%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP119^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.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 : Wed Feb 25 08:55:42 AM UTC 2026
% Result : Theorem 2.07s 1.24s
% Output : Refutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 20 unt; 0 typ; 1 def)
% Number of atoms : 44 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 69 ( 10 ~; 4 |; 0 &; 54 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 70 usr; 15 con; 0-6 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
list_a: $tType ).
thf(type_def_8,type,
list_list_a: $tType ).
thf(type_def_9,type,
list_list_list_a: $tType ).
thf(func_def_0,type,
list_list_list_a: $tType ).
thf(func_def_1,type,
list_list_a: $tType ).
thf(func_def_2,type,
list_a: $tType ).
thf(func_def_3,type,
a: $tType ).
thf(func_def_4,type,
finite40241356em_a_a: ( a > a > a ) > $o ).
thf(func_def_5,type,
abel_s1075322906list_a: ( list_a > list_a > list_a ) > $o ).
thf(func_def_6,type,
abel_semigroup_a: ( a > a > a ) > $o ).
thf(func_def_7,type,
abel_s374399671list_a: ( list_a > list_a > list_a ) > $o ).
thf(func_def_8,type,
abel_s2117090225ioms_a: ( a > a > a ) > $o ).
thf(func_def_9,type,
semigr656274520list_a: ( list_list_a > list_list_a > list_list_a ) > $o ).
thf(func_def_10,type,
semigroup_list_a: ( list_a > list_a > list_a ) > $o ).
thf(func_def_11,type,
semigroup_a: ( a > a > a ) > $o ).
thf(func_def_12,type,
semilattice_a: ( a > a > a ) > $o ).
thf(func_def_13,type,
semilattice_axioms_a: ( a > a > a ) > $o ).
thf(func_def_14,type,
lattic1885654924_set_a: ( a > a > a ) > $o ).
thf(func_def_15,type,
append_list_list_a: list_list_list_a > list_list_list_a > list_list_list_a ).
thf(func_def_16,type,
append_list_a: list_list_a > list_list_a > list_list_a ).
thf(func_def_17,type,
append_a: list_a > list_a > list_a ).
thf(func_def_18,type,
bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
thf(func_def_19,type,
bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
thf(func_def_20,type,
bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
thf(func_def_21,type,
bind_a_a: list_a > ( a > list_a ) > list_a ).
thf(func_def_22,type,
butlast_list_a: list_list_a > list_list_a ).
thf(func_def_23,type,
butlast_a: list_a > list_a ).
thf(func_def_24,type,
concat_list_a: list_list_list_a > list_list_a ).
thf(func_def_25,type,
concat_a: list_list_a > list_a ).
thf(func_def_26,type,
insert_list_a: list_a > list_list_a > list_list_a ).
thf(func_def_27,type,
insert_a: a > list_a > list_a ).
thf(func_def_28,type,
last_list_a: list_list_a > list_a ).
thf(func_def_29,type,
last_a: list_a > a ).
thf(func_def_30,type,
cons_list_list_a: list_list_a > list_list_list_a > list_list_list_a ).
thf(func_def_31,type,
cons_list_a: list_a > list_list_a > list_list_a ).
thf(func_def_32,type,
cons_a: a > list_a > list_a ).
thf(func_def_33,type,
nil_list_list_a: list_list_list_a ).
thf(func_def_34,type,
nil_list_a: list_list_a ).
thf(func_def_35,type,
nil_a: list_a ).
thf(func_def_36,type,
list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
thf(func_def_37,type,
list_ex1_a: ( a > $o ) > list_a > $o ).
thf(func_def_38,type,
maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
thf(func_def_39,type,
maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
thf(func_def_40,type,
maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
thf(func_def_41,type,
maps_a_a: ( a > list_a ) > list_a > list_a ).
thf(func_def_42,type,
lexordp_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
thf(func_def_43,type,
lexordp_a: ( a > a > $o ) > list_a > list_a > $o ).
thf(func_def_44,type,
lexordp_eq_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
thf(func_def_45,type,
lexordp_eq_a: ( a > a > $o ) > list_a > list_a > $o ).
thf(func_def_46,type,
product_lists_list_a: list_list_list_a > list_list_list_a ).
thf(func_def_47,type,
product_lists_a: list_list_a > list_list_a ).
thf(func_def_48,type,
rotate1_list_a: list_list_a > list_list_a ).
thf(func_def_49,type,
rotate1_a: list_a > list_a ).
thf(func_def_50,type,
subseqs_list_a: list_list_a > list_list_list_a ).
thf(func_def_51,type,
subseqs_a: list_a > list_list_a ).
thf(func_def_52,type,
modula1376131916tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(func_def_53,type,
modula397570059tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(func_def_54,type,
modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_55,type,
modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_56,type,
modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_57,type,
modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_58,type,
modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_59,type,
modula1962211574trib_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(func_def_60,type,
transp_a: ( a > a > $o ) > $o ).
thf(func_def_61,type,
a2: a ).
thf(func_def_62,type,
b: a ).
thf(func_def_63,type,
c: a ).
thf(func_def_64,type,
inf: a > a > a ).
thf(func_def_65,type,
less: a > a > $o ).
thf(func_def_66,type,
sup: a > a > a ).
thf(func_def_84,type,
sK0: a ).
thf(func_def_85,type,
sK1: a ).
thf(func_def_86,type,
sK2: a ).
thf(func_def_87,type,
sK3: a ).
thf(func_def_88,type,
sK4: a ).
thf(func_def_89,type,
sK5: a ).
thf(f1084,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1068,f1083]) ).
thf(f1083,plain,
~ spl6_5,
inference(avatar_contradiction_clause,[status(thm)],[f1082]) ).
thf(f1082,plain,
( $false
| ~ spl6_5 ),
inference(subsumption_resolution,[status(thm)],[f1081,f903]) ).
thf(f903,plain,
! [X0: a] :
( $true
!= ( less @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f822]) ).
thf(f822,plain,
! [X0: a] :
( $true
!= ( less @ X0 @ X0 ) ),
inference(flattening,[status(thm)],[f658]) ).
thf(f658,plain,
! [X0: a] :
( $true
!= ( less @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f657]) ).
thf(f657,plain,
! [X0: a] :
~ ( less @ X0 @ X0 ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
! [X3: a] :
~ ( less @ X3 @ X3 ),
file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',fact_10_local_Oless__irrefl) ).
thf(f1081,plain,
( ( $true
= ( less @ b @ b ) )
| ~ spl6_5 ),
inference(forward_demodulation,[status(thm)],[f1079,f936]) ).
thf(f936,plain,
! [X0: a] :
( ( sup @ X0 @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f817]) ).
thf(f817,plain,
! [X0: a] :
( ( sup @ X0 @ X0 )
= X0 ),
inference(rectify,[status(thm)],[f55]) ).
thf(f55,axiom,
! [X3: a] :
( ( sup @ X3 @ X3 )
= X3 ),
file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',fact_54_local_Osup__idem) ).
thf(f1079,plain,
( ( $true
= ( less @ b @ ( sup @ b @ b ) ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f889,f1029]) ).
thf(f1029,plain,
( ( b = c )
| ~ spl6_5 ),
inference(avatar_component_clause,[status(thm)],[f1027]) ).
thf(f1027,definition,
( spl6_5
<=> ( b = c ) ),
introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition]) ).
thf(f889,plain,
( ( less @ b @ ( sup @ b @ c ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f708]) ).
thf(f708,plain,
( ( less @ b @ ( sup @ b @ c ) )
= $true ),
inference(fool_elimination,[status(thm)],[f707]) ).
thf(f707,plain,
less @ b @ ( sup @ b @ c ),
inference(rectify,[status(thm)],[f356]) ).
thf(f356,axiom,
less @ b @ ( sup @ b @ c ),
file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',conj_3) ).
thf(f1068,plain,
spl6_5,
inference(avatar_split_clause,[status(thm)],[f1046,f1027]) ).
thf(f1046,plain,
b = c,
inference(superposition,[status(thm)],[f911,f927]) ).
thf(f927,plain,
( c
= ( inf @ c @ ( sup @ b @ c ) ) ),
inference(cnf_transformation,[status(thm)],[f357]) ).
thf(f357,axiom,
( c
= ( inf @ c @ ( sup @ b @ c ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',conj_4) ).
thf(f911,plain,
( b
= ( inf @ c @ ( sup @ b @ c ) ) ),
inference(cnf_transformation,[status(thm)],[f354]) ).
thf(f354,axiom,
( b
= ( inf @ c @ ( sup @ b @ c ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP119^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 03:26:40 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : ITP119^1 : TPTP v9.2.1. Released v7.5.0.
% 0.07/0.31 % Domain : Interactive Theorem Proving
% 0.07/0.31 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_144__3260118_1
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.07/0.31 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Des21]
% 0.07/0.31 % Names : Modular_Distrib_Lattice/prob_144__3260118_1 [Des21]
% 0.07/0.31
% 0.07/0.31 % Status : ContradictoryAxioms
% 0.07/0.31 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.36 v7.5.0
% 0.07/0.31 % Syntax : Number of formulae : 425 ( 211 unt; 67 typ; 0 def)
% 0.07/0.31 % Number of atoms : 818 ( 483 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 13 ( 2 avg)
% 0.07/0.31 % Number of connectives : 3280 ( 180 ~; 24 |; 99 &;2599 @)
% 0.07/0.31 % ( 0 <=>; 378 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 21 ( 6 avg)
% 0.07/0.31 % Number of types : 5 ( 4 usr)
% 0.07/0.31 % Number of type conns : 485 ( 485 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 65 ( 63 usr; 7 con; 0-6 aty)
% 0.07/0.31 % Number of variables : 1176 ( 18 ^;1063 !; 95 ?;1176 :)
% 0.07/0.31 % SPC : TH0_CAX_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This file was generated by Sledgehammer 2021-02-23 15:43:54.694
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % Could-be-implicit typings (4)
% 0.07/0.31 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.07/0.31 list_list_list_a: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.07/0.31 list_list_a: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.07/0.31 list_a: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(ty_n_tf__a,type,
% 0.07/0.31 a: $tType ).
% 0.07/0.31
% 0.07/0.31 % Explicit typings (63)
% 0.07/0.31 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 0.07/0.31 finite40241356em_a_a: ( a > a > a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Oabel__semigroup_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 abel_s1075322906list_a: ( list_a > list_a > list_a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 0.07/0.31 abel_semigroup_a: ( a > a > a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Oabel__semigroup__axioms_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 abel_s374399671list_a: ( list_a > list_a > list_a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Oabel__semigroup__axioms_001tf__a,type,
% 0.07/0.31 abel_s2117090225ioms_a: ( a > a > a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Osemigroup_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.07/0.31 semigr656274520list_a: ( list_list_a > list_list_a > list_list_a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Osemigroup_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 semigroup_list_a: ( list_a > list_a > list_a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 0.07/0.31 semigroup_a: ( a > a > a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 0.07/0.31 semilattice_a: ( a > a > a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Lattices_Osemilattice__axioms_001tf__a,type,
% 0.07/0.31 semilattice_axioms_a: ( a > a > a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 0.07/0.31 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oappend_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.07/0.31 append_list_list_a: list_list_list_a > list_list_list_a > list_list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oappend_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 append_list_a: list_list_a > list_list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oappend_001tf__a,type,
% 0.07/0.31 append_a: list_a > list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.07/0.31 bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Obind_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Obind_001tf__a_001tf__a,type,
% 0.07/0.31 bind_a_a: list_a > ( a > list_a ) > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 butlast_list_a: list_list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Obutlast_001tf__a,type,
% 0.07/0.31 butlast_a: list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oconcat_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 concat_list_a: list_list_list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oconcat_001tf__a,type,
% 0.07/0.31 concat_a: list_list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oinsert_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 insert_list_a: list_a > list_list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oinsert_001tf__a,type,
% 0.07/0.31 insert_a: a > list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olast_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 last_list_a: list_list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olast_001tf__a,type,
% 0.07/0.31 last_a: list_a > a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.07/0.31 cons_list_list_a: list_list_a > list_list_list_a > list_list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 cons_list_a: list_a > list_list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 0.07/0.31 cons_a: a > list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.07/0.31 nil_list_list_a: list_list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 nil_list_a: list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 0.07/0.31 nil_a: list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist__ex1_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist__ex1_001tf__a,type,
% 0.07/0.31 list_ex1_a: ( a > $o ) > list_a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.07/0.31 maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Omaps_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Omaps_001tf__a_001tf__a,type,
% 0.07/0.31 maps_a_a: ( a > list_a ) > list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oord_Olexordp_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 lexordp_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oord_Olexordp_001tf__a,type,
% 0.07/0.31 lexordp_a: ( a > a > $o ) > list_a > list_a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oord_Olexordp__eq_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 lexordp_eq_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oord_Olexordp__eq_001tf__a,type,
% 0.07/0.31 lexordp_eq_a: ( a > a > $o ) > list_a > list_a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oproduct__lists_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 product_lists_list_a: list_list_list_a > list_list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Oproduct__lists_001tf__a,type,
% 0.07/0.31 product_lists_a: list_list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Orotate1_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 rotate1_list_a: list_list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Orotate1_001tf__a,type,
% 0.07/0.31 rotate1_a: list_a > list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Osubseqs_001t__List__Olist_Itf__a_J,type,
% 0.07/0.31 subseqs_list_a: list_list_a > list_list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Osubseqs_001tf__a,type,
% 0.07/0.31 subseqs_a: list_a > list_list_a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_OM5__lattice_001tf__a,type,
% 0.07/0.31 modula1376131916tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_ON5__lattice_001tf__a,type,
% 0.07/0.31 modula397570059tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 0.07/0.31 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 0.07/0.31 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 0.07/0.31 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 0.07/0.31 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 0.07/0.31 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ono__distrib_001tf__a,type,
% 0.07/0.31 modula1962211574trib_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Relation_Otransp_001tf__a,type,
% 0.07/0.31 transp_a: ( a > a > $o ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_a,type,
% 0.07/0.31 a2: a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_b,type,
% 0.07/0.31 b: a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_c,type,
% 0.07/0.31 c: a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_inf,type,
% 0.07/0.31 inf: a > a > a ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_less,type,
% 0.07/0.31 less: a > a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_sup,type,
% 0.07/0.31 sup: a > a > a ).
% 0.07/0.31
% 0.07/0.31 % Relevant facts (352)
% 0.07/0.31 thf(fact_0_local_Odual__order_Oasym,axiom,
% 0.07/0.31 ! [B: a,A: a] :
% 0.07/0.31 ( ( less @ B @ A )
% 0.07/0.31 => ~ ( less @ A @ B ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.dual_order.asym
% 0.07/0.31 thf(fact_1_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 0.07/0.31 ! [B: a,A: a] :
% 0.07/0.31 ( ( less @ B @ A )
% 0.07/0.31 => ( A != B ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.dual_order.strict_implies_not_eq
% 0.07/0.31 thf(fact_2_local_Odual__order_Ostrict__trans,axiom,
% 0.07/0.31 ! [B: a,A: a,C: a] :
% 0.07/0.31 ( ( less @ B @ A )
% 0.07/0.31 => ( ( less @ C @ B )
% 0.07/0.31 => ( less @ C @ A ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.dual_order.strict_trans
% 0.07/0.31 thf(fact_3_local_Oless__asym,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ~ ( less @ Y @ X ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_asym
% 0.07/0.31 thf(fact_4_local_Oless__asym_H,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( less @ A @ B )
% 0.07/0.31 => ~ ( less @ B @ A ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_asym'
% 0.07/0.31 thf(fact_5_local_Oless__imp__neq,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ( X != Y ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_imp_neq
% 0.07/0.31 thf(fact_6_local_Oless__imp__not__eq,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ( X != Y ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_imp_not_eq
% 0.07/0.31 thf(fact_7_local_Oless__imp__not__eq2,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ( Y != X ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_imp_not_eq2
% 0.07/0.31 thf(fact_8_local_Oless__imp__not__less,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ~ ( less @ Y @ X ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_imp_not_less
% 0.07/0.31 thf(fact_9_local_Oless__imp__triv,axiom,
% 0.07/0.31 ! [X: a,Y: a,P: $o] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ( ( less @ Y @ X )
% 0.07/0.31 => P ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_imp_triv
% 0.07/0.31 thf(fact_10_local_Oless__irrefl,axiom,
% 0.07/0.31 ! [X: a] :
% 0.07/0.31 ~ ( less @ X @ X ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_irrefl
% 0.07/0.31 thf(fact_11_local_Oless__not__sym,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ~ ( less @ Y @ X ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_not_sym
% 0.07/0.31 thf(fact_12_local_Oless__trans,axiom,
% 0.07/0.31 ! [X: a,Y: a,Z: a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ( ( less @ Y @ Z )
% 0.07/0.31 => ( less @ X @ Z ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_trans
% 0.07/0.31 thf(fact_13_local_Oord__eq__less__trans,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( A = B )
% 0.07/0.31 => ( ( less @ B @ C )
% 0.07/0.31 => ( less @ A @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.ord_eq_less_trans
% 0.07/0.31 thf(fact_14_local_Oord__less__eq__trans,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( less @ A @ B )
% 0.07/0.31 => ( ( B = C )
% 0.07/0.31 => ( less @ A @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.ord_less_eq_trans
% 0.07/0.31 thf(fact_15_local_Oorder_Oasym,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( less @ A @ B )
% 0.07/0.31 => ~ ( less @ B @ A ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.order.asym
% 0.07/0.31 thf(fact_16_local_Oorder_Oirrefl,axiom,
% 0.07/0.31 ! [A: a] :
% 0.07/0.31 ~ ( less @ A @ A ) ).
