482,48,h466,h483]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h336,h481,h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h450,h482])],[h481,49,h450,h482]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h479,h480,h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h336,h481])],[h480,50,h336,h481]) ).
thf(52,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h496,h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h477,h478]),tab_bq(discharge,[h479,h480])],[h17,33,51,h477,h478,h479,h480]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h476,h468,h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h496]),tab_negall(eigenvar,eigen__125)],[h468,52,h496]) ).
thf(54,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h471,h472,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h475,h466]),tab_bq(discharge,[h476,h468])],[h19,26,53,h475,h466,h476,h468]) ).
thf(h509,assumption,
~ ! [X1: term > $o,X2: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( eigen__146 @ X3 @ X4 @ ( comp @ X6 @ X5 ) )
=> ( eigen__146 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 ) )
=> ~ ! [X3: subst,X4: term,X5: subst,X6: subst] :
( ( eigen__146 @ ( comp @ X3 @ X6 ) @ ( sub @ X4 @ X6 ) @ X5 )
=> ( eigen__146 @ X3 @ X4 @ ( comp @ X6 @ X5 ) ) ) )
=> ~ ! [X3: subst > term > term] :
( ~ ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X3 @ X4 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ~ ! [X4: term] :
( ( eigen__146 @ id @ X4 @ id )
=> ( eigen__146 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
=> ( eigen__146 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
= ( eigen__146 @ id @ X3 @ id ) ) )
=> ~ ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h510,assumption,
~ ! [X1: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( eigen__146 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( eigen__146 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ~ ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( eigen__146 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( eigen__146 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) ) )
=> ~ ! [X2: subst > term > term] :
( ~ ( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ~ ! [X3: term] :
( ( eigen__146 @ id @ X3 @ id )
=> ( eigen__146 @ id @ ( X2 @ id @ X3 ) @ id ) ) )
=> ( eigen__146 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X2: term] :
( ( eigen__147 @ X2 )
= ( eigen__146 @ id @ X2 @ id ) ) )
=> ~ ! [X2: term] :
( ( eigen__147 @ X2 )
=> ( eigen__147 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) ) )
=> ( eigen__147 @ ( lam @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h511,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__146 @ id @ X2 @ id )
=> ( eigen__146 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__146 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X1: term] :
( ( eigen__147 @ X1 )
= ( eigen__146 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term] :
( ( eigen__147 @ X1 )
=> ( eigen__147 @ ( sub @ eigen__148 @ ( push @ X1 @ id ) ) ) ) )
=> ( eigen__147 @ ( lam @ eigen__148 ) ) ),
introduced(assumption,[]) ).
thf(h512,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__146 @ id @ X2 @ id )
=> ( eigen__146 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__146 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X1: term] :
( ( eigen__147 @ X1 )
= ( eigen__146 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term] :
( ( eigen__147 @ X1 )
=> ( eigen__147 @ ( sub @ eigen__148 @ ( push @ X1 @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h513,assumption,
~ ( eigen__147 @ ( lam @ eigen__148 ) ),
introduced(assumption,[]) ).
thf(h514,assumption,
~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__146 @ id @ X2 @ id )
=> ( eigen__146 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__146 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) )
=> ~ ! [X1: term] :
( ( eigen__147 @ X1 )
= ( eigen__146 @ id @ X1 @ id ) ) ),
introduced(assumption,[]) ).
thf(h515,assumption,
! [X1: term] :
( ( eigen__147 @ X1 )
=> ( eigen__147 @ ( sub @ eigen__148 @ ( push @ X1 @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h516,assumption,
~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__146 @ id @ X2 @ id )
=> ( eigen__146 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__146 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h517,assumption,
! [X1: term] :
( ( eigen__147 @ X1 )
= ( eigen__146 @ id @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h518,assumption,
~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h519,assumption,
! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__146 @ id @ X2 @ id )
=> ( eigen__146 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__146 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ),
introduced(assumption,[]) ).
thf(h520,assumption,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) ),
introduced(assumption,[]) ).
thf(h521,assumption,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__146 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__146 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(55,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(61,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h477,h478,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[55,56,57,58,59,60,h14,h15,h398]) ).
thf(h522,assumption,
~ ! [X1: term] :
( ~ ( ~ ( ~ ( ~ ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( eigen__158 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( eigen__158 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ~ ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( eigen__158 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( eigen__158 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) ) )
=> ~ ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( eigen__158 @ id @ X2 @ id ) ) )
=> ~ ! [X2: term,X3: term] :
( ~ ( ( eigen__158 @ id @ X2 @ id )
=> ~ ( eigen__158 @ id @ X3 @ id ) )
=> ( eigen__158 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ~ ! [X2: subst > term > term] :
( ~ ( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ~ ! [X3: term] :
( ( eigen__158 @ id @ X3 @ id )
=> ( eigen__158 @ id @ ( X2 @ id @ X3 ) @ id ) ) )
=> ( eigen__158 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ( eigen__158 @ id @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h523,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__158 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__158 @ id @ X1 @ id )
=> ~ ( eigen__158 @ id @ X2 @ id ) )
=> ( eigen__158 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__158 @ id @ X2 @ id )
=> ( eigen__158 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__158 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) )
=> ( eigen__158 @ id @ eigen__159 @ id ) ),
introduced(assumption,[]) ).