% 0.07/0.31
% 0.07/0.31 % local.order.irrefl
% 0.07/0.31 thf(fact_17_local_Oorder_Ostrict__implies__not__eq,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( less @ A @ B )
% 0.07/0.31 => ( A != B ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.order.strict_implies_not_eq
% 0.07/0.31 thf(fact_18_local_Oorder_Ostrict__trans,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( less @ A @ B )
% 0.07/0.31 => ( ( less @ B @ C )
% 0.07/0.31 => ( less @ A @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.order.strict_trans
% 0.07/0.31 thf(fact_19_local_Oinf_Oassoc,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( inf @ ( inf @ A @ B ) @ C )
% 0.07/0.31 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.assoc
% 0.07/0.31 thf(fact_20_local_Oinf_Ocommute,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( inf @ A @ B )
% 0.07/0.31 = ( inf @ B @ A ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.commute
% 0.07/0.31 thf(fact_21_local_Oinf_Oleft__commute,axiom,
% 0.07/0.31 ! [B: a,A: a,C: a] :
% 0.07/0.31 ( ( inf @ B @ ( inf @ A @ C ) )
% 0.07/0.31 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.left_commute
% 0.07/0.31 thf(fact_22_local_Oinf__assoc,axiom,
% 0.07/0.31 ! [X: a,Y: a,Z: a] :
% 0.07/0.31 ( ( inf @ ( inf @ X @ Y ) @ Z )
% 0.07/0.31 = ( inf @ X @ ( inf @ Y @ Z ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf_assoc
% 0.07/0.31 thf(fact_23_local_Oinf__commute,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( inf @ X @ Y )
% 0.07/0.31 = ( inf @ Y @ X ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf_commute
% 0.07/0.31 thf(fact_24_local_Oinf__left__commute,axiom,
% 0.07/0.31 ! [X: a,Y: a,Z: a] :
% 0.07/0.31 ( ( inf @ X @ ( inf @ Y @ Z ) )
% 0.07/0.31 = ( inf @ Y @ ( inf @ X @ Z ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf_left_commute
% 0.07/0.31 thf(fact_25_local_Osup_Oassoc,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( sup @ ( sup @ A @ B ) @ C )
% 0.07/0.31 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.assoc
% 0.07/0.31 thf(fact_26_local_Osup_Ocommute,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( sup @ A @ B )
% 0.07/0.31 = ( sup @ B @ A ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.commute
% 0.07/0.31 thf(fact_27_local_Osup_Oleft__commute,axiom,
% 0.07/0.31 ! [B: a,A: a,C: a] :
% 0.07/0.31 ( ( sup @ B @ ( sup @ A @ C ) )
% 0.07/0.31 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.left_commute
% 0.07/0.31 thf(fact_28_local_Osup__assoc,axiom,
% 0.07/0.31 ! [X: a,Y: a,Z: a] :
% 0.07/0.31 ( ( sup @ ( sup @ X @ Y ) @ Z )
% 0.07/0.31 = ( sup @ X @ ( sup @ Y @ Z ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup_assoc
% 0.07/0.31 thf(fact_29_local_Osup__commute,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( sup @ X @ Y )
% 0.07/0.31 = ( sup @ Y @ X ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup_commute
% 0.07/0.31 thf(fact_30_local_Osup__left__commute,axiom,
% 0.07/0.31 ! [X: a,Y: a,Z: a] :
% 0.07/0.31 ( ( sup @ X @ ( sup @ Y @ Z ) )
% 0.07/0.31 = ( sup @ Y @ ( sup @ X @ Z ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup_left_commute
% 0.07/0.31 thf(fact_31_local_Oinf_Ostrict__boundedE,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( less @ A @ ( inf @ B @ C ) )
% 0.07/0.31 => ~ ( ( less @ A @ B )
% 0.07/0.31 => ~ ( less @ A @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.strict_boundedE
% 0.07/0.31 thf(fact_32_local_Oinf_Ostrict__coboundedI1,axiom,
% 0.07/0.31 ! [A: a,C: a,B: a] :
% 0.07/0.31 ( ( less @ A @ C )
% 0.07/0.31 => ( less @ ( inf @ A @ B ) @ C ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.strict_coboundedI1
% 0.07/0.31 thf(fact_33_local_Oinf_Ostrict__coboundedI2,axiom,
% 0.07/0.31 ! [B: a,C: a,A: a] :
% 0.07/0.31 ( ( less @ B @ C )
% 0.07/0.31 => ( less @ ( inf @ A @ B ) @ C ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.strict_coboundedI2
% 0.07/0.31 thf(fact_34_local_Oinf_Ostrict__order__iff,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( less @ A @ B )
% 0.07/0.31 = ( ( A
% 0.07/0.31 = ( inf @ A @ B ) )
% 0.07/0.31 & ( A != B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.strict_order_iff
% 0.07/0.31 thf(fact_35_local_Oless__infI1,axiom,
% 0.07/0.31 ! [A: a,X: a,B: a] :
% 0.07/0.31 ( ( less @ A @ X )
% 0.07/0.31 => ( less @ ( inf @ A @ B ) @ X ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_infI1
% 0.07/0.31 thf(fact_36_local_Oless__infI2,axiom,
% 0.07/0.31 ! [B: a,X: a,A: a] :
% 0.07/0.31 ( ( less @ B @ X )
% 0.07/0.31 => ( less @ ( inf @ A @ B ) @ X ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_infI2
% 0.07/0.31 thf(fact_37_local_Oless__supI1,axiom,
% 0.07/0.31 ! [X: a,A: a,B: a] :
% 0.07/0.31 ( ( less @ X @ A )
% 0.07/0.31 => ( less @ X @ ( sup @ A @ B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_supI1
% 0.07/0.31 thf(fact_38_local_Oless__supI2,axiom,
% 0.07/0.31 ! [X: a,B: a,A: a] :
% 0.07/0.31 ( ( less @ X @ B )
% 0.07/0.31 => ( less @ X @ ( sup @ A @ B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.less_supI2
% 0.07/0.31 thf(fact_39_local_Osup_Ostrict__boundedE,axiom,
% 0.07/0.31 ! [B: a,C: a,A: a] :
% 0.07/0.31 ( ( less @ ( sup @ B @ C ) @ A )
% 0.07/0.31 => ~ ( ( less @ B @ A )
% 0.07/0.31 => ~ ( less @ C @ A ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.strict_boundedE
% 0.07/0.31 thf(fact_40_local_Osup_Ostrict__coboundedI1,axiom,
% 0.07/0.31 ! [C: a,A: a,B: a] :
% 0.07/0.31 ( ( less @ C @ A )
% 0.07/0.31 => ( less @ C @ ( sup @ A @ B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.strict_coboundedI1
% 0.07/0.31 thf(fact_41_local_Osup_Ostrict__coboundedI2,axiom,
% 0.07/0.31 ! [C: a,B: a,A: a] :
% 0.07/0.31 ( ( less @ C @ B )
% 0.07/0.31 => ( less @ C @ ( sup @ A @ B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.strict_coboundedI2
% 0.07/0.31 thf(fact_42_local_Osup_Ostrict__order__iff,axiom,
% 0.07/0.31 ! [B: a,A: a] :
% 0.07/0.31 ( ( less @ B @ A )
% 0.07/0.31 = ( ( A
% 0.07/0.31 = ( sup @ A @ B ) )
% 0.07/0.31 & ( A != B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.strict_order_iff
% 0.07/0.31 thf(fact_43_local_Odistrib__imp1,axiom,
% 0.07/0.31 ! [X: a,Y: a,Z: a] :
% 0.07/0.31 ( ! [X2: a,Y2: a,Z2: a] :
% 0.07/0.31 ( ( inf @ X2 @ ( sup @ Y2 @ Z2 ) )
% 0.07/0.31 = ( sup @ ( inf @ X2 @ Y2 ) @ ( inf @ X2 @ Z2 ) ) )
% 0.07/0.31 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 0.07/0.31 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.distrib_imp1
% 0.07/0.31 thf(fact_44_local_Odistrib__imp2,axiom,
% 0.07/0.31 ! [X: a,Y: a,Z: a] :
% 0.07/0.31 ( ! [X2: a,Y2: a,Z2: a] :
% 0.07/0.31 ( ( sup @ X2 @ ( inf @ Y2 @ Z2 ) )
% 0.07/0.31 = ( inf @ ( sup @ X2 @ Y2 ) @ ( sup @ X2 @ Z2 ) ) )
% 0.07/0.31 => ( ( inf @ X @ ( sup @ Y @ Z ) )
% 0.07/0.31 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.distrib_imp2
% 0.07/0.31 thf(fact_45_local_Oinf_Oidem,axiom,
% 0.07/0.31 ! [A: a] :
% 0.07/0.31 ( ( inf @ A @ A )
% 0.07/0.31 = A ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.idem
% 0.07/0.31 thf(fact_46_local_Oinf_Oleft__idem,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( inf @ A @ ( inf @ A @ B ) )
% 0.07/0.31 = ( inf @ A @ B ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.left_idem
% 0.07/0.31 thf(fact_47_local_Oinf_Oright__idem,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( inf @ ( inf @ A @ B ) @ B )
% 0.07/0.31 = ( inf @ A @ B ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf.right_idem
% 0.07/0.31 thf(fact_48_local_Oinf__idem,axiom,
% 0.07/0.31 ! [X: a] :
% 0.07/0.31 ( ( inf @ X @ X )
% 0.07/0.31 = X ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf_idem
% 0.07/0.31 thf(fact_49_local_Oinf__left__idem,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.07/0.31 = ( inf @ X @ Y ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf_left_idem
% 0.07/0.31 thf(fact_50_local_Oinf__right__idem,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.07/0.31 = ( inf @ X @ Y ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf_right_idem
% 0.07/0.31 thf(fact_51_local_Osup_Oidem,axiom,
% 0.07/0.31 ! [A: a] :
% 0.07/0.31 ( ( sup @ A @ A )
% 0.07/0.31 = A ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.idem
% 0.07/0.31 thf(fact_52_local_Osup_Oleft__idem,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( sup @ A @ ( sup @ A @ B ) )
% 0.07/0.31 = ( sup @ A @ B ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.left_idem
% 0.07/0.31 thf(fact_53_local_Osup_Oright__idem,axiom,
% 0.07/0.31 ! [A: a,B: a] :
% 0.07/0.31 ( ( sup @ ( sup @ A @ B ) @ B )
% 0.07/0.31 = ( sup @ A @ B ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup.right_idem
% 0.07/0.31 thf(fact_54_local_Osup__idem,axiom,
% 0.07/0.31 ! [X: a] :
% 0.07/0.31 ( ( sup @ X @ X )
% 0.07/0.31 = X ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup_idem
% 0.07/0.31 thf(fact_55_local_Osup__left__idem,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.07/0.31 = ( sup @ X @ Y ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup_left_idem
% 0.07/0.31 thf(fact_56_M5__lattice__def,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
% 0.07/0.31 = ( ( ( inf @ A @ B )
% 0.07/0.31 = ( inf @ B @ C ) )
% 0.07/0.31 & ( ( inf @ C @ A )
% 0.07/0.31 = ( inf @ B @ C ) )
% 0.07/0.31 & ( ( sup @ A @ B )
% 0.07/0.31 = ( sup @ B @ C ) )
% 0.07/0.31 & ( ( sup @ C @ A )
% 0.07/0.31 = ( sup @ B @ C ) )
% 0.07/0.31 & ( less @ ( inf @ A @ B ) @ ( sup @ A @ B ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % M5_lattice_def
% 0.07/0.31 thf(fact_57_N5__lattice__def,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula397570059tice_a @ inf @ less @ sup @ A @ B @ C )
% 0.07/0.31 = ( ( ( inf @ A @ C )
% 0.07/0.31 = ( inf @ B @ C ) )
% 0.07/0.31 & ( less @ A @ B )
% 0.07/0.31 & ( ( sup @ A @ C )
% 0.07/0.31 = ( sup @ B @ C ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % N5_lattice_def
% 0.07/0.31 thf(fact_58_no__distrib__def,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C )
% 0.07/0.31 = ( less @ ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % no_distrib_def
% 0.07/0.31 thf(fact_59_local_Oinf__sup__absorb,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.07/0.31 = X ) ).
% 0.07/0.31
% 0.07/0.31 % local.inf_sup_absorb
% 0.07/0.31 thf(fact_60_local_Osup__inf__absorb,axiom,
% 0.07/0.31 ! [X: a,Y: a] :
% 0.07/0.31 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.07/0.31 = X ) ).
% 0.07/0.31
% 0.07/0.31 % local.sup_inf_absorb
% 0.07/0.31 thf(fact_61_local_Oa__join__d,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.07/0.31 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.a_join_d
% 0.07/0.31 thf(fact_62_local_Ob__join__d,axiom,
% 0.07/0.31 ! [B: a,A: a,C: a] :
% 0.07/0.31 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.07/0.31 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.b_join_d
% 0.07/0.31 thf(fact_63_local_Od__aux__def,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 0.07/0.31 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.d_aux_def
% 0.07/0.31 thf(fact_64_local_Od__b__c__a,axiom,
% 0.07/0.31 ! [B: a,C: a,A: a] :
% 0.07/0.31 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 0.07/0.31 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.d_b_c_a
% 0.07/0.31 thf(fact_65_local_Od__c__a__b,axiom,
% 0.07/0.31 ! [C: a,A: a,B: a] :
% 0.07/0.31 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 0.07/0.31 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.d_c_a_b
% 0.07/0.31 thf(fact_66_local_Oa__meet__e,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.07/0.31 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.a_meet_e
% 0.07/0.31 thf(fact_67_local_Ob__meet__e,axiom,
% 0.07/0.31 ! [B: a,A: a,C: a] :
% 0.07/0.31 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.07/0.31 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.b_meet_e
% 0.07/0.31 thf(fact_68_local_Oc__meet__e,axiom,
% 0.07/0.31 ! [C: a,A: a,B: a] :
% 0.07/0.31 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.07/0.31 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.c_meet_e
% 0.07/0.31 thf(fact_69_local_Oe__aux__def,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 0.07/0.31 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.e_aux_def
% 0.07/0.31 thf(fact_70_local_Oe__b__c__a,axiom,
% 0.07/0.31 ! [B: a,C: a,A: a] :
% 0.07/0.31 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 0.07/0.31 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.e_b_c_a
% 0.07/0.31 thf(fact_71_local_Oe__c__a__b,axiom,
% 0.07/0.31 ! [C: a,A: a,B: a] :
% 0.07/0.31 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 0.07/0.31 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.e_c_a_b
% 0.07/0.31 thf(fact_72_local_Ocomp__fun__idem__sup,axiom,
% 0.07/0.31 finite40241356em_a_a @ sup ).
% 0.07/0.31
% 0.07/0.31 % local.comp_fun_idem_sup
% 0.07/0.31 thf(fact_73_local_Ocomp__fun__idem__inf,axiom,
% 0.07/0.31 finite40241356em_a_a @ inf ).
% 0.07/0.31
% 0.07/0.31 % local.comp_fun_idem_inf
% 0.07/0.31 thf(fact_74_local_Oc__aux__def,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.07/0.31 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.c_aux_def
% 0.07/0.31 thf(fact_75_local_Ob__aux__def,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.07/0.31 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.b_aux_def
% 0.07/0.31 thf(fact_76_local_Oa__aux__def,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 0.07/0.31 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.a_aux_def
% 0.07/0.31 thf(fact_77_lattice_Ono__distrib_Ocong,axiom,
% 0.07/0.31 modula1962211574trib_a = modula1962211574trib_a ).
% 0.07/0.31
% 0.07/0.31 % lattice.no_distrib.cong
% 0.07/0.31 thf(fact_78_lattice_ON5__lattice_Ocong,axiom,
% 0.07/0.31 modula397570059tice_a = modula397570059tice_a ).
% 0.07/0.31
% 0.07/0.31 % lattice.N5_lattice.cong
% 0.07/0.31 thf(fact_79_lattice_OM5__lattice_Ocong,axiom,
% 0.07/0.31 modula1376131916tice_a = modula1376131916tice_a ).
% 0.07/0.31
% 0.07/0.31 % lattice.M5_lattice.cong
% 0.07/0.31 thf(fact_80_lattice_Oe__aux_Ocong,axiom,
% 0.07/0.31 modula1144073633_aux_a = modula1144073633_aux_a ).
% 0.07/0.31
% 0.07/0.31 % lattice.e_aux.cong
% 0.07/0.31 thf(fact_81_lattice_Od__aux_Ocong,axiom,
% 0.07/0.31 modula1936294176_aux_a = modula1936294176_aux_a ).
% 0.07/0.31
% 0.07/0.31 % lattice.d_aux.cong
% 0.07/0.31 thf(fact_82_local_Oc__a,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.07/0.31 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.c_a
% 0.07/0.31 thf(fact_83_local_Ob__a,axiom,
% 0.07/0.31 ! [A: a,B: a,C: a] :
% 0.07/0.31 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.07/0.31 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.b_a
% 0.07/0.31 thf(fact_84_local_Osup_Osemigroup__axioms,axiom,
% 0.07/0.31 semigroup_a @ sup ).
% 0.07/0.31
% 0.07/0.31 % local.sup.semigroup_axioms
% 0.07/0.31 thf(fact_85_local_Oinf_Osemigroup__axioms,axiom,
% 0.07/0.31 semigroup_a @ inf ).
% 0.07/0.31
% 0.07/0.31 % local.inf.semigroup_axioms
% 0.07/0.31 thf(fact_86_local_Osup_Osemilattice__axioms,axiom,
% 0.07/0.31 semilattice_a @ sup ).
% 0.07/0.31
% 0.07/0.31 % local.sup.semilattice_axioms
% 0.07/0.31 thf(fact_87_local_Oinf_Osemilattice__axioms,axiom,
% 0.07/0.31 semilattice_a @ inf ).
% 0.07/0.31
% 0.07/0.31 % local.inf.semilattice_axioms
% 0.07/0.31 thf(fact_88_lattice_Oa__aux_Ocong,axiom,
% 0.07/0.31 modula17988509_aux_a = modula17988509_aux_a ).
% 0.07/0.31
% 0.07/0.31 % lattice.a_aux.cong
% 0.07/0.31 thf(fact_89_lattice_Ob__aux_Ocong,axiom,
% 0.07/0.31 modula1373251614_aux_a = modula1373251614_aux_a ).
% 0.07/0.31
% 0.07/0.31 % lattice.b_aux.cong
% 0.07/0.31 thf(fact_90_lattice_Oc__aux_Ocong,axiom,
% 0.07/0.31 modula581031071_aux_a = modula581031071_aux_a ).
% 0.07/0.31
% 0.07/0.31 % lattice.c_aux.cong
% 0.07/0.31 thf(fact_91_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.07/0.31 abel_semigroup_a @ sup ).
% 0.07/0.31
% 0.07/0.31 % local.sup.abel_semigroup_axioms
% 0.07/0.31 thf(fact_92_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.07/0.31 abel_semigroup_a @ inf ).
% 0.07/0.31
% 0.07/0.31 % local.inf.abel_semigroup_axioms
% 0.07/0.31 thf(fact_93_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.07/0.31 lattic1885654924_set_a @ sup ).
% 0.07/0.31
% 0.07/0.31 % local.Sup_fin.semilattice_set_axioms
% 0.07/0.31 thf(fact_94_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.07/0.31 lattic1885654924_set_a @ inf ).
% 0.07/0.31
% 0.07/0.31 % local.Inf_fin.semilattice_set_axioms
% 0.07/0.31 thf(fact_95_local_Olexordp__eq__refl,axiom,
% 0.07/0.31 ! [Xs: list_a] : ( lexordp_eq_a @ less @ Xs @ Xs ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq_refl
% 0.07/0.31 thf(fact_96_local_Olexordp__eq_ONil,axiom,
% 0.07/0.31 ! [Ys: list_a] : ( lexordp_eq_a @ less @ nil_a @ Ys ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq.Nil
% 0.07/0.31 thf(fact_97_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.07/0.31 ! [F: list_a > list_a > list_a] :
% 0.07/0.31 ( ( abel_s1075322906list_a @ F )
% 0.07/0.31 => ( semigroup_list_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup.axioms(1)
% 0.07/0.31 thf(fact_98_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ( abel_semigroup_a @ F )
% 0.07/0.31 => ( semigroup_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup.axioms(1)
% 0.07/0.31 thf(fact_99_semilattice__set_Oaxioms,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ( lattic1885654924_set_a @ F )
% 0.07/0.31 => ( semilattice_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice_set.axioms
% 0.07/0.31 thf(fact_100_semilattice__set_Ointro,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ( semilattice_a @ F )
% 0.07/0.31 => ( lattic1885654924_set_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice_set.intro
% 0.07/0.31 thf(fact_101_semilattice__set__def,axiom,
% 0.07/0.31 lattic1885654924_set_a = semilattice_a ).
% 0.07/0.31
% 0.07/0.31 % semilattice_set_def
% 0.07/0.31 thf(fact_102_local_Olexordp__eq__simps_I1_J,axiom,
% 0.07/0.31 ! [Ys: list_a] : ( lexordp_eq_a @ less @ nil_a @ Ys ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq_simps(1)
% 0.07/0.31 thf(fact_103_local_Olexordp__eq__simps_I2_J,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ( ( lexordp_eq_a @ less @ Xs @ nil_a )
% 0.07/0.31 = ( Xs = nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq_simps(2)
% 0.07/0.31 thf(fact_104_abel__semigroup_Oleft__commute,axiom,
% 0.07/0.31 ! [F: a > a > a,B: a,A: a,C: a] :
% 0.07/0.31 ( ( abel_semigroup_a @ F )
% 0.07/0.31 => ( ( F @ B @ ( F @ A @ C ) )
% 0.07/0.31 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup.left_commute
% 0.07/0.31 thf(fact_105_abel__semigroup_Ocommute,axiom,
% 0.07/0.31 ! [F: a > a > a,A: a,B: a] :
% 0.07/0.31 ( ( abel_semigroup_a @ F )
% 0.07/0.31 => ( ( F @ A @ B )
% 0.07/0.31 = ( F @ B @ A ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup.commute
% 0.07/0.31 thf(fact_106_semigroup_Ointro,axiom,
% 0.07/0.31 ! [F: list_a > list_a > list_a] :
% 0.07/0.31 ( ! [A2: list_a,B2: list_a,C2: list_a] :
% 0.07/0.31 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 0.07/0.31 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 0.07/0.31 => ( semigroup_list_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % semigroup.intro
% 0.07/0.31 thf(fact_107_semigroup_Ointro,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ! [A2: a,B2: a,C2: a] :
% 0.07/0.31 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 0.07/0.31 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 0.07/0.31 => ( semigroup_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % semigroup.intro
% 0.07/0.31 thf(fact_108_semigroup_Oassoc,axiom,
% 0.07/0.31 ! [F: list_a > list_a > list_a,A: list_a,B: list_a,C: list_a] :
% 0.07/0.31 ( ( semigroup_list_a @ F )
% 0.07/0.31 => ( ( F @ ( F @ A @ B ) @ C )
% 0.07/0.31 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % semigroup.assoc
% 0.07/0.31 thf(fact_109_semigroup_Oassoc,axiom,
% 0.07/0.31 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.07/0.31 ( ( semigroup_a @ F )
% 0.07/0.31 => ( ( F @ ( F @ A @ B ) @ C )
% 0.07/0.31 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % semigroup.assoc
% 0.07/0.31 thf(fact_110_semigroup__def,axiom,
% 0.07/0.31 ( semigroup_list_a
% 0.07/0.31 = ( ^ [F2: list_a > list_a > list_a] :
% 0.07/0.31 ! [A3: list_a,B3: list_a,C3: list_a] :
% 0.07/0.31 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 0.07/0.31 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % semigroup_def
% 0.07/0.31 thf(fact_111_semigroup__def,axiom,
% 0.07/0.31 ( semigroup_a
% 0.07/0.31 = ( ^ [F2: a > a > a] :
% 0.07/0.31 ! [A3: a,B3: a,C3: a] :
% 0.07/0.31 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 0.07/0.31 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % semigroup_def
% 0.07/0.31 thf(fact_112_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,Xs: list_list_a] :
% 0.07/0.31 ( ( lexordp_eq_list_a @ Less @ Xs @ nil_list_a )
% 0.07/0.31 = ( Xs = nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_simps(2)
% 0.07/0.31 thf(fact_113_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Xs: list_a] :
% 0.07/0.31 ( ( lexordp_eq_a @ Less @ Xs @ nil_a )
% 0.07/0.31 = ( Xs = nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_simps(2)
% 0.07/0.31 thf(fact_114_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,Ys: list_list_a] : ( lexordp_eq_list_a @ Less @ nil_list_a @ Ys ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_simps(1)
% 0.07/0.31 thf(fact_115_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Ys: list_a] : ( lexordp_eq_a @ Less @ nil_a @ Ys ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_simps(1)
% 0.07/0.31 thf(fact_116_local_Olexordp__eq_Osimps,axiom,
% 0.07/0.31 ! [A1: list_a,A22: list_a] :
% 0.07/0.31 ( ( lexordp_eq_a @ less @ A1 @ A22 )
% 0.07/0.31 = ( ? [Ys2: list_a] :
% 0.07/0.31 ( ( A1 = nil_a )
% 0.07/0.31 & ( A22 = Ys2 ) )
% 0.07/0.31 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A22
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ( less @ X3 @ Y3 ) )
% 0.07/0.31 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A22
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ~ ( less @ X3 @ Y3 )
% 0.07/0.31 & ~ ( less @ Y3 @ X3 )
% 0.07/0.31 & ( lexordp_eq_a @ less @ Xs2 @ Ys2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq.simps
% 0.07/0.31 thf(fact_117_local_Olexordp__eq_Oinducts,axiom,
% 0.07/0.31 ! [X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 0.07/0.31 ( ( lexordp_eq_a @ less @ X1 @ X22 )
% 0.07/0.31 => ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ( less @ X2 @ Y2 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ~ ( less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( less @ Y2 @ X2 )
% 0.07/0.31 => ( ( lexordp_eq_a @ less @ Xs3 @ Ys3 )
% 0.07/0.31 => ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.07/0.31 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq.inducts
% 0.07/0.31 thf(fact_118_local_Olexordp__eq_Ocases,axiom,
% 0.07/0.31 ! [A1: list_a,A22: list_a] :
% 0.07/0.31 ( ( lexordp_eq_a @ less @ A1 @ A22 )
% 0.07/0.31 => ( ( A1 != nil_a )
% 0.07/0.31 => ( ! [X2: a] :
% 0.07/0.31 ( ? [Xs3: list_a] :
% 0.07/0.31 ( A1
% 0.07/0.31 = ( cons_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Y2: a] :
% 0.07/0.31 ( ? [Ys3: list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 = ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ~ ( less @ X2 @ Y2 ) ) )
% 0.07/0.31 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Ys3: list_a] :
% 0.07/0.31 ( ( A22
% 0.07/0.31 = ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ~ ( less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( less @ Y2 @ X2 )
% 0.07/0.31 => ~ ( lexordp_eq_a @ less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq.cases
% 0.07/0.31 thf(fact_119_local_Olexordp__eq_OCons__eq,axiom,
% 0.07/0.31 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ~ ( less @ X @ Y )
% 0.07/0.31 => ( ~ ( less @ Y @ X )
% 0.07/0.31 => ( ( lexordp_eq_a @ less @ Xs @ Ys )
% 0.07/0.31 => ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq.Cons_eq
% 0.07/0.31 thf(fact_120_local_Olexordp__eq_OCons,axiom,
% 0.07/0.31 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq.Cons
% 0.07/0.31 thf(fact_121_list_Oinject,axiom,
% 0.07/0.31 ! [X21: list_a,X222: list_list_a,Y21: list_a,Y22: list_list_a] :
% 0.07/0.31 ( ( ( cons_list_a @ X21 @ X222 )
% 0.07/0.31 = ( cons_list_a @ Y21 @ Y22 ) )
% 0.07/0.31 = ( ( X21 = Y21 )
% 0.07/0.31 & ( X222 = Y22 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.inject
% 0.07/0.31 thf(fact_122_list_Oinject,axiom,
% 0.07/0.31 ! [X21: a,X222: list_a,Y21: a,Y22: list_a] :
% 0.07/0.31 ( ( ( cons_a @ X21 @ X222 )
% 0.07/0.31 = ( cons_a @ Y21 @ Y22 ) )
% 0.07/0.31 = ( ( X21 = Y21 )
% 0.07/0.31 & ( X222 = Y22 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.inject
% 0.07/0.31 thf(fact_123_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a,Y: list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) )
% 0.07/0.31 = ( ( Less @ X @ Y )
% 0.07/0.31 | ( ~ ( Less @ Y @ X )
% 0.07/0.31 & ( lexordp_eq_list_a @ Less @ Xs @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_simps(4)
% 0.07/0.31 thf(fact_124_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X: a,Xs: list_a,Y: a,Ys: list_a] :
% 0.07/0.31 ( ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 0.07/0.31 = ( ( Less @ X @ Y )
% 0.07/0.31 | ( ~ ( Less @ Y @ X )
% 0.07/0.31 & ( lexordp_eq_a @ Less @ Xs @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_simps(4)
% 0.07/0.31 thf(fact_125_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a] :
% 0.07/0.31 ~ ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_simps(3)
% 0.07/0.31 thf(fact_126_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X: a,Xs: list_a] :
% 0.07/0.31 ~ ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_simps(3)
% 0.07/0.31 thf(fact_127_local_Olexordp__eq__simps_I4_J,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a,Y: a,Ys: list_a] :
% 0.07/0.31 ( ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 0.07/0.31 = ( ( less @ X @ Y )
% 0.07/0.31 | ( ~ ( less @ Y @ X )
% 0.07/0.31 & ( lexordp_eq_a @ less @ Xs @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq_simps(4)
% 0.07/0.31 thf(fact_128_local_Olexordp__eq__simps_I3_J,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a] :
% 0.07/0.31 ~ ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq_simps(3)
% 0.07/0.31 thf(fact_129_map__tailrec__rev_Oinduct,axiom,
% 0.07/0.31 ! [P: ( list_a > a ) > list_list_a > list_a > $o,A0: list_a > a,A1: list_list_a,A22: list_a] :
% 0.07/0.31 ( ! [F3: list_a > a,X_1: list_a] : ( P @ F3 @ nil_list_a @ X_1 )
% 0.07/0.31 => ( ! [F3: list_a > a,A2: list_a,As: list_list_a,Bs: list_a] :
% 0.07/0.31 ( ( P @ F3 @ As @ ( cons_a @ ( F3 @ A2 ) @ Bs ) )
% 0.07/0.31 => ( P @ F3 @ ( cons_list_a @ A2 @ As ) @ Bs ) )
% 0.07/0.31 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % map_tailrec_rev.induct
% 0.07/0.31 thf(fact_130_map__tailrec__rev_Oinduct,axiom,
% 0.07/0.31 ! [P: ( a > list_a ) > list_a > list_list_a > $o,A0: a > list_a,A1: list_a,A22: list_list_a] :
% 0.07/0.31 ( ! [F3: a > list_a,X_1: list_list_a] : ( P @ F3 @ nil_a @ X_1 )
% 0.07/0.31 => ( ! [F3: a > list_a,A2: a,As: list_a,Bs: list_list_a] :
% 0.07/0.31 ( ( P @ F3 @ As @ ( cons_list_a @ ( F3 @ A2 ) @ Bs ) )
% 0.07/0.31 => ( P @ F3 @ ( cons_a @ A2 @ As ) @ Bs ) )
% 0.07/0.31 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % map_tailrec_rev.induct
% 0.07/0.31 thf(fact_131_map__tailrec__rev_Oinduct,axiom,
% 0.07/0.31 ! [P: ( list_a > list_a ) > list_list_a > list_list_a > $o,A0: list_a > list_a,A1: list_list_a,A22: list_list_a] :
% 0.07/0.31 ( ! [F3: list_a > list_a,X_1: list_list_a] : ( P @ F3 @ nil_list_a @ X_1 )
% 0.07/0.31 => ( ! [F3: list_a > list_a,A2: list_a,As: list_list_a,Bs: list_list_a] :
% 0.07/0.31 ( ( P @ F3 @ As @ ( cons_list_a @ ( F3 @ A2 ) @ Bs ) )
% 0.07/0.31 => ( P @ F3 @ ( cons_list_a @ A2 @ As ) @ Bs ) )
% 0.07/0.31 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % map_tailrec_rev.induct
% 0.07/0.31 thf(fact_132_map__tailrec__rev_Oinduct,axiom,
% 0.07/0.31 ! [P: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A22: list_a] :
% 0.07/0.31 ( ! [F3: a > a,X_1: list_a] : ( P @ F3 @ nil_a @ X_1 )
% 0.07/0.31 => ( ! [F3: a > a,A2: a,As: list_a,Bs: list_a] :
% 0.07/0.31 ( ( P @ F3 @ As @ ( cons_a @ ( F3 @ A2 ) @ Bs ) )
% 0.07/0.31 => ( P @ F3 @ ( cons_a @ A2 @ As ) @ Bs ) )
% 0.07/0.31 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % map_tailrec_rev.induct
% 0.07/0.31 thf(fact_133_list__nonempty__induct,axiom,
% 0.07/0.31 ! [Xs: list_list_a,P: list_list_a > $o] :
% 0.07/0.31 ( ( Xs != nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a] :
% 0.07/0.31 ( ( Xs3 != nil_list_a )
% 0.07/0.31 => ( ( P @ Xs3 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) ) ) )
% 0.07/0.31 => ( P @ Xs ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list_nonempty_induct
% 0.07/0.31 thf(fact_134_list__nonempty__induct,axiom,
% 0.07/0.31 ! [Xs: list_a,P: list_a > $o] :
% 0.07/0.31 ( ( Xs != nil_a )
% 0.07/0.31 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a] :
% 0.07/0.31 ( ( Xs3 != nil_a )
% 0.07/0.31 => ( ( P @ Xs3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) ) ) )
% 0.07/0.31 => ( P @ Xs ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list_nonempty_induct
% 0.07/0.31 thf(fact_135_successively_Oinduct,axiom,
% 0.07/0.31 ! [P: ( list_a > list_a > $o ) > list_list_a > $o,A0: list_a > list_a > $o,A1: list_list_a] :
% 0.07/0.31 ( ! [P2: list_a > list_a > $o] : ( P @ P2 @ nil_list_a )
% 0.07/0.31 => ( ! [P2: list_a > list_a > $o,X2: list_a] : ( P @ P2 @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.07/0.31 => ( ! [P2: list_a > list_a > $o,X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.07/0.31 ( ( P @ P2 @ ( cons_list_a @ Y2 @ Xs3 ) )
% 0.07/0.31 => ( P @ P2 @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) )
% 0.07/0.31 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % successively.induct
% 0.07/0.31 thf(fact_136_successively_Oinduct,axiom,
% 0.07/0.31 ! [P: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.07/0.31 ( ! [P2: a > a > $o] : ( P @ P2 @ nil_a )
% 0.07/0.31 => ( ! [P2: a > a > $o,X2: a] : ( P @ P2 @ ( cons_a @ X2 @ nil_a ) )
% 0.07/0.31 => ( ! [P2: a > a > $o,X2: a,Y2: a,Xs3: list_a] :
% 0.07/0.31 ( ( P @ P2 @ ( cons_a @ Y2 @ Xs3 ) )
% 0.07/0.31 => ( P @ P2 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) )
% 0.07/0.31 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % successively.induct
% 0.07/0.31 thf(fact_137_remdups__adj_Oinduct,axiom,
% 0.07/0.31 ! [P: list_list_a > $o,A0: list_list_a] :
% 0.07/0.31 ( ( P @ nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.07/0.31 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.07/0.31 ( ( ( X2 = Y2 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) ) )
% 0.07/0.31 => ( ( ( X2 != Y2 )
% 0.07/0.31 => ( P @ ( cons_list_a @ Y2 @ Xs3 ) ) )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) ) )
% 0.07/0.31 => ( P @ A0 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % remdups_adj.induct
% 0.07/0.31 thf(fact_138_remdups__adj_Oinduct,axiom,
% 0.07/0.31 ! [P: list_a > $o,A0: list_a] :
% 0.07/0.31 ( ( P @ nil_a )
% 0.07/0.31 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a] :
% 0.07/0.31 ( ( ( X2 = Y2 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) ) )
% 0.07/0.31 => ( ( ( X2 != Y2 )
% 0.07/0.31 => ( P @ ( cons_a @ Y2 @ Xs3 ) ) )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) ) )
% 0.07/0.31 => ( P @ A0 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % remdups_adj.induct
% 0.07/0.31 thf(fact_139_sorted__wrt_Oinduct,axiom,
% 0.07/0.31 ! [P: ( list_a > list_a > $o ) > list_list_a > $o,A0: list_a > list_a > $o,A1: list_list_a] :
% 0.07/0.31 ( ! [P2: list_a > list_a > $o] : ( P @ P2 @ nil_list_a )
% 0.07/0.31 => ( ! [P2: list_a > list_a > $o,X2: list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ( P @ P2 @ Ys3 )
% 0.07/0.31 => ( P @ P2 @ ( cons_list_a @ X2 @ Ys3 ) ) )
% 0.07/0.31 => ( P @ A0 @ A1 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % sorted_wrt.induct
% 0.07/0.31 thf(fact_140_sorted__wrt_Oinduct,axiom,
% 0.07/0.31 ! [P: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.07/0.31 ( ! [P2: a > a > $o] : ( P @ P2 @ nil_a )
% 0.07/0.31 => ( ! [P2: a > a > $o,X2: a,Ys3: list_a] :
% 0.07/0.31 ( ( P @ P2 @ Ys3 )
% 0.07/0.31 => ( P @ P2 @ ( cons_a @ X2 @ Ys3 ) ) )
% 0.07/0.31 => ( P @ A0 @ A1 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % sorted_wrt.induct
% 0.07/0.31 thf(fact_141_remdups__adj_Ocases,axiom,
% 0.07/0.31 ! [X: list_list_a] :
% 0.07/0.31 ( ( X != nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a] :
% 0.07/0.31 ( X
% 0.07/0.31 != ( cons_list_a @ X2 @ nil_list_a ) )
% 0.07/0.31 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.07/0.31 ( X
% 0.07/0.31 != ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % remdups_adj.cases
% 0.07/0.31 thf(fact_142_remdups__adj_Ocases,axiom,
% 0.07/0.31 ! [X: list_a] :
% 0.07/0.31 ( ( X != nil_a )
% 0.07/0.31 => ( ! [X2: a] :
% 0.07/0.31 ( X
% 0.07/0.31 != ( cons_a @ X2 @ nil_a ) )
% 0.07/0.31 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.07/0.31 ( X
% 0.07/0.31 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % remdups_adj.cases
% 0.07/0.31 thf(fact_143_transpose_Ocases,axiom,
% 0.07/0.31 ! [X: list_list_list_a] :
% 0.07/0.31 ( ( X != nil_list_list_a )
% 0.07/0.31 => ( ! [Xss: list_list_list_a] :
% 0.07/0.31 ( X
% 0.07/0.31 != ( cons_list_list_a @ nil_list_a @ Xss ) )
% 0.07/0.31 => ~ ! [X2: list_a,Xs3: list_list_a,Xss: list_list_list_a] :
% 0.07/0.31 ( X
% 0.07/0.31 != ( cons_list_list_a @ ( cons_list_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % transpose.cases
% 0.07/0.31 thf(fact_144_transpose_Ocases,axiom,
% 0.07/0.31 ! [X: list_list_a] :
% 0.07/0.31 ( ( X != nil_list_a )
% 0.07/0.31 => ( ! [Xss: list_list_a] :
% 0.07/0.31 ( X
% 0.07/0.31 != ( cons_list_a @ nil_a @ Xss ) )
% 0.07/0.31 => ~ ! [X2: a,Xs3: list_a,Xss: list_list_a] :
% 0.07/0.31 ( X
% 0.07/0.31 != ( cons_list_a @ ( cons_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % transpose.cases
% 0.07/0.31 thf(fact_145_shuffles_Oinduct,axiom,
% 0.07/0.31 ! [P: list_list_a > list_list_a > $o,A0: list_list_a,A1: list_list_a] :
% 0.07/0.31 ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.07/0.31 => ( ! [Xs3: list_list_a] : ( P @ Xs3 @ nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a,Y2: list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ( P @ Xs3 @ ( cons_list_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ( P @ ( cons_list_a @ X2 @ Xs3 ) @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) )
% 0.07/0.31 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % shuffles.induct
% 0.07/0.31 thf(fact_146_shuffles_Oinduct,axiom,
% 0.07/0.31 ! [P: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.07/0.31 ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.07/0.31 => ( ! [Xs3: list_a] : ( P @ Xs3 @ nil_a )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a,Y2: a,Ys3: list_a] :
% 0.07/0.31 ( ( P @ Xs3 @ ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ( P @ ( cons_a @ X2 @ Xs3 ) @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) )
% 0.07/0.31 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % shuffles.induct
% 0.07/0.31 thf(fact_147_induct__list012,axiom,
% 0.07/0.31 ! [P: list_list_a > $o,Xs: list_list_a] :
% 0.07/0.31 ( ( P @ nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.07/0.31 => ( ! [X2: list_a,Y2: list_a,Zs: list_list_a] :
% 0.07/0.31 ( ( P @ Zs )
% 0.07/0.31 => ( ( P @ ( cons_list_a @ Y2 @ Zs ) )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Zs ) ) ) ) )
% 0.07/0.31 => ( P @ Xs ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % induct_list012
% 0.07/0.31 thf(fact_148_induct__list012,axiom,
% 0.07/0.31 ! [P: list_a > $o,Xs: list_a] :
% 0.07/0.31 ( ( P @ nil_a )
% 0.07/0.31 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Zs: list_a] :
% 0.07/0.31 ( ( P @ Zs )
% 0.07/0.31 => ( ( P @ ( cons_a @ Y2 @ Zs ) )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Zs ) ) ) ) )
% 0.07/0.31 => ( P @ Xs ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % induct_list012
% 0.07/0.31 thf(fact_149_splice_Oinduct,axiom,
% 0.07/0.31 ! [P: list_list_a > list_list_a > $o,A0: list_list_a,A1: list_list_a] :
% 0.07/0.31 ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ( P @ Ys3 @ Xs3 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ Ys3 ) )
% 0.07/0.31 => ( P @ A0 @ A1 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % splice.induct
% 0.07/0.31 thf(fact_150_splice_Oinduct,axiom,
% 0.07/0.31 ! [P: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.07/0.31 ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ( P @ Ys3 @ Xs3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ Ys3 ) )
% 0.07/0.31 => ( P @ A0 @ A1 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % splice.induct
% 0.07/0.31 thf(fact_151_list__induct2_H,axiom,
% 0.07/0.31 ! [P: list_a > list_list_a > $o,Xs: list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( P @ nil_a @ nil_list_a )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a] : ( P @ ( cons_a @ X2 @ Xs3 ) @ nil_list_a )
% 0.07/0.31 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a,Y2: list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list_induct2'
% 0.07/0.31 thf(fact_152_list__induct2_H,axiom,
% 0.07/0.31 ! [P: list_list_a > list_a > $o,Xs: list_list_a,Ys: list_a] :
% 0.07/0.31 ( ( P @ nil_list_a @ nil_a )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a] : ( P @ ( cons_list_a @ X2 @ Xs3 ) @ nil_a )
% 0.07/0.31 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_list_a @ ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a,Y2: a,Ys3: list_a] :
% 0.07/0.31 ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list_induct2'
% 0.07/0.31 thf(fact_153_list__induct2_H,axiom,
% 0.07/0.31 ! [P: list_list_a > list_list_a > $o,Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( P @ nil_list_a @ nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a] : ( P @ ( cons_list_a @ X2 @ Xs3 ) @ nil_list_a )
% 0.07/0.31 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_list_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a,Y2: list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list_induct2'
% 0.07/0.31 thf(fact_154_list__induct2_H,axiom,
% 0.07/0.31 ! [P: list_a > list_a > $o,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( P @ nil_a @ nil_a )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a] : ( P @ ( cons_a @ X2 @ Xs3 ) @ nil_a )
% 0.07/0.31 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a,Y2: a,Ys3: list_a] :
% 0.07/0.31 ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list_induct2'
% 0.07/0.31 thf(fact_155_neq__Nil__conv,axiom,
% 0.07/0.31 ! [Xs: list_list_a] :
% 0.07/0.31 ( ( Xs != nil_list_a )
% 0.07/0.31 = ( ? [Y3: list_a,Ys2: list_list_a] :
% 0.07/0.31 ( Xs
% 0.07/0.31 = ( cons_list_a @ Y3 @ Ys2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % neq_Nil_conv
% 0.07/0.31 thf(fact_156_neq__Nil__conv,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ( ( Xs != nil_a )
% 0.07/0.31 = ( ? [Y3: a,Ys2: list_a] :
% 0.07/0.31 ( Xs
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % neq_Nil_conv
% 0.07/0.31 thf(fact_157_list_Oinducts,axiom,
% 0.07/0.31 ! [P: list_list_a > $o,List: list_list_a] :
% 0.07/0.31 ( ( P @ nil_list_a )
% 0.07/0.31 => ( ! [X12: list_a,X23: list_list_a] :
% 0.07/0.31 ( ( P @ X23 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X12 @ X23 ) ) )
% 0.07/0.31 => ( P @ List ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.inducts
% 0.07/0.31 thf(fact_158_list_Oinducts,axiom,
% 0.07/0.31 ! [P: list_a > $o,List: list_a] :
% 0.07/0.31 ( ( P @ nil_a )
% 0.07/0.31 => ( ! [X12: a,X23: list_a] :
% 0.07/0.31 ( ( P @ X23 )
% 0.07/0.31 => ( P @ ( cons_a @ X12 @ X23 ) ) )
% 0.07/0.31 => ( P @ List ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.inducts
% 0.07/0.31 thf(fact_159_list_Oexhaust,axiom,
% 0.07/0.31 ! [Y: list_list_a] :
% 0.07/0.31 ( ( Y != nil_list_a )
% 0.07/0.31 => ~ ! [X212: list_a,X223: list_list_a] :
% 0.07/0.31 ( Y
% 0.07/0.31 != ( cons_list_a @ X212 @ X223 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.exhaust
% 0.07/0.31 thf(fact_160_list_Oexhaust,axiom,
% 0.07/0.31 ! [Y: list_a] :
% 0.07/0.31 ( ( Y != nil_a )
% 0.07/0.31 => ~ ! [X212: a,X223: list_a] :
% 0.07/0.31 ( Y
% 0.07/0.31 != ( cons_a @ X212 @ X223 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.exhaust
% 0.07/0.31 thf(fact_161_list_OdiscI,axiom,
% 0.07/0.31 ! [List: list_list_a,X21: list_a,X222: list_list_a] :
% 0.07/0.31 ( ( List
% 0.07/0.31 = ( cons_list_a @ X21 @ X222 ) )
% 0.07/0.31 => ( List != nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.discI
% 0.07/0.31 thf(fact_162_list_OdiscI,axiom,
% 0.07/0.31 ! [List: list_a,X21: a,X222: list_a] :
% 0.07/0.31 ( ( List
% 0.07/0.31 = ( cons_a @ X21 @ X222 ) )
% 0.07/0.31 => ( List != nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.discI
% 0.07/0.31 thf(fact_163_list_Odistinct_I1_J,axiom,
% 0.07/0.31 ! [X21: list_a,X222: list_list_a] :
% 0.07/0.31 ( nil_list_a
% 0.07/0.31 != ( cons_list_a @ X21 @ X222 ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.distinct(1)
% 0.07/0.31 thf(fact_164_list_Odistinct_I1_J,axiom,
% 0.07/0.31 ! [X21: a,X222: list_a] :
% 0.07/0.31 ( nil_a
% 0.07/0.31 != ( cons_a @ X21 @ X222 ) ) ).