thf(h524,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__158 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__158 @ id @ X1 @ id )
=> ~ ( eigen__158 @ id @ X2 @ id ) )
=> ( eigen__158 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) )
=> ~ ! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__158 @ id @ X2 @ id )
=> ( eigen__158 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__158 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h525,assumption,
~ ( eigen__158 @ id @ eigen__159 @ id ),
introduced(assumption,[]) ).
thf(h526,assumption,
~ ( ~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__158 @ id @ X1 @ id ) ) )
=> ~ ! [X1: term,X2: term] :
( ~ ( ( eigen__158 @ id @ X1 @ id )
=> ~ ( eigen__158 @ id @ X2 @ id ) )
=> ( eigen__158 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h527,assumption,
! [X1: subst > term > term] :
( ~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ~ ! [X2: term] :
( ( eigen__158 @ id @ X2 @ id )
=> ( eigen__158 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( eigen__158 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ),
introduced(assumption,[]) ).
thf(h528,assumption,
~ ( ~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) )
=> ~ ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__158 @ id @ X1 @ id ) ) ),
introduced(assumption,[]) ).
thf(h529,assumption,
! [X1: term,X2: term] :
( ~ ( ( eigen__158 @ id @ X1 @ id )
=> ~ ( eigen__158 @ id @ X2 @ id ) )
=> ( eigen__158 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ),
introduced(assumption,[]) ).
thf(h530,assumption,
~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ~ ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h531,assumption,
! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__158 @ id @ X1 @ id ) ),
introduced(assumption,[]) ).
thf(h532,assumption,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) ),
introduced(assumption,[]) ).
thf(h533,assumption,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__158 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__158 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(62,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(68,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h523,h522,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[62,63,64,65,66,67,h14,h15,h398]) ).
thf(69,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h530,h531,h528,h529,h526,h527,h524,h525,h523,h522,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h532,h533])],[h530,68,h532,h533]) ).
thf(70,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h528,h529,h526,h527,h524,h525,h523,h522,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h530,h531])],[h528,69,h530,h531]) ).
thf(71,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h526,h527,h524,h525,h523,h522,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h528,h529])],[h526,70,h528,h529]) ).
thf(72,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h524,h525,h523,h522,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h526,h527])],[h524,71,h526,h527]) ).
thf(73,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h523,h522,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h524,h525])],[h523,72,h524,h525]) ).
thf(74,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h522,h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h523]),tab_negall(eigenvar,eigen__159)],[h522,73,h523]) ).
thf(75,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h374,h342,h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h522]),tab_negall(eigenvar,eigen__158)],[h342,74,h522]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h466,h483,h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h374,h342])],[h483,75,h374,h342]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h450,h482,h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h466,h483])],[h482,76,h466,h483]) ).
thf(78,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h336,h481,h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h450,h482])],[h481,77,h450,h482]) ).
thf(79,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h479,h480,h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h336,h481])],[h480,78,h336,h481]) ).
thf(80,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h475,h466,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h477,h478]),tab_bq(discharge,[h479,h480])],[h17,61,79,h477,h478,h479,h480]) ).
thf(h534,assumption,
( eigen__169
!= ( sub @ eigen__169 @ id ) ),
introduced(assumption,[]) ).
thf(81,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(86,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(87,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h477,h478,h534,h476,h468,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[81,82,83,84,85,86,h14,h15,h398]) ).
thf(88,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(92,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(94,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h479,h480,h534,h476,h468,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[88,89,90,91,92,93,h14,h15,h398]) ).
thf(95,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h534,h476,h468,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h477,h478]),tab_bq(discharge,[h479,h480])],[h17,87,94,h477,h478,h479,h480]) ).
thf(96,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h476,h468,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h534]),tab_negall(eigenvar,eigen__169)],[h468,95,h534]) ).
thf(97,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h475,h466]),tab_bq(discharge,[h476,h468])],[h19,80,96,h475,h466,h476,h468]) ).
thf(98,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h518,h519,h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h520,h521])],[h518,97,h520,h521]) ).
thf(99,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h516,h517,h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h518,h519])],[h516,98,h518,h519]) ).
thf(100,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h514,h515,h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h516,h517])],[h514,99,h516,h517]) ).
thf(101,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h512,h513,h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h514,h515])],[h512,100,h514,h515]) ).
thf(102,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h511,h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h512,h513])],[h511,101,h512,h513]) ).
thf(103,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h510,h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h511]),tab_negall(eigenvar,eigen__148)],[h510,102,h511]) ).
thf(104,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h509,h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h510]),tab_negall(eigenvar,eigen__147)],[h509,103,h510]) ).
thf(105,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h466,h460,h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h509]),tab_negall(eigenvar,eigen__146)],[h460,104,h509]) ).
thf(106,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h473,h474,h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h466,h460])],[h474,105,h466,h460]) ).
thf(107,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h469,h410,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h471,h472]),tab_bq(discharge,[h473,h474])],[h21,54,106,h471,h472,h473,h474]) ).
thf(108,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h470,h412,h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[h410,h412]) ).