% 0.07/0.31
% 0.07/0.31 % list.distinct(1)
% 0.07/0.31 thf(fact_165_not__Cons__self2,axiom,
% 0.07/0.31 ! [X: list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( cons_list_a @ X @ Xs )
% 0.07/0.31 != Xs ) ).
% 0.07/0.31
% 0.07/0.31 % not_Cons_self2
% 0.07/0.31 thf(fact_166_not__Cons__self2,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a] :
% 0.07/0.31 ( ( cons_a @ X @ Xs )
% 0.07/0.31 != Xs ) ).
% 0.07/0.31
% 0.07/0.31 % not_Cons_self2
% 0.07/0.31 thf(fact_167_ord_Olexordp__eq_OCons__eq,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ~ ( Less @ X @ Y )
% 0.07/0.31 => ( ~ ( Less @ Y @ X )
% 0.07/0.31 => ( ( lexordp_eq_list_a @ Less @ Xs @ Ys )
% 0.07/0.31 => ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.Cons_eq
% 0.07/0.31 thf(fact_168_ord_Olexordp__eq_OCons__eq,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ~ ( Less @ X @ Y )
% 0.07/0.31 => ( ~ ( Less @ Y @ X )
% 0.07/0.31 => ( ( lexordp_eq_a @ Less @ Xs @ Ys )
% 0.07/0.31 => ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.Cons_eq
% 0.07/0.31 thf(fact_169_ord_Olexordp__eq_OCons,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( Less @ X @ Y )
% 0.07/0.31 => ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.Cons
% 0.07/0.31 thf(fact_170_ord_Olexordp__eq_OCons,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( Less @ X @ Y )
% 0.07/0.31 => ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.Cons
% 0.07/0.31 thf(fact_171_ord_Olexordp__eq_Oinducts,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X1: list_list_a,X22: list_list_a,P: list_list_a > list_list_a > $o] :
% 0.07/0.31 ( ( lexordp_eq_list_a @ Less @ X1 @ X22 )
% 0.07/0.31 => ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.07/0.31 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ~ ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( Less @ Y2 @ X2 )
% 0.07/0.31 => ( ( lexordp_eq_list_a @ Less @ Xs3 @ Ys3 )
% 0.07/0.31 => ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.07/0.31 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.inducts
% 0.07/0.31 thf(fact_172_ord_Olexordp__eq_Oinducts,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 0.07/0.31 ( ( lexordp_eq_a @ Less @ X1 @ X22 )
% 0.07/0.31 => ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ~ ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( Less @ Y2 @ X2 )
% 0.07/0.31 => ( ( lexordp_eq_a @ Less @ Xs3 @ Ys3 )
% 0.07/0.31 => ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.07/0.31 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.inducts
% 0.07/0.31 thf(fact_173_ord_Olexordp__eq_Osimps,axiom,
% 0.07/0.31 ( lexordp_eq_list_a
% 0.07/0.31 = ( ^ [Less2: list_a > list_a > $o,A12: list_list_a,A23: list_list_a] :
% 0.07/0.31 ( ? [Ys2: list_list_a] :
% 0.07/0.31 ( ( A12 = nil_list_a )
% 0.07/0.31 & ( A23 = Ys2 ) )
% 0.07/0.31 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 0.07/0.31 ( ( A12
% 0.07/0.31 = ( cons_list_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_list_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ( Less2 @ X3 @ Y3 ) )
% 0.07/0.31 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 0.07/0.31 ( ( A12
% 0.07/0.31 = ( cons_list_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_list_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ~ ( Less2 @ X3 @ Y3 )
% 0.07/0.31 & ~ ( Less2 @ Y3 @ X3 )
% 0.07/0.31 & ( lexordp_eq_list_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.simps
% 0.07/0.31 thf(fact_174_ord_Olexordp__eq_Osimps,axiom,
% 0.07/0.31 ( lexordp_eq_a
% 0.07/0.31 = ( ^ [Less2: a > a > $o,A12: list_a,A23: list_a] :
% 0.07/0.31 ( ? [Ys2: list_a] :
% 0.07/0.31 ( ( A12 = nil_a )
% 0.07/0.31 & ( A23 = Ys2 ) )
% 0.07/0.31 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.07/0.31 ( ( A12
% 0.07/0.31 = ( cons_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ( Less2 @ X3 @ Y3 ) )
% 0.07/0.31 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.07/0.31 ( ( A12
% 0.07/0.31 = ( cons_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ~ ( Less2 @ X3 @ Y3 )
% 0.07/0.31 & ~ ( Less2 @ Y3 @ X3 )
% 0.07/0.31 & ( lexordp_eq_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.simps
% 0.07/0.31 thf(fact_175_ord_Olexordp__eq_Ocases,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,A1: list_list_a,A22: list_list_a] :
% 0.07/0.31 ( ( lexordp_eq_list_a @ Less @ A1 @ A22 )
% 0.07/0.31 => ( ( A1 != nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a] :
% 0.07/0.31 ( ? [Xs3: list_list_a] :
% 0.07/0.31 ( A1
% 0.07/0.31 = ( cons_list_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Y2: list_a] :
% 0.07/0.31 ( ? [Ys3: list_list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 = ( cons_list_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ~ ( Less @ X2 @ Y2 ) ) )
% 0.07/0.31 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_list_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Ys3: list_list_a] :
% 0.07/0.31 ( ( A22
% 0.07/0.31 = ( cons_list_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ~ ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( Less @ Y2 @ X2 )
% 0.07/0.31 => ~ ( lexordp_eq_list_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.cases
% 0.07/0.31 thf(fact_176_ord_Olexordp__eq_Ocases,axiom,
% 0.07/0.31 ! [Less: a > a > $o,A1: list_a,A22: list_a] :
% 0.07/0.31 ( ( lexordp_eq_a @ Less @ A1 @ A22 )
% 0.07/0.31 => ( ( A1 != nil_a )
% 0.07/0.31 => ( ! [X2: a] :
% 0.07/0.31 ( ? [Xs3: list_a] :
% 0.07/0.31 ( A1
% 0.07/0.31 = ( cons_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Y2: a] :
% 0.07/0.31 ( ? [Ys3: list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 = ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ~ ( Less @ X2 @ Y2 ) ) )
% 0.07/0.31 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Ys3: list_a] :
% 0.07/0.31 ( ( A22
% 0.07/0.31 = ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ~ ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( Less @ Y2 @ X2 )
% 0.07/0.31 => ~ ( lexordp_eq_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.cases
% 0.07/0.31 thf(fact_177_ord_Olexordp__eq_Ocong,axiom,
% 0.07/0.31 lexordp_eq_a = lexordp_eq_a ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.cong
% 0.07/0.31 thf(fact_178_ord_Olexordp__eq__refl,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Xs: list_a] : ( lexordp_eq_a @ Less @ Xs @ Xs ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_refl
% 0.07/0.31 thf(fact_179_ord_Olexordp__eq_ONil,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,Ys: list_list_a] : ( lexordp_eq_list_a @ Less @ nil_list_a @ Ys ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.Nil
% 0.07/0.31 thf(fact_180_ord_Olexordp__eq_ONil,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Ys: list_a] : ( lexordp_eq_a @ Less @ nil_a @ Ys ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq.Nil
% 0.07/0.31 thf(fact_181_local_Olexordp_ONil,axiom,
% 0.07/0.31 ! [Y: a,Ys: list_a] : ( lexordp_a @ less @ nil_a @ ( cons_a @ Y @ Ys ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp.Nil
% 0.07/0.31 thf(fact_182_local_Olexordp_Ocases,axiom,
% 0.07/0.31 ! [A1: list_a,A22: list_a] :
% 0.07/0.31 ( ( lexordp_a @ less @ A1 @ A22 )
% 0.07/0.31 => ( ( ( A1 = nil_a )
% 0.07/0.31 => ! [Y2: a,Ys3: list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 != ( cons_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: a] :
% 0.07/0.31 ( ? [Xs3: list_a] :
% 0.07/0.31 ( A1
% 0.07/0.31 = ( cons_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Y2: a] :
% 0.07/0.31 ( ? [Ys3: list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 = ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ~ ( less @ X2 @ Y2 ) ) )
% 0.07/0.31 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Ys3: list_a] :
% 0.07/0.31 ( ( A22
% 0.07/0.31 = ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ~ ( less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( less @ Y2 @ X2 )
% 0.07/0.31 => ~ ( lexordp_a @ less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp.cases
% 0.07/0.31 thf(fact_183_local_Olexordp_Oinducts,axiom,
% 0.07/0.31 ! [X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 0.07/0.31 ( ( lexordp_a @ less @ X1 @ X22 )
% 0.07/0.31 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ( less @ X2 @ Y2 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ~ ( less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( less @ Y2 @ X2 )
% 0.07/0.31 => ( ( lexordp_a @ less @ Xs3 @ Ys3 )
% 0.07/0.31 => ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.07/0.31 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp.inducts
% 0.07/0.31 thf(fact_184_local_Olexordp_Osimps,axiom,
% 0.07/0.31 ! [A1: list_a,A22: list_a] :
% 0.07/0.31 ( ( lexordp_a @ less @ A1 @ A22 )
% 0.07/0.31 = ( ? [Y3: a,Ys2: list_a] :
% 0.07/0.31 ( ( A1 = nil_a )
% 0.07/0.31 & ( A22
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) ) )
% 0.07/0.31 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A22
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ( less @ X3 @ Y3 ) )
% 0.07/0.31 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A22
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ~ ( less @ X3 @ Y3 )
% 0.07/0.31 & ~ ( less @ Y3 @ X3 )
% 0.07/0.31 & ( lexordp_a @ less @ Xs2 @ Ys2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp.simps
% 0.07/0.31 thf(fact_185_local_Olexordp__antisym,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( lexordp_a @ less @ Xs @ Ys )
% 0.07/0.31 => ~ ( lexordp_a @ less @ Ys @ Xs ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_antisym
% 0.07/0.31 thf(fact_186_local_Olexordp__irreflexive,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ( ! [X2: a] :
% 0.07/0.31 ~ ( less @ X2 @ X2 )
% 0.07/0.31 => ~ ( lexordp_a @ less @ Xs @ Xs ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_irreflexive
% 0.07/0.31 thf(fact_187_local_Olexordp__irreflexive_H,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ~ ( lexordp_a @ less @ Xs @ Xs ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_irreflexive'
% 0.07/0.31 thf(fact_188_local_Olexordp_OCons__eq,axiom,
% 0.07/0.31 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ~ ( less @ X @ Y )
% 0.07/0.31 => ( ~ ( less @ Y @ X )
% 0.07/0.31 => ( ( lexordp_a @ less @ Xs @ Ys )
% 0.07/0.31 => ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp.Cons_eq
% 0.07/0.31 thf(fact_189_local_Olexordp_OCons,axiom,
% 0.07/0.31 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp.Cons
% 0.07/0.31 thf(fact_190_local_Olexordp__into__lexordp__eq,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( lexordp_a @ less @ Xs @ Ys )
% 0.07/0.31 => ( lexordp_eq_a @ less @ Xs @ Ys ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_into_lexordp_eq
% 0.07/0.31 thf(fact_191_ord_Olexordp__simps_I3_J,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a,Y: list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) )
% 0.07/0.31 = ( ( Less @ X @ Y )
% 0.07/0.31 | ( ~ ( Less @ Y @ X )
% 0.07/0.31 & ( lexordp_list_a @ Less @ Xs @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_simps(3)
% 0.07/0.31 thf(fact_192_ord_Olexordp__simps_I3_J,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X: a,Xs: list_a,Y: a,Ys: list_a] :
% 0.07/0.31 ( ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 0.07/0.31 = ( ( Less @ X @ Y )
% 0.07/0.31 | ( ~ ( Less @ Y @ X )
% 0.07/0.31 & ( lexordp_a @ Less @ Xs @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_simps(3)
% 0.07/0.31 thf(fact_193_ord_Olexordp__simps_I2_J,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,Xs: list_list_a] :
% 0.07/0.31 ~ ( lexordp_list_a @ Less @ Xs @ nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_simps(2)
% 0.07/0.31 thf(fact_194_ord_Olexordp__simps_I2_J,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Xs: list_a] :
% 0.07/0.31 ~ ( lexordp_a @ Less @ Xs @ nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_simps(2)
% 0.07/0.31 thf(fact_195_ord_Olexordp__simps_I1_J,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,Ys: list_list_a] :
% 0.07/0.31 ( ( lexordp_list_a @ Less @ nil_list_a @ Ys )
% 0.07/0.31 = ( Ys != nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_simps(1)
% 0.07/0.31 thf(fact_196_ord_Olexordp__simps_I1_J,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Ys: list_a] :
% 0.07/0.31 ( ( lexordp_a @ Less @ nil_a @ Ys )
% 0.07/0.31 = ( Ys != nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_simps(1)
% 0.07/0.31 thf(fact_197_local_Olexordp__simps_I3_J,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a,Y: a,Ys: list_a] :
% 0.07/0.31 ( ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 0.07/0.31 = ( ( less @ X @ Y )
% 0.07/0.31 | ( ~ ( less @ Y @ X )
% 0.07/0.31 & ( lexordp_a @ less @ Xs @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_simps(3)
% 0.07/0.31 thf(fact_198_local_Olexordp__simps_I1_J,axiom,
% 0.07/0.31 ! [Ys: list_a] :
% 0.07/0.31 ( ( lexordp_a @ less @ nil_a @ Ys )
% 0.07/0.31 = ( Ys != nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_simps(1)
% 0.07/0.31 thf(fact_199_local_Olexordp__simps_I2_J,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ~ ( lexordp_a @ less @ Xs @ nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_simps(2)
% 0.07/0.31 thf(fact_200_ord_Olexordp_Ocong,axiom,
% 0.07/0.31 lexordp_a = lexordp_a ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.cong
% 0.07/0.31 thf(fact_201_ord_Olexordp__irreflexive,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Xs: list_a] :
% 0.07/0.31 ( ! [X2: a] :
% 0.07/0.31 ~ ( Less @ X2 @ X2 )
% 0.07/0.31 => ~ ( lexordp_a @ Less @ Xs @ Xs ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_irreflexive
% 0.07/0.31 thf(fact_202_ord_Olexordp_OCons__eq,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ~ ( Less @ X @ Y )
% 0.07/0.31 => ( ~ ( Less @ Y @ X )
% 0.07/0.31 => ( ( lexordp_list_a @ Less @ Xs @ Ys )
% 0.07/0.31 => ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.Cons_eq
% 0.07/0.31 thf(fact_203_ord_Olexordp_OCons__eq,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ~ ( Less @ X @ Y )
% 0.07/0.31 => ( ~ ( Less @ Y @ X )
% 0.07/0.31 => ( ( lexordp_a @ Less @ Xs @ Ys )
% 0.07/0.31 => ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.Cons_eq
% 0.07/0.31 thf(fact_204_ord_Olexordp_OCons,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( Less @ X @ Y )
% 0.07/0.31 => ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.Cons
% 0.07/0.31 thf(fact_205_ord_Olexordp_OCons,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( Less @ X @ Y )
% 0.07/0.31 => ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.Cons
% 0.07/0.31 thf(fact_206_ord_Olexordp__into__lexordp__eq,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( lexordp_a @ Less @ Xs @ Ys )
% 0.07/0.31 => ( lexordp_eq_a @ Less @ Xs @ Ys ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_into_lexordp_eq
% 0.07/0.31 thf(fact_207_ord_Olexordp_ONil,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,Y: list_a,Ys: list_list_a] : ( lexordp_list_a @ Less @ nil_list_a @ ( cons_list_a @ Y @ Ys ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.Nil
% 0.07/0.31 thf(fact_208_ord_Olexordp_ONil,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Y: a,Ys: list_a] : ( lexordp_a @ Less @ nil_a @ ( cons_a @ Y @ Ys ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.Nil
% 0.07/0.31 thf(fact_209_ord_Olexordp_Ocases,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,A1: list_list_a,A22: list_list_a] :
% 0.07/0.31 ( ( lexordp_list_a @ Less @ A1 @ A22 )
% 0.07/0.31 => ( ( ( A1 = nil_list_a )
% 0.07/0.31 => ! [Y2: list_a,Ys3: list_list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 != ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: list_a] :
% 0.07/0.31 ( ? [Xs3: list_list_a] :
% 0.07/0.31 ( A1
% 0.07/0.31 = ( cons_list_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Y2: list_a] :
% 0.07/0.31 ( ? [Ys3: list_list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 = ( cons_list_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ~ ( Less @ X2 @ Y2 ) ) )
% 0.07/0.31 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_list_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Ys3: list_list_a] :
% 0.07/0.31 ( ( A22
% 0.07/0.31 = ( cons_list_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ~ ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( Less @ Y2 @ X2 )
% 0.07/0.31 => ~ ( lexordp_list_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.cases
% 0.07/0.31 thf(fact_210_ord_Olexordp_Ocases,axiom,
% 0.07/0.31 ! [Less: a > a > $o,A1: list_a,A22: list_a] :
% 0.07/0.31 ( ( lexordp_a @ Less @ A1 @ A22 )
% 0.07/0.31 => ( ( ( A1 = nil_a )
% 0.07/0.31 => ! [Y2: a,Ys3: list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 != ( cons_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: a] :
% 0.07/0.31 ( ? [Xs3: list_a] :
% 0.07/0.31 ( A1
% 0.07/0.31 = ( cons_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Y2: a] :
% 0.07/0.31 ( ? [Ys3: list_a] :
% 0.07/0.31 ( A22
% 0.07/0.31 = ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ~ ( Less @ X2 @ Y2 ) ) )
% 0.07/0.31 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 0.07/0.31 ( ( A1
% 0.07/0.31 = ( cons_a @ X2 @ Xs3 ) )
% 0.07/0.31 => ! [Ys3: list_a] :
% 0.07/0.31 ( ( A22
% 0.07/0.31 = ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ~ ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( Less @ Y2 @ X2 )
% 0.07/0.31 => ~ ( lexordp_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.cases
% 0.07/0.31 thf(fact_211_ord_Olexordp_Osimps,axiom,
% 0.07/0.31 ( lexordp_list_a
% 0.07/0.31 = ( ^ [Less2: list_a > list_a > $o,A12: list_list_a,A23: list_list_a] :
% 0.07/0.31 ( ? [Y3: list_a,Ys2: list_list_a] :
% 0.07/0.31 ( ( A12 = nil_list_a )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_list_a @ Y3 @ Ys2 ) ) )
% 0.07/0.31 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 0.07/0.31 ( ( A12
% 0.07/0.31 = ( cons_list_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_list_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ( Less2 @ X3 @ Y3 ) )
% 0.07/0.31 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 0.07/0.31 ( ( A12
% 0.07/0.31 = ( cons_list_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_list_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ~ ( Less2 @ X3 @ Y3 )
% 0.07/0.31 & ~ ( Less2 @ Y3 @ X3 )
% 0.07/0.31 & ( lexordp_list_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.simps
% 0.07/0.31 thf(fact_212_ord_Olexordp_Osimps,axiom,
% 0.07/0.31 ( lexordp_a
% 0.07/0.31 = ( ^ [Less2: a > a > $o,A12: list_a,A23: list_a] :
% 0.07/0.31 ( ? [Y3: a,Ys2: list_a] :
% 0.07/0.31 ( ( A12 = nil_a )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) ) )
% 0.07/0.31 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.07/0.31 ( ( A12
% 0.07/0.31 = ( cons_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ( Less2 @ X3 @ Y3 ) )
% 0.07/0.31 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.07/0.31 ( ( A12
% 0.07/0.31 = ( cons_a @ X3 @ Xs2 ) )
% 0.07/0.31 & ( A23
% 0.07/0.31 = ( cons_a @ Y3 @ Ys2 ) )
% 0.07/0.31 & ~ ( Less2 @ X3 @ Y3 )
% 0.07/0.31 & ~ ( Less2 @ Y3 @ X3 )
% 0.07/0.31 & ( lexordp_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.simps
% 0.07/0.31 thf(fact_213_ord_Olexordp_Oinducts,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X1: list_list_a,X22: list_list_a,P: list_list_a > list_list_a > $o] :
% 0.07/0.31 ( ( lexordp_list_a @ Less @ X1 @ X22 )
% 0.07/0.31 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_list_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 0.07/0.31 ( ~ ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( Less @ Y2 @ X2 )
% 0.07/0.31 => ( ( lexordp_list_a @ Less @ Xs3 @ Ys3 )
% 0.07/0.31 => ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.07/0.31 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.inducts
% 0.07/0.31 thf(fact_214_ord_Olexordp_Oinducts,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 0.07/0.31 ( ( lexordp_a @ Less @ X1 @ X22 )
% 0.07/0.31 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 0.07/0.31 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 0.07/0.31 ( ~ ( Less @ X2 @ Y2 )
% 0.07/0.31 => ( ~ ( Less @ Y2 @ X2 )
% 0.07/0.31 => ( ( lexordp_a @ Less @ Xs3 @ Ys3 )
% 0.07/0.31 => ( ( P @ Xs3 @ Ys3 )
% 0.07/0.31 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 0.07/0.31 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp.inducts
% 0.07/0.31 thf(fact_215_local_Olexordp__append__rightI,axiom,
% 0.07/0.31 ! [Ys: list_a,Xs: list_a] :
% 0.07/0.31 ( ( Ys != nil_a )
% 0.07/0.31 => ( lexordp_a @ less @ Xs @ ( append_a @ Xs @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_append_rightI
% 0.07/0.31 thf(fact_216_local_Olexordp__append__left__rightI,axiom,
% 0.07/0.31 ! [X: a,Y: a,Us: list_a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( less @ X @ Y )
% 0.07/0.31 => ( lexordp_a @ less @ ( append_a @ Us @ ( cons_a @ X @ Xs ) ) @ ( append_a @ Us @ ( cons_a @ Y @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_append_left_rightI
% 0.07/0.31 thf(fact_217_semilattice_Oaxioms_I1_J,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ( semilattice_a @ F )
% 0.07/0.31 => ( abel_semigroup_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice.axioms(1)
% 0.07/0.31 thf(fact_218_local_Olexordp__append__leftD,axiom,
% 0.07/0.31 ! [Xs: list_a,Us: list_a,Vs: list_a] :
% 0.07/0.31 ( ( lexordp_a @ less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) )
% 0.07/0.31 => ( ! [A2: a] :
% 0.07/0.31 ~ ( less @ A2 @ A2 )
% 0.07/0.31 => ( lexordp_a @ less @ Us @ Vs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_append_leftD
% 0.07/0.31 thf(fact_219_local_Olexordp__append__leftI,axiom,
% 0.07/0.31 ! [Us: list_a,Vs: list_a,Xs: list_a] :
% 0.07/0.31 ( ( lexordp_a @ less @ Us @ Vs )
% 0.07/0.31 => ( lexordp_a @ less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_append_leftI
% 0.07/0.31 thf(fact_220_local_Olexordp__eq__pref,axiom,
% 0.07/0.31 ! [U: list_a,V: list_a] : ( lexordp_eq_a @ less @ U @ ( append_a @ U @ V ) ) ).
% 0.07/0.31
% 0.07/0.31 % local.lexordp_eq_pref
% 0.07/0.31 thf(fact_221_same__append__eq,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Xs @ Ys )
% 0.07/0.31 = ( append_list_a @ Xs @ Zs2 ) )
% 0.07/0.31 = ( Ys = Zs2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % same_append_eq
% 0.07/0.31 thf(fact_222_same__append__eq,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a,Zs2: list_a] :
% 0.07/0.31 ( ( ( append_a @ Xs @ Ys )
% 0.07/0.31 = ( append_a @ Xs @ Zs2 ) )
% 0.07/0.31 = ( Ys = Zs2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % same_append_eq
% 0.07/0.31 thf(fact_223_append__same__eq,axiom,
% 0.07/0.31 ! [Ys: list_list_a,Xs: list_list_a,Zs2: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Ys @ Xs )
% 0.07/0.31 = ( append_list_a @ Zs2 @ Xs ) )
% 0.07/0.31 = ( Ys = Zs2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_same_eq
% 0.07/0.31 thf(fact_224_append__same__eq,axiom,
% 0.07/0.31 ! [Ys: list_a,Xs: list_a,Zs2: list_a] :
% 0.07/0.31 ( ( ( append_a @ Ys @ Xs )
% 0.07/0.31 = ( append_a @ Zs2 @ Xs ) )
% 0.07/0.31 = ( Ys = Zs2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_same_eq
% 0.07/0.31 thf(fact_225_append__assoc,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.07/0.31 ( ( append_list_a @ ( append_list_a @ Xs @ Ys ) @ Zs2 )
% 0.07/0.31 = ( append_list_a @ Xs @ ( append_list_a @ Ys @ Zs2 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_assoc
% 0.07/0.31 thf(fact_226_append__assoc,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a,Zs2: list_a] :
% 0.07/0.31 ( ( append_a @ ( append_a @ Xs @ Ys ) @ Zs2 )
% 0.07/0.31 = ( append_a @ Xs @ ( append_a @ Ys @ Zs2 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_assoc
% 0.07/0.31 thf(fact_227_append_Oassoc,axiom,
% 0.07/0.31 ! [A: list_list_a,B: list_list_a,C: list_list_a] :
% 0.07/0.31 ( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
% 0.07/0.31 = ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append.assoc
% 0.07/0.31 thf(fact_228_append_Oassoc,axiom,
% 0.07/0.31 ! [A: list_a,B: list_a,C: list_a] :
% 0.07/0.31 ( ( append_a @ ( append_a @ A @ B ) @ C )
% 0.07/0.31 = ( append_a @ A @ ( append_a @ B @ C ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append.assoc
% 0.07/0.31 thf(fact_229_append_Oright__neutral,axiom,
% 0.07/0.31 ! [A: list_list_a] :
% 0.07/0.31 ( ( append_list_a @ A @ nil_list_a )
% 0.07/0.31 = A ) ).
% 0.07/0.31
% 0.07/0.31 % append.right_neutral
% 0.07/0.31 thf(fact_230_append_Oright__neutral,axiom,
% 0.07/0.31 ! [A: list_a] :
% 0.07/0.31 ( ( append_a @ A @ nil_a )
% 0.07/0.31 = A ) ).
% 0.07/0.31
% 0.07/0.31 % append.right_neutral
% 0.07/0.31 thf(fact_231_append__is__Nil__conv,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Xs @ Ys )
% 0.07/0.31 = nil_list_a )
% 0.07/0.31 = ( ( Xs = nil_list_a )
% 0.07/0.31 & ( Ys = nil_list_a ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_is_Nil_conv
% 0.07/0.31 thf(fact_232_append__is__Nil__conv,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( ( append_a @ Xs @ Ys )
% 0.07/0.31 = nil_a )
% 0.07/0.31 = ( ( Xs = nil_a )
% 0.07/0.31 & ( Ys = nil_a ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_is_Nil_conv
% 0.07/0.31 thf(fact_233_Nil__is__append__conv,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( nil_list_a
% 0.07/0.31 = ( append_list_a @ Xs @ Ys ) )
% 0.07/0.31 = ( ( Xs = nil_list_a )
% 0.07/0.31 & ( Ys = nil_list_a ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Nil_is_append_conv
% 0.07/0.31 thf(fact_234_Nil__is__append__conv,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( nil_a
% 0.07/0.31 = ( append_a @ Xs @ Ys ) )
% 0.07/0.31 = ( ( Xs = nil_a )
% 0.07/0.31 & ( Ys = nil_a ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Nil_is_append_conv
% 0.07/0.31 thf(fact_235_self__append__conv2,axiom,
% 0.07/0.31 ! [Ys: list_list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( Ys
% 0.07/0.31 = ( append_list_a @ Xs @ Ys ) )
% 0.07/0.31 = ( Xs = nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % self_append_conv2
% 0.07/0.31 thf(fact_236_self__append__conv2,axiom,
% 0.07/0.31 ! [Ys: list_a,Xs: list_a] :
% 0.07/0.31 ( ( Ys
% 0.07/0.31 = ( append_a @ Xs @ Ys ) )
% 0.07/0.31 = ( Xs = nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % self_append_conv2
% 0.07/0.31 thf(fact_237_append__self__conv2,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Xs @ Ys )
% 0.07/0.31 = Ys )
% 0.07/0.31 = ( Xs = nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_self_conv2
% 0.07/0.31 thf(fact_238_append__self__conv2,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( ( append_a @ Xs @ Ys )
% 0.07/0.31 = Ys )
% 0.07/0.31 = ( Xs = nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_self_conv2
% 0.07/0.31 thf(fact_239_self__append__conv,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( Xs
% 0.07/0.31 = ( append_list_a @ Xs @ Ys ) )
% 0.07/0.31 = ( Ys = nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % self_append_conv
% 0.07/0.31 thf(fact_240_self__append__conv,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( Xs
% 0.07/0.31 = ( append_a @ Xs @ Ys ) )
% 0.07/0.31 = ( Ys = nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % self_append_conv
% 0.07/0.31 thf(fact_241_append__self__conv,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Xs @ Ys )
% 0.07/0.31 = Xs )
% 0.07/0.31 = ( Ys = nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_self_conv
% 0.07/0.31 thf(fact_242_append__self__conv,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( ( append_a @ Xs @ Ys )
% 0.07/0.31 = Xs )
% 0.07/0.31 = ( Ys = nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_self_conv
% 0.07/0.31 thf(fact_243_append__Nil2,axiom,
% 0.07/0.31 ! [Xs: list_list_a] :
% 0.07/0.31 ( ( append_list_a @ Xs @ nil_list_a )
% 0.07/0.31 = Xs ) ).
% 0.07/0.31
% 0.07/0.31 % append_Nil2
% 0.07/0.31 thf(fact_244_append__Nil2,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ( ( append_a @ Xs @ nil_a )
% 0.07/0.31 = Xs ) ).
% 0.07/0.31
% 0.07/0.31 % append_Nil2
% 0.07/0.31 thf(fact_245_append1__eq__conv,axiom,
% 0.07/0.31 ! [Xs: list_list_a,X: list_a,Ys: list_list_a,Y: list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) )
% 0.07/0.31 = ( append_list_a @ Ys @ ( cons_list_a @ Y @ nil_list_a ) ) )
% 0.07/0.31 = ( ( Xs = Ys )
% 0.07/0.31 & ( X = Y ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append1_eq_conv
% 0.07/0.31 thf(fact_246_append1__eq__conv,axiom,
% 0.07/0.31 ! [Xs: list_a,X: a,Ys: list_a,Y: a] :
% 0.07/0.31 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 0.07/0.31 = ( append_a @ Ys @ ( cons_a @ Y @ nil_a ) ) )
% 0.07/0.31 = ( ( Xs = Ys )
% 0.07/0.31 & ( X = Y ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append1_eq_conv
% 0.07/0.31 thf(fact_247_append_Oleft__neutral,axiom,
% 0.07/0.31 ! [A: list_list_a] :
% 0.07/0.31 ( ( append_list_a @ nil_list_a @ A )
% 0.07/0.31 = A ) ).
% 0.07/0.31
% 0.07/0.31 % append.left_neutral
% 0.07/0.31 thf(fact_248_append_Oleft__neutral,axiom,
% 0.07/0.31 ! [A: list_a] :
% 0.07/0.31 ( ( append_a @ nil_a @ A )
% 0.07/0.31 = A ) ).
% 0.07/0.31
% 0.07/0.31 % append.left_neutral
% 0.07/0.31 thf(fact_249_append__Nil,axiom,
% 0.07/0.31 ! [Ys: list_list_a] :
% 0.07/0.31 ( ( append_list_a @ nil_list_a @ Ys )
% 0.07/0.31 = Ys ) ).
% 0.07/0.31
% 0.07/0.31 % append_Nil
% 0.07/0.31 thf(fact_250_append__Nil,axiom,
% 0.07/0.31 ! [Ys: list_a] :
% 0.07/0.31 ( ( append_a @ nil_a @ Ys )
% 0.07/0.31 = Ys ) ).
% 0.07/0.31
% 0.07/0.31 % append_Nil
% 0.07/0.31 thf(fact_251_eq__Nil__appendI,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( Xs = Ys )
% 0.07/0.31 => ( Xs
% 0.07/0.31 = ( append_list_a @ nil_list_a @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % eq_Nil_appendI
% 0.07/0.31 thf(fact_252_eq__Nil__appendI,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( Xs = Ys )
% 0.07/0.31 => ( Xs
% 0.07/0.31 = ( append_a @ nil_a @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % eq_Nil_appendI
% 0.07/0.31 thf(fact_253_Cons__eq__appendI,axiom,
% 0.07/0.31 ! [X: list_a,Xs1: list_list_a,Ys: list_list_a,Xs: list_list_a,Zs2: list_list_a] :
% 0.07/0.31 ( ( ( cons_list_a @ X @ Xs1 )
% 0.07/0.31 = Ys )
% 0.07/0.31 => ( ( Xs
% 0.07/0.31 = ( append_list_a @ Xs1 @ Zs2 ) )
% 0.07/0.31 => ( ( cons_list_a @ X @ Xs )
% 0.07/0.31 = ( append_list_a @ Ys @ Zs2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Cons_eq_appendI
% 0.07/0.31 thf(fact_254_Cons__eq__appendI,axiom,
% 0.07/0.31 ! [X: a,Xs1: list_a,Ys: list_a,Xs: list_a,Zs2: list_a] :
% 0.07/0.31 ( ( ( cons_a @ X @ Xs1 )
% 0.07/0.31 = Ys )
% 0.07/0.31 => ( ( Xs
% 0.07/0.31 = ( append_a @ Xs1 @ Zs2 ) )
% 0.07/0.31 => ( ( cons_a @ X @ Xs )
% 0.07/0.31 = ( append_a @ Ys @ Zs2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Cons_eq_appendI
% 0.07/0.31 thf(fact_255_append__Cons,axiom,
% 0.07/0.31 ! [X: list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( append_list_a @ ( cons_list_a @ X @ Xs ) @ Ys )
% 0.07/0.31 = ( cons_list_a @ X @ ( append_list_a @ Xs @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_Cons
% 0.07/0.31 thf(fact_256_append__Cons,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( append_a @ ( cons_a @ X @ Xs ) @ Ys )
% 0.07/0.31 = ( cons_a @ X @ ( append_a @ Xs @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_Cons
% 0.07/0.31 thf(fact_257_ord_Olexordp__append__leftD,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,Xs: list_list_a,Us: list_list_a,Vs: list_list_a] :
% 0.07/0.31 ( ( lexordp_list_a @ Less @ ( append_list_a @ Xs @ Us ) @ ( append_list_a @ Xs @ Vs ) )
% 0.07/0.31 => ( ! [A2: list_a] :
% 0.07/0.31 ~ ( Less @ A2 @ A2 )
% 0.07/0.31 => ( lexordp_list_a @ Less @ Us @ Vs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_append_leftD
% 0.07/0.31 thf(fact_258_ord_Olexordp__append__leftD,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Xs: list_a,Us: list_a,Vs: list_a] :
% 0.07/0.31 ( ( lexordp_a @ Less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) )
% 0.07/0.31 => ( ! [A2: a] :
% 0.07/0.31 ~ ( Less @ A2 @ A2 )
% 0.07/0.31 => ( lexordp_a @ Less @ Us @ Vs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_append_leftD
% 0.07/0.31 thf(fact_259_ord_Olexordp__append__leftI,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,Us: list_list_a,Vs: list_list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( lexordp_list_a @ Less @ Us @ Vs )
% 0.07/0.31 => ( lexordp_list_a @ Less @ ( append_list_a @ Xs @ Us ) @ ( append_list_a @ Xs @ Vs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_append_leftI
% 0.07/0.31 thf(fact_260_ord_Olexordp__append__leftI,axiom,
% 0.07/0.31 ! [Less: a > a > $o,Us: list_a,Vs: list_a,Xs: list_a] :
% 0.07/0.31 ( ( lexordp_a @ Less @ Us @ Vs )
% 0.07/0.31 => ( lexordp_a @ Less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_append_leftI
% 0.07/0.31 thf(fact_261_ord_Olexordp__eq__pref,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,U: list_list_a,V: list_list_a] : ( lexordp_eq_list_a @ Less @ U @ ( append_list_a @ U @ V ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_pref
% 0.07/0.31 thf(fact_262_ord_Olexordp__eq__pref,axiom,
% 0.07/0.31 ! [Less: a > a > $o,U: list_a,V: list_a] : ( lexordp_eq_a @ Less @ U @ ( append_a @ U @ V ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_eq_pref
% 0.07/0.31 thf(fact_263_append__eq__append__conv2,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a,Ts: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Xs @ Ys )
% 0.07/0.31 = ( append_list_a @ Zs2 @ Ts ) )
% 0.07/0.31 = ( ? [Us2: list_list_a] :
% 0.07/0.31 ( ( ( Xs
% 0.07/0.31 = ( append_list_a @ Zs2 @ Us2 ) )
% 0.07/0.31 & ( ( append_list_a @ Us2 @ Ys )
% 0.07/0.31 = Ts ) )
% 0.07/0.31 | ( ( ( append_list_a @ Xs @ Us2 )
% 0.07/0.31 = Zs2 )
% 0.07/0.31 & ( Ys
% 0.07/0.31 = ( append_list_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_eq_append_conv2
% 0.07/0.31 thf(fact_264_append__eq__append__conv2,axiom,
% 0.07/0.31 ! [Xs: list_a,Ys: list_a,Zs2: list_a,Ts: list_a] :
% 0.07/0.31 ( ( ( append_a @ Xs @ Ys )
% 0.07/0.31 = ( append_a @ Zs2 @ Ts ) )
% 0.07/0.31 = ( ? [Us2: list_a] :
% 0.07/0.31 ( ( ( Xs
% 0.07/0.31 = ( append_a @ Zs2 @ Us2 ) )
% 0.07/0.31 & ( ( append_a @ Us2 @ Ys )
% 0.07/0.31 = Ts ) )
% 0.07/0.31 | ( ( ( append_a @ Xs @ Us2 )
% 0.07/0.31 = Zs2 )
% 0.07/0.31 & ( Ys
% 0.07/0.31 = ( append_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_eq_append_conv2
% 0.07/0.31 thf(fact_265_append__eq__appendI,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Xs1: list_list_a,Zs2: list_list_a,Ys: list_list_a,Us: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Xs @ Xs1 )
% 0.07/0.31 = Zs2 )
% 0.07/0.31 => ( ( Ys
% 0.07/0.31 = ( append_list_a @ Xs1 @ Us ) )
% 0.07/0.31 => ( ( append_list_a @ Xs @ Ys )
% 0.07/0.31 = ( append_list_a @ Zs2 @ Us ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_eq_appendI
% 0.07/0.31 thf(fact_266_append__eq__appendI,axiom,
% 0.07/0.31 ! [Xs: list_a,Xs1: list_a,Zs2: list_a,Ys: list_a,Us: list_a] :
% 0.07/0.31 ( ( ( append_a @ Xs @ Xs1 )
% 0.07/0.31 = Zs2 )
% 0.07/0.31 => ( ( Ys
% 0.07/0.31 = ( append_a @ Xs1 @ Us ) )
% 0.07/0.31 => ( ( append_a @ Xs @ Ys )
% 0.07/0.31 = ( append_a @ Zs2 @ Us ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_eq_appendI
% 0.07/0.31 thf(fact_267_append_Osemigroup__axioms,axiom,
% 0.07/0.31 semigr656274520list_a @ append_list_a ).