thf(109,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h465,h466,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h469,h410]),tab_bq(discharge,[h470,h412])],[h25,107,108,h469,h410,h470,h412]) ).
thf(110,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(114,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(115,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(116,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h467,h468,h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[110,111,112,113,114,115,h14,h15,h398]) ).
thf(117,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h461,h462,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h465,h466]),tab_bq(discharge,[h467,h468])],[h27,109,116,h465,h466,h467,h468]) ).
thf(118,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(122,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(123,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(124,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h463,h464,h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[118,119,120,121,122,123,h14,h15,h398]) ).
thf(125,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h457,h458,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h461,h462]),tab_bq(discharge,[h463,h464])],[h29,117,124,h461,h462,h463,h464]) ).
thf(126,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(127,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(128,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(129,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(132,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h459,h460,h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[126,127,128,129,130,131,h14,h15,h398]) ).
thf(133,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h453,h454,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h457,h458]),tab_bq(discharge,[h459,h460])],[h31,125,132,h457,h458,h459,h460]) ).
thf(134,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(135,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(136,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(138,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(139,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(140,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h455,h456,h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[134,135,136,137,138,139,h14,h15,h398]) ).
thf(141,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h449,h450,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h453,h454]),tab_bq(discharge,[h455,h456])],[h33,133,140,h453,h454,h455,h456]) ).
thf(142,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(145,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(146,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(147,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(148,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h451,h452,h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[142,143,144,145,146,147,h14,h15,h398]) ).
thf(149,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h445,h446,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h449,h450]),tab_bq(discharge,[h451,h452])],[h38,141,148,h449,h450,h451,h452]) ).
thf(150,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(153,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(154,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(155,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(156,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h447,h448,h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[150,151,152,153,154,155,h14,h15,h398]) ).
thf(157,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h441,h442,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h445,h446]),tab_bq(discharge,[h447,h448])],[h44,149,156,h445,h446,h447,h448]) ).
thf(158,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(159,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(160,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(164,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h443,h444,h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[158,159,160,161,162,163,h14,h15,h398]) ).
thf(165,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h437,h438,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h441,h442]),tab_bq(discharge,[h443,h444])],[h52,157,164,h441,h442,h443,h444]) ).
thf(166,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(167,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(168,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(169,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(172,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h439,h440,h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[166,167,168,169,170,171,h14,h15,h398]) ).
thf(173,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h418,h394,h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h437,h438]),tab_bq(discharge,[h439,h440])],[h56,165,172,h437,h438,h439,h440]) ).
thf(174,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h433,h434,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h418,h394])],[h434,173,h418,h394]) ).
thf(175,plain,
( ~ sP11
| ~ sP4
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(176,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h435,h436,h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[175,h394,h418,h436]) ).
thf(177,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h431,h344,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h433,h434]),tab_bq(discharge,[h435,h436])],[h60,174,176,h433,h434,h435,h436]) ).
thf(178,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h432,h346,h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[h344,h346]) ).
thf(179,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h427,h428,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h431,h344]),tab_bq(discharge,[h432,h346])],[h62,177,178,h431,h344,h432,h346]) ).
thf(180,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(181,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(182,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(183,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(184,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(185,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(186,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h429,h430,h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[180,181,182,183,184,185,h14,h15,h398]) ).
thf(187,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h425,h336,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h427,h428]),tab_bq(discharge,[h429,h430])],[h70,179,186,h427,h428,h429,h430]) ).
thf(188,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h426,h338,h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[h336,h338]) ).
thf(189,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h421,h422,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h425,h336]),tab_bq(discharge,[h426,h338])],[h72,187,188,h425,h336,h426,h338]) ).
thf(190,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(191,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(192,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(193,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(194,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(195,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(196,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h423,h424,h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[190,191,192,193,194,195,h14,h15,h398]) ).
thf(197,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h417,h418,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h421,h422]),tab_bq(discharge,[h423,h424])],[h74,189,196,h421,h422,h423,h424]) ).
thf(198,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(199,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(200,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(201,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(202,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(203,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(204,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h419,h420,h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[198,199,200,201,202,203,h14,h15,h398]) ).
thf(205,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h413,h414,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h417,h418]),tab_bq(discharge,[h419,h420])],[h78,197,204,h417,h418,h419,h420]) ).
thf(206,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(207,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(208,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(209,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(210,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(211,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(212,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h415,h416,h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[206,207,208,209,210,211,h14,h15,h398]) ).
thf(213,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h409,h410,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h413,h414]),tab_bq(discharge,[h415,h416])],[h92,205,212,h413,h414,h415,h416]) ).
thf(214,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(215,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(216,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(217,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(218,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(219,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(220,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h411,h412,h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[214,215,216,217,218,219,h14,h15,h398]) ).
thf(221,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h405,h406,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h409,h410]),tab_bq(discharge,[h411,h412])],[h98,213,220,h409,h410,h411,h412]) ).
thf(222,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(223,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(224,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(225,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(226,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(227,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(228,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h407,h408,h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[222,223,224,225,226,227,h14,h15,h398]) ).
thf(229,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h401,h402,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h405,h406]),tab_bq(discharge,[h407,h408])],[h100,221,228,h405,h406,h407,h408]) ).
thf(230,plain,
( ~ sP31
| ~ sP18
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(231,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(232,plain,
( ~ sP25
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(233,plain,
( ~ sP19
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(234,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(235,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(236,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h403,h404,h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[230,231,232,233,234,235,h14,h15,h398]) ).
thf(237,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h397,h398,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h401,h402]),tab_bq(discharge,[h403,h404])],[h102,229,236,h401,h402,h403,h404]) ).
thf(238,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(239,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(240,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(241,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(242,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(243,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(244,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(245,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(246,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(247,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(248,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(249,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(250,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(251,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h399,h400,h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[238,239,240,241,242,243,244,245,246,247,248,249,250,h9,h11,h14,h15,h236]) ).
thf(252,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h393,h394,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h397,h398]),tab_bq(discharge,[h399,h400])],[h104,237,251,h397,h398,h399,h400]) ).
thf(253,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(254,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(255,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(256,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(257,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(258,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(259,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(260,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(261,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(262,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(263,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(264,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(265,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(266,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h395,h396,h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[253,254,255,256,257,258,259,260,261,262,263,264,265,h9,h11,h14,h15,h236]) ).
thf(267,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h389,h390,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h393,h394]),tab_bq(discharge,[h395,h396])],[h106,252,266,h393,h394,h395,h396]) ).
thf(268,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(269,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(270,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(271,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(272,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(273,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(274,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(275,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(276,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(277,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(278,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(279,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(280,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(281,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h391,h392,h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[268,269,270,271,272,273,274,275,276,277,278,279,280,h9,h11,h14,h15,h236]) ).
thf(282,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h385,h386,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h389,h390]),tab_bq(discharge,[h391,h392])],[h110,267,281,h389,h390,h391,h392]) ).
thf(283,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(284,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(285,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(286,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(287,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(288,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(289,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(290,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(291,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(292,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(293,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(294,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(295,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(296,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h387,h388,h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[283,284,285,286,287,288,289,290,291,292,293,294,295,h9,h11,h14,h15,h236]) ).
thf(297,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h381,h382,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h385,h386]),tab_bq(discharge,[h387,h388])],[h112,282,296,h385,h386,h387,h388]) ).
thf(298,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(299,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(300,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(301,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(302,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(303,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(304,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(305,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(306,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(307,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(308,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(309,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(310,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(311,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h383,h384,h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[298,299,300,301,302,303,304,305,306,307,308,309,310,h9,h11,h14,h15,h236]) ).
thf(312,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h377,h378,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h381,h382]),tab_bq(discharge,[h383,h384])],[h114,297,311,h381,h382,h383,h384]) ).
thf(313,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(314,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(315,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(316,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(317,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(318,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(319,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(320,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(321,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(322,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(323,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(324,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(325,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(326,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h379,h380,h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[313,314,315,316,317,318,319,320,321,322,323,324,325,h9,h11,h14,h15,h236]) ).
thf(327,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h373,h374,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h377,h378]),tab_bq(discharge,[h379,h380])],[h116,312,326,h377,h378,h379,h380]) ).
thf(328,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(329,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(330,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(331,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(332,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(333,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(334,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(335,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(336,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(337,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(338,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(339,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(340,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(341,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h375,h376,h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[328,329,330,331,332,333,334,335,336,337,338,339,340,h9,h11,h14,h15,h236]) ).
thf(342,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h369,h370,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h373,h374]),tab_bq(discharge,[h375,h376])],[h118,327,341,h373,h374,h375,h376]) ).
thf(343,plain,
( sP43
| ~ sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(344,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h371,h372,h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[343,h286,h372]) ).
thf(345,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h365,h366,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h369,h370]),tab_bq(discharge,[h371,h372])],[h120,342,344,h369,h370,h371,h372]) ).
thf(346,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(347,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(348,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(349,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(350,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(351,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(352,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(353,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(354,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(355,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(356,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(357,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(358,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(359,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h367,h368,h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[346,347,348,349,350,351,352,353,354,355,356,357,358,h9,h11,h14,h15,h236]) ).
thf(360,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h361,h362,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h365,h366]),tab_bq(discharge,[h367,h368])],[h122,345,359,h365,h366,h367,h368]) ).
thf(361,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(362,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(363,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(364,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(365,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(366,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(367,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(368,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(369,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(370,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(371,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(372,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(373,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(374,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h363,h364,h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[361,362,363,364,365,366,367,368,369,370,371,372,373,h9,h11,h14,h15,h236]) ).
thf(375,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h357,h358,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h361,h362]),tab_bq(discharge,[h363,h364])],[h124,360,374,h361,h362,h363,h364]) ).
thf(376,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(377,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(378,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(379,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(380,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(381,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(382,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(383,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(384,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(385,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(386,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(387,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(388,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(389,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h359,h360,h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[376,377,378,379,380,381,382,383,384,385,386,387,388,h9,h11,h14,h15,h236]) ).
thf(390,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h355,h316,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h357,h358]),tab_bq(discharge,[h359,h360])],[h128,375,389,h357,h358,h359,h360]) ).
thf(391,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h356,h318,h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[h316,h318]) ).
thf(392,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h351,h352,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h355,h316]),tab_bq(discharge,[h356,h318])],[h146,390,391,h355,h316,h356,h318]) ).