% 0.07/0.31
% 0.07/0.31 % append.semigroup_axioms
% 0.07/0.31 thf(fact_268_append_Osemigroup__axioms,axiom,
% 0.07/0.31 semigroup_list_a @ append_a ).
% 0.07/0.31
% 0.07/0.31 % append.semigroup_axioms
% 0.07/0.31 thf(fact_269_rev__nonempty__induct,axiom,
% 0.07/0.31 ! [Xs: list_list_a,P: list_list_a > $o] :
% 0.07/0.31 ( ( Xs != nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a] :
% 0.07/0.31 ( ( Xs3 != nil_list_a )
% 0.07/0.31 => ( ( P @ Xs3 )
% 0.07/0.31 => ( P @ ( append_list_a @ Xs3 @ ( cons_list_a @ X2 @ nil_list_a ) ) ) ) )
% 0.07/0.31 => ( P @ Xs ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % rev_nonempty_induct
% 0.07/0.31 thf(fact_270_rev__nonempty__induct,axiom,
% 0.07/0.31 ! [Xs: list_a,P: list_a > $o] :
% 0.07/0.31 ( ( Xs != nil_a )
% 0.07/0.31 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a] :
% 0.07/0.31 ( ( Xs3 != nil_a )
% 0.07/0.31 => ( ( P @ Xs3 )
% 0.07/0.31 => ( P @ ( append_a @ Xs3 @ ( cons_a @ X2 @ nil_a ) ) ) ) )
% 0.07/0.31 => ( P @ Xs ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % rev_nonempty_induct
% 0.07/0.31 thf(fact_271_append__eq__Cons__conv,axiom,
% 0.07/0.31 ! [Ys: list_list_a,Zs2: list_list_a,X: list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Ys @ Zs2 )
% 0.07/0.31 = ( cons_list_a @ X @ Xs ) )
% 0.07/0.31 = ( ( ( Ys = nil_list_a )
% 0.07/0.31 & ( Zs2
% 0.07/0.31 = ( cons_list_a @ X @ Xs ) ) )
% 0.07/0.31 | ? [Ys4: list_list_a] :
% 0.07/0.31 ( ( Ys
% 0.07/0.31 = ( cons_list_a @ X @ Ys4 ) )
% 0.07/0.31 & ( ( append_list_a @ Ys4 @ Zs2 )
% 0.07/0.31 = Xs ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_eq_Cons_conv
% 0.07/0.31 thf(fact_272_append__eq__Cons__conv,axiom,
% 0.07/0.31 ! [Ys: list_a,Zs2: list_a,X: a,Xs: list_a] :
% 0.07/0.31 ( ( ( append_a @ Ys @ Zs2 )
% 0.07/0.31 = ( cons_a @ X @ Xs ) )
% 0.07/0.31 = ( ( ( Ys = nil_a )
% 0.07/0.31 & ( Zs2
% 0.07/0.31 = ( cons_a @ X @ Xs ) ) )
% 0.07/0.31 | ? [Ys4: list_a] :
% 0.07/0.31 ( ( Ys
% 0.07/0.31 = ( cons_a @ X @ Ys4 ) )
% 0.07/0.31 & ( ( append_a @ Ys4 @ Zs2 )
% 0.07/0.31 = Xs ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_eq_Cons_conv
% 0.07/0.31 thf(fact_273_Cons__eq__append__conv,axiom,
% 0.07/0.31 ! [X: list_a,Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.07/0.31 ( ( ( cons_list_a @ X @ Xs )
% 0.07/0.31 = ( append_list_a @ Ys @ Zs2 ) )
% 0.07/0.31 = ( ( ( Ys = nil_list_a )
% 0.07/0.31 & ( ( cons_list_a @ X @ Xs )
% 0.07/0.31 = Zs2 ) )
% 0.07/0.31 | ? [Ys4: list_list_a] :
% 0.07/0.31 ( ( ( cons_list_a @ X @ Ys4 )
% 0.07/0.31 = Ys )
% 0.07/0.31 & ( Xs
% 0.07/0.31 = ( append_list_a @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Cons_eq_append_conv
% 0.07/0.31 thf(fact_274_Cons__eq__append__conv,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a,Ys: list_a,Zs2: list_a] :
% 0.07/0.31 ( ( ( cons_a @ X @ Xs )
% 0.07/0.31 = ( append_a @ Ys @ Zs2 ) )
% 0.07/0.31 = ( ( ( Ys = nil_a )
% 0.07/0.31 & ( ( cons_a @ X @ Xs )
% 0.07/0.31 = Zs2 ) )
% 0.07/0.31 | ? [Ys4: list_a] :
% 0.07/0.31 ( ( ( cons_a @ X @ Ys4 )
% 0.07/0.31 = Ys )
% 0.07/0.31 & ( Xs
% 0.07/0.31 = ( append_a @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Cons_eq_append_conv
% 0.07/0.31 thf(fact_275_rev__exhaust,axiom,
% 0.07/0.31 ! [Xs: list_list_a] :
% 0.07/0.31 ( ( Xs != nil_list_a )
% 0.07/0.31 => ~ ! [Ys3: list_list_a,Y2: list_a] :
% 0.07/0.31 ( Xs
% 0.07/0.31 != ( append_list_a @ Ys3 @ ( cons_list_a @ Y2 @ nil_list_a ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % rev_exhaust
% 0.07/0.31 thf(fact_276_rev__exhaust,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ( ( Xs != nil_a )
% 0.07/0.31 => ~ ! [Ys3: list_a,Y2: a] :
% 0.07/0.31 ( Xs
% 0.07/0.31 != ( append_a @ Ys3 @ ( cons_a @ Y2 @ nil_a ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % rev_exhaust
% 0.07/0.31 thf(fact_277_rev__induct,axiom,
% 0.07/0.31 ! [P: list_list_a > $o,Xs: list_list_a] :
% 0.07/0.31 ( ( P @ nil_list_a )
% 0.07/0.31 => ( ! [X2: list_a,Xs3: list_list_a] :
% 0.07/0.31 ( ( P @ Xs3 )
% 0.07/0.31 => ( P @ ( append_list_a @ Xs3 @ ( cons_list_a @ X2 @ nil_list_a ) ) ) )
% 0.07/0.31 => ( P @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % rev_induct
% 0.07/0.31 thf(fact_278_rev__induct,axiom,
% 0.07/0.31 ! [P: list_a > $o,Xs: list_a] :
% 0.07/0.31 ( ( P @ nil_a )
% 0.07/0.31 => ( ! [X2: a,Xs3: list_a] :
% 0.07/0.31 ( ( P @ Xs3 )
% 0.07/0.31 => ( P @ ( append_a @ Xs3 @ ( cons_a @ X2 @ nil_a ) ) ) )
% 0.07/0.31 => ( P @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % rev_induct
% 0.07/0.31 thf(fact_279_ord_Olexordp__append__left__rightI,axiom,
% 0.07/0.31 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Us: list_list_a,Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( Less @ X @ Y )
% 0.07/0.31 => ( lexordp_list_a @ Less @ ( append_list_a @ Us @ ( cons_list_a @ X @ Xs ) ) @ ( append_list_a @ Us @ ( cons_list_a @ Y @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_append_left_rightI
% 0.07/0.31 thf(fact_280_ord_Olexordp__append__left__rightI,axiom,
% 0.07/0.31 ! [Less: a > a > $o,X: a,Y: a,Us: list_a,Xs: list_a,Ys: list_a] :
% 0.07/0.31 ( ( Less @ X @ Y )
% 0.07/0.31 => ( lexordp_a @ Less @ ( append_a @ Us @ ( cons_a @ X @ Xs ) ) @ ( append_a @ Us @ ( cons_a @ Y @ Ys ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_append_left_rightI
% 0.07/0.31 thf(fact_281_ord_Olexordp__append__rightI,axiom,
% 0.07/0.31 ! [Ys: list_list_a,Less: list_a > list_a > $o,Xs: list_list_a] :
% 0.07/0.31 ( ( Ys != nil_list_a )
% 0.07/0.31 => ( lexordp_list_a @ Less @ Xs @ ( append_list_a @ Xs @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_append_rightI
% 0.07/0.31 thf(fact_282_ord_Olexordp__append__rightI,axiom,
% 0.07/0.31 ! [Ys: list_a,Less: a > a > $o,Xs: list_a] :
% 0.07/0.31 ( ( Ys != nil_a )
% 0.07/0.31 => ( lexordp_a @ Less @ Xs @ ( append_a @ Xs @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ord.lexordp_append_rightI
% 0.07/0.31 thf(fact_283_semilattice_Oidem,axiom,
% 0.07/0.31 ! [F: a > a > a,A: a] :
% 0.07/0.31 ( ( semilattice_a @ F )
% 0.07/0.31 => ( ( F @ A @ A )
% 0.07/0.31 = A ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice.idem
% 0.07/0.31 thf(fact_284_semilattice_Oleft__idem,axiom,
% 0.07/0.31 ! [F: a > a > a,A: a,B: a] :
% 0.07/0.31 ( ( semilattice_a @ F )
% 0.07/0.31 => ( ( F @ A @ ( F @ A @ B ) )
% 0.07/0.31 = ( F @ A @ B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice.left_idem
% 0.07/0.31 thf(fact_285_semilattice_Oright__idem,axiom,
% 0.07/0.31 ! [F: a > a > a,A: a,B: a] :
% 0.07/0.31 ( ( semilattice_a @ F )
% 0.07/0.31 => ( ( F @ ( F @ A @ B ) @ B )
% 0.07/0.31 = ( F @ A @ B ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice.right_idem
% 0.07/0.31 thf(fact_286_product__lists_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( product_lists_list_a @ nil_list_list_a )
% 0.07/0.31 = ( cons_list_list_a @ nil_list_a @ nil_list_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % product_lists.simps(1)
% 0.07/0.31 thf(fact_287_product__lists_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( product_lists_a @ nil_list_a )
% 0.07/0.31 = ( cons_list_a @ nil_a @ nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % product_lists.simps(1)
% 0.07/0.31 thf(fact_288_bind__simps_I2_J,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a,F: a > list_list_a] :
% 0.07/0.31 ( ( bind_a_list_a @ ( cons_a @ X @ Xs ) @ F )
% 0.07/0.31 = ( append_list_a @ ( F @ X ) @ ( bind_a_list_a @ Xs @ F ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % bind_simps(2)
% 0.07/0.31 thf(fact_289_bind__simps_I2_J,axiom,
% 0.07/0.31 ! [X: list_a,Xs: list_list_a,F: list_a > list_a] :
% 0.07/0.31 ( ( bind_list_a_a @ ( cons_list_a @ X @ Xs ) @ F )
% 0.07/0.31 = ( append_a @ ( F @ X ) @ ( bind_list_a_a @ Xs @ F ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % bind_simps(2)
% 0.07/0.31 thf(fact_290_bind__simps_I2_J,axiom,
% 0.07/0.31 ! [X: list_a,Xs: list_list_a,F: list_a > list_list_a] :
% 0.07/0.31 ( ( bind_list_a_list_a @ ( cons_list_a @ X @ Xs ) @ F )
% 0.07/0.31 = ( append_list_a @ ( F @ X ) @ ( bind_list_a_list_a @ Xs @ F ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % bind_simps(2)
% 0.07/0.31 thf(fact_291_bind__simps_I2_J,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a,F: a > list_a] :
% 0.07/0.31 ( ( bind_a_a @ ( cons_a @ X @ Xs ) @ F )
% 0.07/0.31 = ( append_a @ ( F @ X ) @ ( bind_a_a @ Xs @ F ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % bind_simps(2)
% 0.07/0.31 thf(fact_292_bind__simps_I1_J,axiom,
% 0.07/0.31 ! [F: a > list_list_a] :
% 0.07/0.31 ( ( bind_a_list_a @ nil_a @ F )
% 0.07/0.31 = nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % bind_simps(1)
% 0.07/0.31 thf(fact_293_bind__simps_I1_J,axiom,
% 0.07/0.31 ! [F: list_a > list_a] :
% 0.07/0.31 ( ( bind_list_a_a @ nil_list_a @ F )
% 0.07/0.31 = nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % bind_simps(1)
% 0.07/0.31 thf(fact_294_bind__simps_I1_J,axiom,
% 0.07/0.31 ! [F: list_a > list_list_a] :
% 0.07/0.31 ( ( bind_list_a_list_a @ nil_list_a @ F )
% 0.07/0.31 = nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % bind_simps(1)
% 0.07/0.31 thf(fact_295_bind__simps_I1_J,axiom,
% 0.07/0.31 ! [F: a > list_a] :
% 0.07/0.31 ( ( bind_a_a @ nil_a @ F )
% 0.07/0.31 = nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % bind_simps(1)
% 0.07/0.31 thf(fact_296_abel__semigroup__def,axiom,
% 0.07/0.31 ( abel_s1075322906list_a
% 0.07/0.31 = ( ^ [F2: list_a > list_a > list_a] :
% 0.07/0.31 ( ( semigroup_list_a @ F2 )
% 0.07/0.31 & ( abel_s374399671list_a @ F2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup_def
% 0.07/0.31 thf(fact_297_abel__semigroup__def,axiom,
% 0.07/0.31 ( abel_semigroup_a
% 0.07/0.31 = ( ^ [F2: a > a > a] :
% 0.07/0.31 ( ( semigroup_a @ F2 )
% 0.07/0.31 & ( abel_s2117090225ioms_a @ F2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup_def
% 0.07/0.31 thf(fact_298_abel__semigroup_Ointro,axiom,
% 0.07/0.31 ! [F: list_a > list_a > list_a] :
% 0.07/0.31 ( ( semigroup_list_a @ F )
% 0.07/0.31 => ( ( abel_s374399671list_a @ F )
% 0.07/0.31 => ( abel_s1075322906list_a @ F ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup.intro
% 0.07/0.31 thf(fact_299_abel__semigroup_Ointro,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ( semigroup_a @ F )
% 0.07/0.31 => ( ( abel_s2117090225ioms_a @ F )
% 0.07/0.31 => ( abel_semigroup_a @ F ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup.intro
% 0.07/0.31 thf(fact_300_abel__semigroup__axioms_Ointro,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ! [A2: a,B2: a] :
% 0.07/0.31 ( ( F @ A2 @ B2 )
% 0.07/0.31 = ( F @ B2 @ A2 ) )
% 0.07/0.31 => ( abel_s2117090225ioms_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup_axioms.intro
% 0.07/0.31 thf(fact_301_abel__semigroup__axioms__def,axiom,
% 0.07/0.31 ( abel_s2117090225ioms_a
% 0.07/0.31 = ( ^ [F2: a > a > a] :
% 0.07/0.31 ! [A3: a,B3: a] :
% 0.07/0.31 ( ( F2 @ A3 @ B3 )
% 0.07/0.31 = ( F2 @ B3 @ A3 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup_axioms_def
% 0.07/0.31 thf(fact_302_abel__semigroup_Oaxioms_I2_J,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ( abel_semigroup_a @ F )
% 0.07/0.31 => ( abel_s2117090225ioms_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % abel_semigroup.axioms(2)
% 0.07/0.31 thf(fact_303_semilattice_Ointro,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ( abel_semigroup_a @ F )
% 0.07/0.31 => ( ( semilattice_axioms_a @ F )
% 0.07/0.31 => ( semilattice_a @ F ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice.intro
% 0.07/0.31 thf(fact_304_semilattice__def,axiom,
% 0.07/0.31 ( semilattice_a
% 0.07/0.31 = ( ^ [F2: a > a > a] :
% 0.07/0.31 ( ( abel_semigroup_a @ F2 )
% 0.07/0.31 & ( semilattice_axioms_a @ F2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice_def
% 0.07/0.31 thf(fact_305_semilattice_Oaxioms_I2_J,axiom,
% 0.07/0.31 ! [F: a > a > a] :
% 0.07/0.31 ( ( semilattice_a @ F )
% 0.07/0.31 => ( semilattice_axioms_a @ F ) ) ).
% 0.07/0.31
% 0.07/0.31 % semilattice.axioms(2)
% 0.07/0.31 thf(fact_306_subseqs_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( subseqs_list_a @ nil_list_a )
% 0.07/0.31 = ( cons_list_list_a @ nil_list_a @ nil_list_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % subseqs.simps(1)
% 0.07/0.31 thf(fact_307_subseqs_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( subseqs_a @ nil_a )
% 0.07/0.31 = ( cons_list_a @ nil_a @ nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % subseqs.simps(1)
% 0.07/0.31 thf(fact_308_maps__simps_I1_J,axiom,
% 0.07/0.31 ! [F: a > list_list_a,X: a,Xs: list_a] :
% 0.07/0.31 ( ( maps_a_list_a @ F @ ( cons_a @ X @ Xs ) )
% 0.07/0.31 = ( append_list_a @ ( F @ X ) @ ( maps_a_list_a @ F @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % maps_simps(1)
% 0.07/0.31 thf(fact_309_maps__simps_I1_J,axiom,
% 0.07/0.31 ! [F: list_a > list_a,X: list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( maps_list_a_a @ F @ ( cons_list_a @ X @ Xs ) )
% 0.07/0.31 = ( append_a @ ( F @ X ) @ ( maps_list_a_a @ F @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % maps_simps(1)
% 0.07/0.31 thf(fact_310_maps__simps_I1_J,axiom,
% 0.07/0.31 ! [F: list_a > list_list_a,X: list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( maps_list_a_list_a @ F @ ( cons_list_a @ X @ Xs ) )
% 0.07/0.31 = ( append_list_a @ ( F @ X ) @ ( maps_list_a_list_a @ F @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % maps_simps(1)
% 0.07/0.31 thf(fact_311_maps__simps_I1_J,axiom,
% 0.07/0.31 ! [F: a > list_a,X: a,Xs: list_a] :
% 0.07/0.31 ( ( maps_a_a @ F @ ( cons_a @ X @ Xs ) )
% 0.07/0.31 = ( append_a @ ( F @ X ) @ ( maps_a_a @ F @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % maps_simps(1)
% 0.07/0.31 thf(fact_312_maps__simps_I2_J,axiom,
% 0.07/0.31 ! [F: a > list_list_a] :
% 0.07/0.31 ( ( maps_a_list_a @ F @ nil_a )
% 0.07/0.31 = nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % maps_simps(2)
% 0.07/0.31 thf(fact_313_maps__simps_I2_J,axiom,
% 0.07/0.31 ! [F: list_a > list_a] :
% 0.07/0.31 ( ( maps_list_a_a @ F @ nil_list_a )
% 0.07/0.31 = nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % maps_simps(2)
% 0.07/0.31 thf(fact_314_maps__simps_I2_J,axiom,
% 0.07/0.31 ! [F: list_a > list_list_a] :
% 0.07/0.31 ( ( maps_list_a_list_a @ F @ nil_list_a )
% 0.07/0.31 = nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % maps_simps(2)
% 0.07/0.31 thf(fact_315_maps__simps_I2_J,axiom,
% 0.07/0.31 ! [F: a > list_a] :
% 0.07/0.31 ( ( maps_a_a @ F @ nil_a )
% 0.07/0.31 = nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % maps_simps(2)
% 0.07/0.31 thf(fact_316_local_Otransp__less,axiom,
% 0.07/0.31 transp_a @ less ).