thf(393,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(394,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(395,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(396,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(397,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(398,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(399,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(400,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(401,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(402,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(403,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(404,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(405,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(406,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h353,h354,h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[393,394,395,396,397,398,399,400,401,402,403,404,405,h9,h11,h14,h15,h236]) ).
thf(407,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h347,h348,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h351,h352]),tab_bq(discharge,[h353,h354])],[h150,392,406,h351,h352,h353,h354]) ).
thf(408,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(409,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(410,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(411,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(412,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(413,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(414,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(415,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(416,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(417,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(418,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(419,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(420,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(421,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h349,h350,h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[408,409,410,411,412,413,414,415,416,417,418,419,420,h9,h11,h14,h15,h236]) ).
thf(422,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h343,h344,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h347,h348]),tab_bq(discharge,[h349,h350])],[h152,407,421,h347,h348,h349,h350]) ).
thf(423,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(424,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(425,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(426,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(427,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(428,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(429,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(430,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(431,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(432,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(433,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(434,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(435,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(436,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h345,h346,h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[423,424,425,426,427,428,429,430,431,432,433,434,435,h9,h11,h14,h15,h236]) ).
thf(437,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h339,h340,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h343,h344]),tab_bq(discharge,[h345,h346])],[h156,422,436,h343,h344,h345,h346]) ).
thf(438,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(439,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(440,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(441,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(442,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(443,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(444,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(445,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(446,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(447,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(448,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(449,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(450,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(451,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h341,h342,h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[438,439,440,441,442,443,444,445,446,447,448,449,450,h9,h11,h14,h15,h236]) ).
thf(452,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h335,h336,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h339,h340]),tab_bq(discharge,[h341,h342])],[h166,437,451,h339,h340,h341,h342]) ).
thf(453,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(454,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(455,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(456,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(457,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(458,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(459,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(460,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(461,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(462,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(463,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(464,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(465,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(466,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h337,h338,h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[453,454,455,456,457,458,459,460,461,462,463,464,465,h9,h11,h14,h15,h236]) ).
thf(467,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h331,h332,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h335,h336]),tab_bq(discharge,[h337,h338])],[h168,452,466,h335,h336,h337,h338]) ).
thf(468,plain,
( sP20
| ~ sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(469,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h333,h334,h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[468,h270,h334]) ).
thf(470,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h327,h328,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h331,h332]),tab_bq(discharge,[h333,h334])],[h172,467,469,h331,h332,h333,h334]) ).
thf(471,plain,
~ sP33,
inference(prop_rule,[status(thm)],[]) ).
thf(472,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h329,h330,h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[471,h330]) ).
thf(473,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h323,h324,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h327,h328]),tab_bq(discharge,[h329,h330])],[h178,470,472,h327,h328,h329,h330]) ).
thf(474,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(475,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(476,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(477,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(478,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(479,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(480,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(481,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(482,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(483,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(484,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(485,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(486,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(487,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h325,h326,h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[474,475,476,477,478,479,480,481,482,483,484,485,486,h9,h11,h14,h15,h236]) ).
thf(488,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h319,h320,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h323,h324]),tab_bq(discharge,[h325,h326])],[h180,473,487,h323,h324,h325,h326]) ).
thf(489,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(490,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(491,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(492,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(493,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(494,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(495,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(496,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(497,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(498,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(499,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(500,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(501,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(502,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h321,h322,h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[489,490,491,492,493,494,495,496,497,498,499,500,501,h9,h11,h14,h15,h236]) ).
thf(503,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h315,h316,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h319,h320]),tab_bq(discharge,[h321,h322])],[h182,488,502,h319,h320,h321,h322]) ).
thf(504,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(505,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(506,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(507,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(508,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(509,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(510,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(511,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(512,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(513,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(514,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(515,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(516,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(517,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h317,h318,h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[504,505,506,507,508,509,510,511,512,513,514,515,516,h9,h11,h14,h15,h236]) ).
thf(518,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h311,h312,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h315,h316]),tab_bq(discharge,[h317,h318])],[h184,503,517,h315,h316,h317,h318]) ).
thf(519,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(520,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(521,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(522,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(523,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(524,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(525,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(526,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(527,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(528,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(529,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(530,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(531,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(532,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h313,h314,h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[519,520,521,522,523,524,525,526,527,528,529,530,531,h9,h11,h14,h15,h236]) ).
thf(533,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h307,h308,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h311,h312]),tab_bq(discharge,[h313,h314])],[h188,518,532,h311,h312,h313,h314]) ).
thf(534,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(535,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(536,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(537,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(538,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(539,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(540,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(541,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(542,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(543,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(544,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(545,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(546,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(547,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h309,h310,h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[534,535,536,537,538,539,540,541,542,543,544,545,546,h9,h11,h14,h15,h236]) ).
thf(548,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h303,h304,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h307,h308]),tab_bq(discharge,[h309,h310])],[h190,533,547,h307,h308,h309,h310]) ).
thf(549,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(550,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(551,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(552,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(553,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(554,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(555,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(556,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(557,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(558,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(559,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(560,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(561,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(562,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h305,h306,h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[549,550,551,552,553,554,555,556,557,558,559,560,561,h9,h11,h14,h15,h236]) ).
thf(563,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h299,h300,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h303,h304]),tab_bq(discharge,[h305,h306])],[h192,548,562,h303,h304,h305,h306]) ).
thf(564,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(565,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(566,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(567,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(568,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(569,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(570,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(571,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(572,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(573,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(574,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(575,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(576,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(577,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h301,h302,h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[564,565,566,567,568,569,570,571,572,573,574,575,576,h9,h11,h14,h15,h236]) ).
thf(578,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h297,h282,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h299,h300]),tab_bq(discharge,[h301,h302])],[h194,563,577,h299,h300,h301,h302]) ).
thf(579,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h298,h284,h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[h282,h284]) ).
thf(580,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h293,h294,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h297,h282]),tab_bq(discharge,[h298,h284])],[h196,578,579,h297,h282,h298,h284]) ).
thf(581,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(582,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(583,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(584,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(585,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(586,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(587,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(588,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(589,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(590,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(591,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(592,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(593,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(594,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h295,h296,h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[581,582,583,584,585,586,587,588,589,590,591,592,593,h9,h11,h14,h15,h236]) ).
thf(595,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h289,h290,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h293,h294]),tab_bq(discharge,[h295,h296])],[h204,580,594,h293,h294,h295,h296]) ).
thf(596,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(597,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(598,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(599,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(600,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(601,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(602,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(603,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(604,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(605,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(606,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(607,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(608,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(609,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h291,h292,h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[596,597,598,599,600,601,602,603,604,605,606,607,608,h9,h11,h14,h15,h236]) ).
thf(610,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h285,h286,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h289,h290]),tab_bq(discharge,[h291,h292])],[h208,595,609,h289,h290,h291,h292]) ).
thf(611,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(612,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(613,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(614,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(615,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(616,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(617,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(618,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(619,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(620,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(621,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(622,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(623,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(624,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h287,h288,h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[611,612,613,614,615,616,617,618,619,620,621,622,623,h9,h11,h14,h15,h236]) ).
thf(625,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h281,h282,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h285,h286]),tab_bq(discharge,[h287,h288])],[h212,610,624,h285,h286,h287,h288]) ).
thf(626,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(627,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(628,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(629,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(630,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(631,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(632,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(633,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(634,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(635,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(636,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(637,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(638,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(639,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h283,h284,h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[626,627,628,629,630,631,632,633,634,635,636,637,638,h9,h11,h14,h15,h236]) ).
thf(640,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h277,h278,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h281,h282]),tab_bq(discharge,[h283,h284])],[h216,625,639,h281,h282,h283,h284]) ).
thf(641,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(642,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(643,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(644,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(645,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(646,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(647,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(648,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(649,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(650,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(651,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(652,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(653,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(654,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h279,h280,h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[641,642,643,644,645,646,647,648,649,650,651,652,653,h9,h11,h14,h15,h236]) ).
thf(655,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h273,h274,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h277,h278]),tab_bq(discharge,[h279,h280])],[h218,640,654,h277,h278,h279,h280]) ).
thf(656,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(657,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(658,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(659,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(660,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(661,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(662,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(663,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(664,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(665,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(666,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(667,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(668,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(669,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h275,h276,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[656,657,658,659,660,661,662,663,664,665,666,667,668,h9,h11,h14,h15,h236]) ).
thf(670,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h273,h274]),tab_bq(discharge,[h275,h276])],[h224,655,669,h273,h274,h275,h276]) ).
thf(671,plain,
( ~ sP39
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(672,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(673,plain,
( ~ sP48
| ~ sP44
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(674,plain,
( ~ sP24
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(675,plain,
( ~ sP45
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(676,plain,
( ~ sP42
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(677,plain,
( ~ sP2
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(678,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(679,plain,
( ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(680,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(681,plain,
( ~ sP36
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(682,plain,
( ~ sP35
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(683,plain,
( ~ sP1
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(684,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h271,h272,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[671,672,673,674,675,676,677,678,679,680,681,682,683,h9,h11,h14,h15,h236]) ).
thf(685,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_bq(discharge,[h269,h270]),tab_bq(discharge,[h271,h272])],[h232,670,684,h269,h270,h271,h272]) ).
thf(686,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h267,h268])],[h265,685,h267,h268]) ).
thf(687,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h265,h266])],[h263,686,h265,h266]) ).
thf(688,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h263,h264])],[h261,687,h263,h264]) ).
thf(689,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h259,h260,h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h261,h262])],[h259,688,h261,h262]) ).
thf(690,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h257,h258,h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h259,h260])],[h257,689,h259,h260]) ).
thf(691,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h255,h256,h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h257,h258])],[h255,690,h257,h258]) ).
thf(692,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h253,h254,h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h255,h256])],[h253,691,h255,h256]) ).
thf(693,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h251,h252,h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h253,h254])],[h251,692,h253,h254]) ).
thf(694,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h249,h250,h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h251,h252])],[h249,693,h251,h252]) ).
thf(695,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h247,h248,h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h249,h250])],[h247,694,h249,h250]) ).
thf(696,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h245,h246,h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h247,h248])],[h245,695,h247,h248]) ).