% 0.07/0.31
% 0.07/0.31 % local.transp_less
% 0.07/0.31 thf(fact_317_insert__Nil,axiom,
% 0.07/0.31 ! [X: list_a] :
% 0.07/0.31 ( ( insert_list_a @ X @ nil_list_a )
% 0.07/0.31 = ( cons_list_a @ X @ nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % insert_Nil
% 0.07/0.31 thf(fact_318_insert__Nil,axiom,
% 0.07/0.31 ! [X: a] :
% 0.07/0.31 ( ( insert_a @ X @ nil_a )
% 0.07/0.31 = ( cons_a @ X @ nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % insert_Nil
% 0.07/0.31 thf(fact_319_concat__eq__append__conv,axiom,
% 0.07/0.31 ! [Xss2: list_list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.07/0.31 ( ( ( concat_list_a @ Xss2 )
% 0.07/0.31 = ( append_list_a @ Ys @ Zs2 ) )
% 0.07/0.31 = ( ( ( Xss2 = nil_list_list_a )
% 0.07/0.31 => ( ( Ys = nil_list_a )
% 0.07/0.31 & ( Zs2 = nil_list_a ) ) )
% 0.07/0.31 & ( ( Xss2 != nil_list_list_a )
% 0.07/0.31 => ? [Xss1: list_list_list_a,Xs2: list_list_a,Xs4: list_list_a,Xss22: list_list_list_a] :
% 0.07/0.31 ( ( Xss2
% 0.07/0.31 = ( append_list_list_a @ Xss1 @ ( cons_list_list_a @ ( append_list_a @ Xs2 @ Xs4 ) @ Xss22 ) ) )
% 0.07/0.31 & ( Ys
% 0.07/0.31 = ( append_list_a @ ( concat_list_a @ Xss1 ) @ Xs2 ) )
% 0.07/0.31 & ( Zs2
% 0.07/0.31 = ( append_list_a @ Xs4 @ ( concat_list_a @ Xss22 ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % concat_eq_append_conv
% 0.07/0.31 thf(fact_320_concat__eq__append__conv,axiom,
% 0.07/0.31 ! [Xss2: list_list_a,Ys: list_a,Zs2: list_a] :
% 0.07/0.31 ( ( ( concat_a @ Xss2 )
% 0.07/0.31 = ( append_a @ Ys @ Zs2 ) )
% 0.07/0.31 = ( ( ( Xss2 = nil_list_a )
% 0.07/0.31 => ( ( Ys = nil_a )
% 0.07/0.31 & ( Zs2 = nil_a ) ) )
% 0.07/0.31 & ( ( Xss2 != nil_list_a )
% 0.07/0.31 => ? [Xss1: list_list_a,Xs2: list_a,Xs4: list_a,Xss22: list_list_a] :
% 0.07/0.31 ( ( Xss2
% 0.07/0.31 = ( append_list_a @ Xss1 @ ( cons_list_a @ ( append_a @ Xs2 @ Xs4 ) @ Xss22 ) ) )
% 0.07/0.31 & ( Ys
% 0.07/0.31 = ( append_a @ ( concat_a @ Xss1 ) @ Xs2 ) )
% 0.07/0.31 & ( Zs2
% 0.07/0.31 = ( append_a @ Xs4 @ ( concat_a @ Xss22 ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % concat_eq_append_conv
% 0.07/0.31 thf(fact_321_rotate1_Osimps_I2_J,axiom,
% 0.07/0.31 ! [X: list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( rotate1_list_a @ ( cons_list_a @ X @ Xs ) )
% 0.07/0.31 = ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % rotate1.simps(2)
% 0.07/0.31 thf(fact_322_rotate1_Osimps_I2_J,axiom,
% 0.07/0.31 ! [X: a,Xs: list_a] :
% 0.07/0.31 ( ( rotate1_a @ ( cons_a @ X @ Xs ) )
% 0.07/0.31 = ( append_a @ Xs @ ( cons_a @ X @ nil_a ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % rotate1.simps(2)
% 0.07/0.31 thf(fact_323_rotate1__is__Nil__conv,axiom,
% 0.07/0.31 ! [Xs: list_list_a] :
% 0.07/0.31 ( ( ( rotate1_list_a @ Xs )
% 0.07/0.31 = nil_list_a )
% 0.07/0.31 = ( Xs = nil_list_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % rotate1_is_Nil_conv
% 0.07/0.31 thf(fact_324_rotate1__is__Nil__conv,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ( ( ( rotate1_a @ Xs )
% 0.07/0.31 = nil_a )
% 0.07/0.31 = ( Xs = nil_a ) ) ).
% 0.07/0.31
% 0.07/0.31 % rotate1_is_Nil_conv
% 0.07/0.31 thf(fact_325_concat__append,axiom,
% 0.07/0.31 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 0.07/0.31 ( ( concat_list_a @ ( append_list_list_a @ Xs @ Ys ) )
% 0.07/0.31 = ( append_list_a @ ( concat_list_a @ Xs ) @ ( concat_list_a @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % concat_append
% 0.07/0.31 thf(fact_326_concat__append,axiom,
% 0.07/0.31 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( concat_a @ ( append_list_a @ Xs @ Ys ) )
% 0.07/0.31 = ( append_a @ ( concat_a @ Xs ) @ ( concat_a @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % concat_append
% 0.07/0.31 thf(fact_327_concat_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( concat_list_a @ nil_list_list_a )
% 0.07/0.31 = nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % concat.simps(1)
% 0.07/0.31 thf(fact_328_concat_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( concat_a @ nil_list_a )
% 0.07/0.31 = nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % concat.simps(1)
% 0.07/0.31 thf(fact_329_concat_Osimps_I2_J,axiom,
% 0.07/0.31 ! [X: list_list_a,Xs: list_list_list_a] :
% 0.07/0.31 ( ( concat_list_a @ ( cons_list_list_a @ X @ Xs ) )
% 0.07/0.31 = ( append_list_a @ X @ ( concat_list_a @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % concat.simps(2)
% 0.07/0.31 thf(fact_330_concat_Osimps_I2_J,axiom,
% 0.07/0.31 ! [X: list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( concat_a @ ( cons_list_a @ X @ Xs ) )
% 0.07/0.31 = ( append_a @ X @ ( concat_a @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % concat.simps(2)
% 0.07/0.31 thf(fact_331_rotate1_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( rotate1_list_a @ nil_list_a )
% 0.07/0.31 = nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % rotate1.simps(1)
% 0.07/0.31 thf(fact_332_rotate1_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( rotate1_a @ nil_a )
% 0.07/0.31 = nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % rotate1.simps(1)
% 0.07/0.31 thf(fact_333_concat__eq__appendD,axiom,
% 0.07/0.31 ! [Xss2: list_list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 0.07/0.31 ( ( ( concat_list_a @ Xss2 )
% 0.07/0.31 = ( append_list_a @ Ys @ Zs2 ) )
% 0.07/0.31 => ( ( Xss2 != nil_list_list_a )
% 0.07/0.31 => ? [Xss12: list_list_list_a,Xs3: list_list_a,Xs5: list_list_a,Xss23: list_list_list_a] :
% 0.07/0.31 ( ( Xss2
% 0.07/0.31 = ( append_list_list_a @ Xss12 @ ( cons_list_list_a @ ( append_list_a @ Xs3 @ Xs5 ) @ Xss23 ) ) )
% 0.07/0.31 & ( Ys
% 0.07/0.31 = ( append_list_a @ ( concat_list_a @ Xss12 ) @ Xs3 ) )
% 0.07/0.31 & ( Zs2
% 0.07/0.31 = ( append_list_a @ Xs5 @ ( concat_list_a @ Xss23 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % concat_eq_appendD
% 0.07/0.31 thf(fact_334_concat__eq__appendD,axiom,
% 0.07/0.31 ! [Xss2: list_list_a,Ys: list_a,Zs2: list_a] :
% 0.07/0.31 ( ( ( concat_a @ Xss2 )
% 0.07/0.31 = ( append_a @ Ys @ Zs2 ) )
% 0.07/0.31 => ( ( Xss2 != nil_list_a )
% 0.07/0.31 => ? [Xss12: list_list_a,Xs3: list_a,Xs5: list_a,Xss23: list_list_a] :
% 0.07/0.31 ( ( Xss2
% 0.07/0.31 = ( append_list_a @ Xss12 @ ( cons_list_a @ ( append_a @ Xs3 @ Xs5 ) @ Xss23 ) ) )
% 0.07/0.31 & ( Ys
% 0.07/0.31 = ( append_a @ ( concat_a @ Xss12 ) @ Xs3 ) )
% 0.07/0.31 & ( Zs2
% 0.07/0.31 = ( append_a @ Xs5 @ ( concat_a @ Xss23 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % concat_eq_appendD
% 0.07/0.31 thf(fact_335_butlast__snoc,axiom,
% 0.07/0.31 ! [Xs: list_list_a,X: list_a] :
% 0.07/0.31 ( ( butlast_list_a @ ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) ) )
% 0.07/0.31 = Xs ) ).
% 0.07/0.31
% 0.07/0.31 % butlast_snoc
% 0.07/0.31 thf(fact_336_butlast__snoc,axiom,
% 0.07/0.31 ! [Xs: list_a,X: a] :
% 0.07/0.31 ( ( butlast_a @ ( append_a @ Xs @ ( cons_a @ X @ nil_a ) ) )
% 0.07/0.31 = Xs ) ).
% 0.07/0.31
% 0.07/0.31 % butlast_snoc
% 0.07/0.31 thf(fact_337_list__ex1__simps_I1_J,axiom,
% 0.07/0.31 ! [P: list_a > $o] :
% 0.07/0.31 ~ ( list_ex1_list_a @ P @ nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % list_ex1_simps(1)
% 0.07/0.31 thf(fact_338_list__ex1__simps_I1_J,axiom,
% 0.07/0.31 ! [P: a > $o] :
% 0.07/0.31 ~ ( list_ex1_a @ P @ nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % list_ex1_simps(1)
% 0.07/0.31 thf(fact_339_butlast__append,axiom,
% 0.07/0.31 ! [Ys: list_list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( ( Ys = nil_list_a )
% 0.07/0.31 => ( ( butlast_list_a @ ( append_list_a @ Xs @ Ys ) )
% 0.07/0.31 = ( butlast_list_a @ Xs ) ) )
% 0.07/0.31 & ( ( Ys != nil_list_a )
% 0.07/0.31 => ( ( butlast_list_a @ ( append_list_a @ Xs @ Ys ) )
% 0.07/0.31 = ( append_list_a @ Xs @ ( butlast_list_a @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % butlast_append
% 0.07/0.31 thf(fact_340_butlast__append,axiom,
% 0.07/0.31 ! [Ys: list_a,Xs: list_a] :
% 0.07/0.31 ( ( ( Ys = nil_a )
% 0.07/0.31 => ( ( butlast_a @ ( append_a @ Xs @ Ys ) )
% 0.07/0.31 = ( butlast_a @ Xs ) ) )
% 0.07/0.31 & ( ( Ys != nil_a )
% 0.07/0.31 => ( ( butlast_a @ ( append_a @ Xs @ Ys ) )
% 0.07/0.31 = ( append_a @ Xs @ ( butlast_a @ Ys ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % butlast_append
% 0.07/0.31 thf(fact_341_butlast_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( butlast_list_a @ nil_list_a )
% 0.07/0.31 = nil_list_a ) ).
% 0.07/0.31
% 0.07/0.31 % butlast.simps(1)
% 0.07/0.31 thf(fact_342_butlast_Osimps_I1_J,axiom,
% 0.07/0.31 ( ( butlast_a @ nil_a )
% 0.07/0.31 = nil_a ) ).
% 0.07/0.31
% 0.07/0.31 % butlast.simps(1)
% 0.07/0.31 thf(fact_343_butlast_Osimps_I2_J,axiom,
% 0.07/0.31 ! [Xs: list_list_a,X: list_a] :
% 0.07/0.31 ( ( ( Xs = nil_list_a )
% 0.07/0.31 => ( ( butlast_list_a @ ( cons_list_a @ X @ Xs ) )
% 0.07/0.31 = nil_list_a ) )
% 0.07/0.31 & ( ( Xs != nil_list_a )
% 0.07/0.31 => ( ( butlast_list_a @ ( cons_list_a @ X @ Xs ) )
% 0.07/0.31 = ( cons_list_a @ X @ ( butlast_list_a @ Xs ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % butlast.simps(2)
% 0.07/0.31 thf(fact_344_butlast_Osimps_I2_J,axiom,
% 0.07/0.31 ! [Xs: list_a,X: a] :
% 0.07/0.31 ( ( ( Xs = nil_a )
% 0.07/0.31 => ( ( butlast_a @ ( cons_a @ X @ Xs ) )
% 0.07/0.31 = nil_a ) )
% 0.07/0.31 & ( ( Xs != nil_a )
% 0.07/0.31 => ( ( butlast_a @ ( cons_a @ X @ Xs ) )
% 0.07/0.31 = ( cons_a @ X @ ( butlast_a @ Xs ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % butlast.simps(2)
% 0.07/0.31 thf(fact_345_append__butlast__last__id,axiom,
% 0.07/0.31 ! [Xs: list_list_a] :
% 0.07/0.31 ( ( Xs != nil_list_a )
% 0.07/0.31 => ( ( append_list_a @ ( butlast_list_a @ Xs ) @ ( cons_list_a @ ( last_list_a @ Xs ) @ nil_list_a ) )
% 0.07/0.31 = Xs ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_butlast_last_id
% 0.07/0.31 thf(fact_346_append__butlast__last__id,axiom,
% 0.07/0.31 ! [Xs: list_a] :
% 0.07/0.31 ( ( Xs != nil_a )
% 0.07/0.31 => ( ( append_a @ ( butlast_a @ Xs ) @ ( cons_a @ ( last_a @ Xs ) @ nil_a ) )
% 0.07/0.31 = Xs ) ) ).
% 0.07/0.31
% 0.07/0.31 % append_butlast_last_id
% 0.07/0.31 thf(fact_347_snoc__eq__iff__butlast,axiom,
% 0.07/0.31 ! [Xs: list_list_a,X: list_a,Ys: list_list_a] :
% 0.07/0.31 ( ( ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) )
% 0.07/0.31 = Ys )
% 0.07/0.31 = ( ( Ys != nil_list_a )
% 0.07/0.31 & ( ( butlast_list_a @ Ys )
% 0.07/0.31 = Xs )
% 0.07/0.31 & ( ( last_list_a @ Ys )
% 0.07/0.31 = X ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % snoc_eq_iff_butlast
% 0.07/0.31 thf(fact_348_snoc__eq__iff__butlast,axiom,
% 0.07/0.31 ! [Xs: list_a,X: a,Ys: list_a] :
% 0.07/0.31 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 0.07/0.31 = Ys )
% 0.07/0.31 = ( ( Ys != nil_a )
% 0.07/0.31 & ( ( butlast_a @ Ys )
% 0.07/0.31 = Xs )
% 0.07/0.31 & ( ( last_a @ Ys )
% 0.07/0.31 = X ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % snoc_eq_iff_butlast
% 0.07/0.31 thf(fact_349_last__appendR,axiom,
% 0.07/0.31 ! [Ys: list_list_a,Xs: list_list_a] :
% 0.07/0.31 ( ( Ys != nil_list_a )
% 0.07/0.31 => ( ( last_list_a @ ( append_list_a @ Xs @ Ys ) )
% 0.07/0.31 = ( last_list_a @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % last_appendR
% 0.07/0.31 thf(fact_350_last__appendR,axiom,
% 0.07/0.31 ! [Ys: list_a,Xs: list_a] :
% 0.07/0.31 ( ( Ys != nil_a )
% 0.07/0.31 => ( ( last_a @ ( append_a @ Xs @ Ys ) )
% 0.07/0.31 = ( last_a @ Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % last_appendR
% 0.07/0.31 thf(fact_351_last__appendL,axiom,
% 0.07/0.31 ! [Ys: list_a,Xs: list_a] :
% 0.07/0.31 ( ( Ys = nil_a )
% 0.07/0.31 => ( ( last_a @ ( append_a @ Xs @ Ys ) )
% 0.07/0.31 = ( last_a @ Xs ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % last_appendL
% 0.07/0.31
% 0.07/0.31 % Conjectures (6)
% 0.07/0.31 thf(conj_0,hypothesis,
% 0.07/0.31 ( b
% 0.07/0.31 = ( inf @ b @ c ) ) ).
% 0.07/0.31
% 0.07/0.31 thf(conj_1,hypothesis,
% 0.07/0.31 ( ( inf @ c @ ( sup @ b @ c ) )
% 0.07/0.31 = b ) ).
% 0.07/0.31
% 0.07/0.31 thf(conj_2,hypothesis,
% 0.07/0.31 ( a2
% 0.07/0.31 = ( sup @ b @ c ) ) ).
% 0.07/0.31
% 0.07/0.31 thf(conj_3,hypothesis,
% 0.07/0.31 less @ b @ ( sup @ b @ c ) ).
% 0.07/0.31
% 0.07/0.31 thf(conj_4,hypothesis,
% 0.07/0.31 ( ( inf @ c @ ( sup @ b @ c ) )
% 0.07/0.31 = c ) ).
% 0.07/0.31
% 0.07/0.31 thf(conj_5,conjecture,
% 0.07/0.31 $false ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 1.95/1.16 ---- Embedded in THF ---
% 1.95/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.95/1.16 %%% Generated on Tue Feb 24 03:26:41 EST 2026
% 1.95/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.95/1.16 %%% Logic specification used:
% 1.95/1.16 %%% thf(spec, logic, $$dhol).
% 1.95/1.16
% 1.95/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2DTF2662.p
% See solution above
% 1.95/1.16 ------------------------
% 1.95/1.19 ---- Cleaned THF ---
% 1.95/1.19 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 1.95/1.19 list_list_list_a: $tType ).
% 1.95/1.19
% 1.95/1.19 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 1.95/1.19 list_list_a: $tType ).
% 1.95/1.19
% 1.95/1.19 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 1.95/1.19 list_a: $tType ).