thf(697,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h243,h244,h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h245,h246])],[h243,696,h245,h246]) ).
thf(698,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h241,h242,h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h243,h244])],[h241,697,h243,h244]) ).
thf(699,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h239,h240,h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h241,h242])],[h239,698,h241,h242]) ).
thf(700,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h237,h238,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h239,h240])],[h237,699,h239,h240]) ).
thf(701,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h237,h238])],[h235,700,h237,h238]) ).
thf(702,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h235,h236])],[h233,701,h235,h236]) ).
thf(703,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h233,h234])],[h231,702,h233,h234]) ).
thf(704,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h231,h232])],[h229,703,h231,h232]) ).
thf(705,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h229,h230])],[h227,704,h229,h230]) ).
thf(706,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h227,h228])],[h225,705,h227,h228]) ).
thf(707,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h225,h226])],[h223,706,h225,h226]) ).
thf(708,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h223,h224])],[h221,707,h223,h224]) ).
thf(709,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h221,h222])],[h219,708,h221,h222]) ).
thf(710,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h219,h220])],[h217,709,h219,h220]) ).
thf(711,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h217,h218])],[h215,710,h217,h218]) ).
thf(712,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h215,h216])],[h213,711,h215,h216]) ).
thf(713,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h213,h214])],[h211,712,h213,h214]) ).
thf(714,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h211,h212])],[h209,713,h211,h212]) ).
thf(715,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h209,h210])],[h207,714,h209,h210]) ).
thf(716,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h207,h208])],[h205,715,h207,h208]) ).
thf(717,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h205,h206])],[h203,716,h205,h206]) ).
thf(718,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h203,h204])],[h201,717,h203,h204]) ).
thf(719,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h201,h202])],[h199,718,h201,h202]) ).
thf(720,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h199,h200])],[h197,719,h199,h200]) ).
thf(721,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h197,h198])],[h195,720,h197,h198]) ).
thf(722,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h195,h196])],[h193,721,h195,h196]) ).
thf(723,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h193,h194])],[h191,722,h193,h194]) ).
thf(724,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h191,h192])],[h189,723,h191,h192]) ).
thf(725,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h189,h190])],[h187,724,h189,h190]) ).
thf(726,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h187,h188])],[h185,725,h187,h188]) ).
thf(727,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h185,h186])],[h183,726,h185,h186]) ).
thf(728,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h183,h184])],[h181,727,h183,h184]) ).
thf(729,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h181,h182])],[h179,728,h181,h182]) ).
thf(730,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h179,h180])],[h177,729,h179,h180]) ).
thf(731,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h177,h178])],[h175,730,h177,h178]) ).
thf(732,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h175,h176])],[h173,731,h175,h176]) ).
thf(733,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h173,h174])],[h171,732,h173,h174]) ).
thf(734,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h171,h172])],[h169,733,h171,h172]) ).
thf(735,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h169,h170])],[h167,734,h169,h170]) ).
thf(736,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h167,h168])],[h165,735,h167,h168]) ).
thf(737,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h165,h166])],[h163,736,h165,h166]) ).
thf(738,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h163,h164])],[h161,737,h163,h164]) ).
thf(739,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h161,h162])],[h159,738,h161,h162]) ).
thf(740,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h159,h160])],[h157,739,h159,h160]) ).
thf(741,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h157,h158])],[h155,740,h157,h158]) ).
thf(742,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h153,h154,h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h155,h156])],[h153,741,h155,h156]) ).
thf(743,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h151,h152,h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h153,h154])],[h151,742,h153,h154]) ).
thf(744,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h149,h150,h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h151,h152])],[h149,743,h151,h152]) ).
thf(745,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h147,h148,h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h149,h150])],[h147,744,h149,h150]) ).
thf(746,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h145,h146,h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h147,h148])],[h145,745,h147,h148]) ).
thf(747,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h143,h144,h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h145,h146])],[h143,746,h145,h146]) ).
thf(748,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h141,h142,h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h143,h144])],[h141,747,h143,h144]) ).
thf(749,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h139,h140,h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h141,h142])],[h139,748,h141,h142]) ).
thf(750,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h137,h138,h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h139,h140])],[h137,749,h139,h140]) ).
thf(751,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h135,h136,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h137,h138])],[h135,750,h137,h138]) ).
thf(752,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h135,h136])],[h133,751,h135,h136]) ).
thf(753,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h133,h134])],[h131,752,h133,h134]) ).
thf(754,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h131,h132])],[h129,753,h131,h132]) ).
thf(755,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h129,h130])],[h127,754,h129,h130]) ).
thf(756,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h127,h128])],[h125,755,h127,h128]) ).
thf(757,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h125,h126])],[h123,756,h125,h126]) ).
thf(758,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h123,h124])],[h121,757,h123,h124]) ).
thf(759,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h119,h120,h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h121,h122])],[h119,758,h121,h122]) ).
thf(760,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h117,h118,h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h119,h120])],[h117,759,h119,h120]) ).
thf(761,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h115,h116,h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h117,h118])],[h115,760,h117,h118]) ).
thf(762,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h113,h114,h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h115,h116])],[h113,761,h115,h116]) ).
thf(763,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h111,h112,h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h113,h114])],[h111,762,h113,h114]) ).
thf(764,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h109,h110,h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h111,h112])],[h109,763,h111,h112]) ).
thf(765,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h107,h108,h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h109,h110])],[h107,764,h109,h110]) ).
thf(766,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h105,h106,h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h107,h108])],[h105,765,h107,h108]) ).
thf(767,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h103,h104,h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h105,h106])],[h103,766,h105,h106]) ).
thf(768,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h101,h102,h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h103,h104])],[h101,767,h103,h104]) ).
thf(769,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h99,h100,h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h101,h102])],[h99,768,h101,h102]) ).
thf(770,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h97,h98,h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h99,h100])],[h97,769,h99,h100]) ).
thf(771,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h95,h96,h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h97,h98])],[h95,770,h97,h98]) ).
thf(772,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h93,h94,h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h95,h96])],[h93,771,h95,h96]) ).
thf(773,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h91,h92,h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h93,h94])],[h91,772,h93,h94]) ).
thf(774,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h89,h90,h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h91,h92])],[h89,773,h91,h92]) ).
thf(775,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h87,h88,h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h89,h90])],[h87,774,h89,h90]) ).
thf(776,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h85,h86,h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h87,h88])],[h85,775,h87,h88]) ).
thf(777,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h83,h84,h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h85,h86])],[h83,776,h85,h86]) ).
thf(778,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h81,h82,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h83,h84])],[h81,777,h83,h84]) ).
thf(779,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h81,h82])],[h79,778,h81,h82]) ).
thf(780,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h79,h80])],[h77,779,h79,h80]) ).
thf(781,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h75,h76,h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h77,h78])],[h75,780,h77,h78]) ).
thf(782,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h73,h74,h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h75,h76])],[h73,781,h75,h76]) ).
thf(783,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h71,h72,h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h73,h74])],[h71,782,h73,h74]) ).
thf(784,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h69,h70,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h71,h72])],[h69,783,h71,h72]) ).
thf(785,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h69,h70])],[h67,784,h69,h70]) ).
thf(786,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h67,h68])],[h65,785,h67,h68]) ).
thf(787,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h65,h66])],[h63,786,h65,h66]) ).
thf(788,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h63,h64])],[h61,787,h63,h64]) ).
thf(789,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h61,h62])],[h59,788,h61,h62]) ).
thf(790,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h59,h60])],[h57,789,h59,h60]) ).
thf(791,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h57,h58])],[h55,790,h57,h58]) ).
thf(792,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h55,h56])],[h53,791,h55,h56]) ).
thf(793,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h53,h54])],[h51,792,h53,h54]) ).
thf(794,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h51,h52])],[h49,793,h51,h52]) ).
thf(795,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h49,h50])],[h47,794,h49,h50]) ).
thf(796,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h47,h48])],[h45,795,h47,h48]) ).
thf(797,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h44,h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h45,h46])],[h43,796,h45,h46]) ).
thf(798,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h43,h44])],[h41,797,h43,h44]) ).
thf(799,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h40,h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h41,h42])],[h39,798,h41,h42]) ).
thf(800,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h39,h40])],[h37,799,h39,h40]) ).
thf(801,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h1,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h37,h38])],[h36,800,h37,h38]) ).
thf(802,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h36,h1])],[h34,801,h36,h1]) ).
thf(803,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h34,h35])],[h32,802,h34,h35]) ).
thf(804,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h32,h33])],[h30,803,h32,h33]) ).
thf(805,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h30,h31])],[h28,804,h30,h31]) ).
thf(806,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h28,h29])],[h26,805,h28,h29]) ).
thf(807,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h26,h27])],[h24,806,h26,h27]) ).
thf(808,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h24,h25])],[h22,807,h24,h25]) ).
thf(809,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h22,h23])],[h20,808,h22,h23]) ).
thf(810,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h18,809,h20,h21]) ).
thf(811,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h16,810,h18,h19]) ).
thf(alg444_1,axiom,
~ sP23 ).
thf(812,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[alg444_1,811,h16,h17]) ).
thf(813,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,812,h14,h15]) ).
thf(814,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,813,h13]) ).
thf(815,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,814,h11,h12]) ).
thf(816,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,815,h9,h10]) ).
thf(817,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,816,h8]) ).
thf(818,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,817,h7]) ).
thf(819,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,818,h6]) ).
thf(820,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,819,h5]) ).
thf(821,plain,
( sP38
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(822,plain,
( sP15
| ~ sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(823,plain,
( sP5
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(824,plain,
( sP27
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(825,plain,
( sP13
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(826,plain,
( sP32
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(827,plain,
( sP28
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(828,plain,
( sP29
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(829,plain,
( sP7
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(830,plain,
( sP14
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(831,plain,
( sP23
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(832,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h0])],[821,822,823,824,825,826,827,828,829,830,831,alg444_1,h3]) ).
thf(833,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,820,832,h1,h2,h3,h4]) ).
thf(0,theorem,
( sP47
= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ X5 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[833,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 09:01:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 12.06/12.09 % SZS status Theorem
% 12.06/12.09 % Mode: cade22grackle2xfee4
% 12.06/12.09 % Steps: 157428
% 12.06/12.09 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------