% 1.95/1.19
% 1.95/1.19 thf(ty_n_tf__a,type,
% 1.95/1.19 a: $tType ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 1.95/1.19 finite40241356em_a_a: ( a > a > a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Groups_Oabel__semigroup_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 abel_s1075322906list_a: ( list_a > list_a > list_a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 1.95/1.19 abel_semigroup_a: ( a > a > a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Groups_Oabel__semigroup__axioms_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 abel_s374399671list_a: ( list_a > list_a > list_a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Groups_Oabel__semigroup__axioms_001tf__a,type,
% 1.95/1.19 abel_s2117090225ioms_a: ( a > a > a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Groups_Osemigroup_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 1.95/1.19 semigr656274520list_a: ( list_list_a > list_list_a > list_list_a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Groups_Osemigroup_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 semigroup_list_a: ( list_a > list_a > list_a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 1.95/1.19 semigroup_a: ( a > a > a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 1.95/1.19 semilattice_a: ( a > a > a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Lattices_Osemilattice__axioms_001tf__a,type,
% 1.95/1.19 semilattice_axioms_a: ( a > a > a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 1.95/1.19 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oappend_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 1.95/1.19 append_list_list_a: list_list_list_a > list_list_list_a > list_list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oappend_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 append_list_a: list_list_a > list_list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oappend_001tf__a,type,
% 1.95/1.19 append_a: list_a > list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001tf__a,type,
% 1.95/1.19 bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Obind_001tf__a_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Obind_001tf__a_001tf__a,type,
% 1.95/1.19 bind_a_a: list_a > ( a > list_a ) > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 butlast_list_a: list_list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Obutlast_001tf__a,type,
% 1.95/1.19 butlast_a: list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oconcat_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 concat_list_a: list_list_list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oconcat_001tf__a,type,
% 1.95/1.19 concat_a: list_list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oinsert_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 insert_list_a: list_a > list_list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oinsert_001tf__a,type,
% 1.95/1.19 insert_a: a > list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olast_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 last_list_a: list_list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olast_001tf__a,type,
% 1.95/1.19 last_a: list_a > a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 1.95/1.19 cons_list_list_a: list_list_a > list_list_list_a > list_list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 cons_list_a: list_a > list_list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 1.95/1.19 cons_a: a > list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 1.95/1.19 nil_list_list_a: list_list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 nil_list_a: list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 1.95/1.19 nil_a: list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olist__ex1_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Olist__ex1_001tf__a,type,
% 1.95/1.19 list_ex1_a: ( a > $o ) > list_a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001tf__a,type,
% 1.95/1.19 maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Omaps_001tf__a_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Omaps_001tf__a_001tf__a,type,
% 1.95/1.19 maps_a_a: ( a > list_a ) > list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oord_Olexordp_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 lexordp_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oord_Olexordp_001tf__a,type,
% 1.95/1.19 lexordp_a: ( a > a > $o ) > list_a > list_a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oord_Olexordp__eq_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 lexordp_eq_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oord_Olexordp__eq_001tf__a,type,
% 1.95/1.19 lexordp_eq_a: ( a > a > $o ) > list_a > list_a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oproduct__lists_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 product_lists_list_a: list_list_list_a > list_list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Oproduct__lists_001tf__a,type,
% 1.95/1.19 product_lists_a: list_list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Orotate1_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 rotate1_list_a: list_list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Orotate1_001tf__a,type,
% 1.95/1.19 rotate1_a: list_a > list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Osubseqs_001t__List__Olist_Itf__a_J,type,
% 1.95/1.19 subseqs_list_a: list_list_a > list_list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_List_Osubseqs_001tf__a,type,
% 1.95/1.19 subseqs_a: list_a > list_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_OM5__lattice_001tf__a,type,
% 1.95/1.19 modula1376131916tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_ON5__lattice_001tf__a,type,
% 1.95/1.19 modula397570059tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 1.95/1.19 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 1.95/1.19 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 1.95/1.19 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 1.95/1.19 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 1.95/1.19 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ono__distrib_001tf__a,type,
% 1.95/1.19 modula1962211574trib_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_c_Relation_Otransp_001tf__a,type,
% 1.95/1.19 transp_a: ( a > a > $o ) > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_v_a,type,
% 1.95/1.19 a2: a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_v_b,type,
% 1.95/1.19 b: a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_v_c,type,
% 1.95/1.19 c: a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_v_inf,type,
% 1.95/1.19 inf: a > a > a ).
% 1.95/1.19
% 1.95/1.19 thf(sy_v_less,type,
% 1.95/1.19 less: a > a > $o ).
% 1.95/1.19
% 1.95/1.19 thf(sy_v_sup,type,
% 1.95/1.19 sup: a > a > a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_0_local_Odual__order_Oasym,axiom,
% 1.95/1.19 ! [B: a,A: a] :
% 1.95/1.19 ( ( less @ B @ A )
% 1.95/1.19 => ~ ( less @ A @ B ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_1_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 1.95/1.19 ! [B: a,A: a] :
% 1.95/1.19 ( ( less @ B @ A )
% 1.95/1.19 => ( A != B ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_2_local_Odual__order_Ostrict__trans,axiom,
% 1.95/1.19 ! [B: a,A: a,C: a] :
% 1.95/1.19 ( ( less @ B @ A )
% 1.95/1.19 => ( ( less @ C @ B )
% 1.95/1.19 => ( less @ C @ A ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_3_local_Oless__asym,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ~ ( less @ Y @ X ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_4_local_Oless__asym_H,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( less @ A @ B )
% 1.95/1.19 => ~ ( less @ B @ A ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_5_local_Oless__imp__neq,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ( X != Y ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_6_local_Oless__imp__not__eq,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ( X != Y ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_7_local_Oless__imp__not__eq2,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ( Y != X ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_8_local_Oless__imp__not__less,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ~ ( less @ Y @ X ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_9_local_Oless__imp__triv,axiom,
% 1.95/1.19 ! [X: a,Y: a,P: $o] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ( ( less @ Y @ X )
% 1.95/1.19 => P ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_10_local_Oless__irrefl,axiom,
% 1.95/1.19 ! [X: a] :
% 1.95/1.19 ~ ( less @ X @ X ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_11_local_Oless__not__sym,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ~ ( less @ Y @ X ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_12_local_Oless__trans,axiom,
% 1.95/1.19 ! [X: a,Y: a,Z: a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ( ( less @ Y @ Z )
% 1.95/1.19 => ( less @ X @ Z ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_13_local_Oord__eq__less__trans,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( A = B )
% 1.95/1.19 => ( ( less @ B @ C )
% 1.95/1.19 => ( less @ A @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_14_local_Oord__less__eq__trans,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( less @ A @ B )
% 1.95/1.19 => ( ( B = C )
% 1.95/1.19 => ( less @ A @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_15_local_Oorder_Oasym,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( less @ A @ B )
% 1.95/1.19 => ~ ( less @ B @ A ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_16_local_Oorder_Oirrefl,axiom,
% 1.95/1.19 ! [A: a] :
% 1.95/1.19 ~ ( less @ A @ A ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_17_local_Oorder_Ostrict__implies__not__eq,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( less @ A @ B )
% 1.95/1.19 => ( A != B ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_18_local_Oorder_Ostrict__trans,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( less @ A @ B )
% 1.95/1.19 => ( ( less @ B @ C )
% 1.95/1.19 => ( less @ A @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_19_local_Oinf_Oassoc,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( inf @ ( inf @ A @ B ) @ C )
% 1.95/1.19 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_20_local_Oinf_Ocommute,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( inf @ A @ B )
% 1.95/1.19 = ( inf @ B @ A ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_21_local_Oinf_Oleft__commute,axiom,
% 1.95/1.19 ! [B: a,A: a,C: a] :
% 1.95/1.19 ( ( inf @ B @ ( inf @ A @ C ) )
% 1.95/1.19 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_22_local_Oinf__assoc,axiom,
% 1.95/1.19 ! [X: a,Y: a,Z: a] :
% 1.95/1.19 ( ( inf @ ( inf @ X @ Y ) @ Z )
% 1.95/1.19 = ( inf @ X @ ( inf @ Y @ Z ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_23_local_Oinf__commute,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( inf @ X @ Y )
% 1.95/1.19 = ( inf @ Y @ X ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_24_local_Oinf__left__commute,axiom,
% 1.95/1.19 ! [X: a,Y: a,Z: a] :
% 1.95/1.19 ( ( inf @ X @ ( inf @ Y @ Z ) )
% 1.95/1.19 = ( inf @ Y @ ( inf @ X @ Z ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_25_local_Osup_Oassoc,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( sup @ ( sup @ A @ B ) @ C )
% 1.95/1.19 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_26_local_Osup_Ocommute,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( sup @ A @ B )
% 1.95/1.19 = ( sup @ B @ A ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_27_local_Osup_Oleft__commute,axiom,
% 1.95/1.19 ! [B: a,A: a,C: a] :
% 1.95/1.19 ( ( sup @ B @ ( sup @ A @ C ) )
% 1.95/1.19 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_28_local_Osup__assoc,axiom,
% 1.95/1.19 ! [X: a,Y: a,Z: a] :
% 1.95/1.19 ( ( sup @ ( sup @ X @ Y ) @ Z )
% 1.95/1.19 = ( sup @ X @ ( sup @ Y @ Z ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_29_local_Osup__commute,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( sup @ X @ Y )
% 1.95/1.19 = ( sup @ Y @ X ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_30_local_Osup__left__commute,axiom,
% 1.95/1.19 ! [X: a,Y: a,Z: a] :
% 1.95/1.19 ( ( sup @ X @ ( sup @ Y @ Z ) )
% 1.95/1.19 = ( sup @ Y @ ( sup @ X @ Z ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_31_local_Oinf_Ostrict__boundedE,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( less @ A @ ( inf @ B @ C ) )
% 1.95/1.19 => ~ ( ( less @ A @ B )
% 1.95/1.19 => ~ ( less @ A @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_32_local_Oinf_Ostrict__coboundedI1,axiom,
% 1.95/1.19 ! [A: a,C: a,B: a] :
% 1.95/1.19 ( ( less @ A @ C )
% 1.95/1.19 => ( less @ ( inf @ A @ B ) @ C ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_33_local_Oinf_Ostrict__coboundedI2,axiom,
% 1.95/1.19 ! [B: a,C: a,A: a] :
% 1.95/1.19 ( ( less @ B @ C )
% 1.95/1.19 => ( less @ ( inf @ A @ B ) @ C ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_34_local_Oinf_Ostrict__order__iff,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( less @ A @ B )
% 1.95/1.19 = ( ( A
% 1.95/1.19 = ( inf @ A @ B ) )
% 1.95/1.19 & ( A != B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_35_local_Oless__infI1,axiom,
% 1.95/1.19 ! [A: a,X: a,B: a] :
% 1.95/1.19 ( ( less @ A @ X )
% 1.95/1.19 => ( less @ ( inf @ A @ B ) @ X ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_36_local_Oless__infI2,axiom,
% 1.95/1.19 ! [B: a,X: a,A: a] :
% 1.95/1.19 ( ( less @ B @ X )
% 1.95/1.19 => ( less @ ( inf @ A @ B ) @ X ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_37_local_Oless__supI1,axiom,
% 1.95/1.19 ! [X: a,A: a,B: a] :
% 1.95/1.19 ( ( less @ X @ A )
% 1.95/1.19 => ( less @ X @ ( sup @ A @ B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_38_local_Oless__supI2,axiom,
% 1.95/1.19 ! [X: a,B: a,A: a] :
% 1.95/1.19 ( ( less @ X @ B )
% 1.95/1.19 => ( less @ X @ ( sup @ A @ B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_39_local_Osup_Ostrict__boundedE,axiom,
% 1.95/1.19 ! [B: a,C: a,A: a] :
% 1.95/1.19 ( ( less @ ( sup @ B @ C ) @ A )
% 1.95/1.19 => ~ ( ( less @ B @ A )
% 1.95/1.19 => ~ ( less @ C @ A ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_40_local_Osup_Ostrict__coboundedI1,axiom,
% 1.95/1.19 ! [C: a,A: a,B: a] :
% 1.95/1.19 ( ( less @ C @ A )
% 1.95/1.19 => ( less @ C @ ( sup @ A @ B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_41_local_Osup_Ostrict__coboundedI2,axiom,
% 1.95/1.19 ! [C: a,B: a,A: a] :
% 1.95/1.19 ( ( less @ C @ B )
% 1.95/1.19 => ( less @ C @ ( sup @ A @ B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_42_local_Osup_Ostrict__order__iff,axiom,
% 1.95/1.19 ! [B: a,A: a] :
% 1.95/1.19 ( ( less @ B @ A )
% 1.95/1.19 = ( ( A
% 1.95/1.19 = ( sup @ A @ B ) )
% 1.95/1.19 & ( A != B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_43_local_Odistrib__imp1,axiom,
% 1.95/1.19 ! [X: a,Y: a,Z: a] :
% 1.95/1.19 ( ! [X2: a,Y2: a,Z2: a] :
% 1.95/1.19 ( ( inf @ X2 @ ( sup @ Y2 @ Z2 ) )
% 1.95/1.19 = ( sup @ ( inf @ X2 @ Y2 ) @ ( inf @ X2 @ Z2 ) ) )
% 1.95/1.19 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 1.95/1.19 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_44_local_Odistrib__imp2,axiom,
% 1.95/1.19 ! [X: a,Y: a,Z: a] :
% 1.95/1.19 ( ! [X2: a,Y2: a,Z2: a] :
% 1.95/1.19 ( ( sup @ X2 @ ( inf @ Y2 @ Z2 ) )
% 1.95/1.19 = ( inf @ ( sup @ X2 @ Y2 ) @ ( sup @ X2 @ Z2 ) ) )
% 1.95/1.19 => ( ( inf @ X @ ( sup @ Y @ Z ) )
% 1.95/1.19 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_45_local_Oinf_Oidem,axiom,
% 1.95/1.19 ! [A: a] :
% 1.95/1.19 ( ( inf @ A @ A )
% 1.95/1.19 = A ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_46_local_Oinf_Oleft__idem,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( inf @ A @ ( inf @ A @ B ) )
% 1.95/1.19 = ( inf @ A @ B ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_47_local_Oinf_Oright__idem,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( inf @ ( inf @ A @ B ) @ B )
% 1.95/1.19 = ( inf @ A @ B ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_48_local_Oinf__idem,axiom,
% 1.95/1.19 ! [X: a] :
% 1.95/1.19 ( ( inf @ X @ X )
% 1.95/1.19 = X ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_49_local_Oinf__left__idem,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( inf @ X @ ( inf @ X @ Y ) )
% 1.95/1.19 = ( inf @ X @ Y ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_50_local_Oinf__right__idem,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 1.95/1.19 = ( inf @ X @ Y ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_51_local_Osup_Oidem,axiom,
% 1.95/1.19 ! [A: a] :
% 1.95/1.19 ( ( sup @ A @ A )
% 1.95/1.19 = A ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_52_local_Osup_Oleft__idem,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( sup @ A @ ( sup @ A @ B ) )
% 1.95/1.19 = ( sup @ A @ B ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_53_local_Osup_Oright__idem,axiom,
% 1.95/1.19 ! [A: a,B: a] :
% 1.95/1.19 ( ( sup @ ( sup @ A @ B ) @ B )
% 1.95/1.19 = ( sup @ A @ B ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_54_local_Osup__idem,axiom,
% 1.95/1.19 ! [X: a] :
% 1.95/1.19 ( ( sup @ X @ X )
% 1.95/1.19 = X ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_55_local_Osup__left__idem,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( sup @ X @ ( sup @ X @ Y ) )
% 1.95/1.19 = ( sup @ X @ Y ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_56_M5__lattice__def,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
% 1.95/1.19 = ( ( ( inf @ A @ B )
% 1.95/1.19 = ( inf @ B @ C ) )
% 1.95/1.19 & ( ( inf @ C @ A )
% 1.95/1.19 = ( inf @ B @ C ) )
% 1.95/1.19 & ( ( sup @ A @ B )
% 1.95/1.19 = ( sup @ B @ C ) )
% 1.95/1.19 & ( ( sup @ C @ A )
% 1.95/1.19 = ( sup @ B @ C ) )
% 1.95/1.19 & ( less @ ( inf @ A @ B ) @ ( sup @ A @ B ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_57_N5__lattice__def,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula397570059tice_a @ inf @ less @ sup @ A @ B @ C )
% 1.95/1.19 = ( ( ( inf @ A @ C )
% 1.95/1.19 = ( inf @ B @ C ) )
% 1.95/1.19 & ( less @ A @ B )
% 1.95/1.19 & ( ( sup @ A @ C )
% 1.95/1.19 = ( sup @ B @ C ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_58_no__distrib__def,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C )
% 1.95/1.19 = ( less @ ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_59_local_Oinf__sup__absorb,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( inf @ X @ ( sup @ X @ Y ) )
% 1.95/1.19 = X ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_60_local_Osup__inf__absorb,axiom,
% 1.95/1.19 ! [X: a,Y: a] :
% 1.95/1.19 ( ( sup @ X @ ( inf @ X @ Y ) )
% 1.95/1.19 = X ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_61_local_Oa__join__d,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 1.95/1.19 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_62_local_Ob__join__d,axiom,
% 1.95/1.19 ! [B: a,A: a,C: a] :
% 1.95/1.19 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 1.95/1.19 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_63_local_Od__aux__def,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 1.95/1.19 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_64_local_Od__b__c__a,axiom,
% 1.95/1.19 ! [B: a,C: a,A: a] :
% 1.95/1.19 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 1.95/1.19 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_65_local_Od__c__a__b,axiom,
% 1.95/1.19 ! [C: a,A: a,B: a] :
% 1.95/1.19 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 1.95/1.19 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_66_local_Oa__meet__e,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 1.95/1.19 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_67_local_Ob__meet__e,axiom,
% 1.95/1.19 ! [B: a,A: a,C: a] :
% 1.95/1.19 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 1.95/1.19 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_68_local_Oc__meet__e,axiom,
% 1.95/1.19 ! [C: a,A: a,B: a] :
% 1.95/1.19 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 1.95/1.19 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_69_local_Oe__aux__def,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 1.95/1.19 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_70_local_Oe__b__c__a,axiom,
% 1.95/1.19 ! [B: a,C: a,A: a] :
% 1.95/1.19 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 1.95/1.19 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_71_local_Oe__c__a__b,axiom,
% 1.95/1.19 ! [C: a,A: a,B: a] :
% 1.95/1.19 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 1.95/1.19 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_72_local_Ocomp__fun__idem__sup,axiom,
% 1.95/1.19 finite40241356em_a_a @ sup ).
% 1.95/1.19
% 1.95/1.19 thf(fact_73_local_Ocomp__fun__idem__inf,axiom,
% 1.95/1.19 finite40241356em_a_a @ inf ).
% 1.95/1.19
% 1.95/1.19 thf(fact_74_local_Oc__aux__def,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 1.95/1.19 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_75_local_Ob__aux__def,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 1.95/1.19 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_76_local_Oa__aux__def,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 1.95/1.19 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_77_lattice_Ono__distrib_Ocong,axiom,
% 1.95/1.19 modula1962211574trib_a = modula1962211574trib_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_78_lattice_ON5__lattice_Ocong,axiom,
% 1.95/1.19 modula397570059tice_a = modula397570059tice_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_79_lattice_OM5__lattice_Ocong,axiom,
% 1.95/1.19 modula1376131916tice_a = modula1376131916tice_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_80_lattice_Oe__aux_Ocong,axiom,
% 1.95/1.19 modula1144073633_aux_a = modula1144073633_aux_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_81_lattice_Od__aux_Ocong,axiom,
% 1.95/1.19 modula1936294176_aux_a = modula1936294176_aux_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_82_local_Oc__a,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 1.95/1.19 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_83_local_Ob__a,axiom,
% 1.95/1.19 ! [A: a,B: a,C: a] :
% 1.95/1.19 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 1.95/1.19 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_84_local_Osup_Osemigroup__axioms,axiom,
% 1.95/1.19 semigroup_a @ sup ).
% 1.95/1.19
% 1.95/1.19 thf(fact_85_local_Oinf_Osemigroup__axioms,axiom,
% 1.95/1.19 semigroup_a @ inf ).
% 1.95/1.19
% 1.95/1.19 thf(fact_86_local_Osup_Osemilattice__axioms,axiom,
% 1.95/1.19 semilattice_a @ sup ).
% 1.95/1.19
% 1.95/1.19 thf(fact_87_local_Oinf_Osemilattice__axioms,axiom,
% 1.95/1.19 semilattice_a @ inf ).
% 1.95/1.19
% 1.95/1.19 thf(fact_88_lattice_Oa__aux_Ocong,axiom,
% 1.95/1.19 modula17988509_aux_a = modula17988509_aux_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_89_lattice_Ob__aux_Ocong,axiom,
% 1.95/1.19 modula1373251614_aux_a = modula1373251614_aux_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_90_lattice_Oc__aux_Ocong,axiom,
% 1.95/1.19 modula581031071_aux_a = modula581031071_aux_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_91_local_Osup_Oabel__semigroup__axioms,axiom,
% 1.95/1.19 abel_semigroup_a @ sup ).
% 1.95/1.19
% 1.95/1.19 thf(fact_92_local_Oinf_Oabel__semigroup__axioms,axiom,
% 1.95/1.19 abel_semigroup_a @ inf ).
% 1.95/1.19
% 1.95/1.19 thf(fact_93_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 1.95/1.19 lattic1885654924_set_a @ sup ).
% 1.95/1.19
% 1.95/1.19 thf(fact_94_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 1.95/1.19 lattic1885654924_set_a @ inf ).
% 1.95/1.19
% 1.95/1.19 thf(fact_95_local_Olexordp__eq__refl,axiom,
% 1.95/1.19 ! [Xs: list_a] : ( lexordp_eq_a @ less @ Xs @ Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_96_local_Olexordp__eq_ONil,axiom,
% 1.95/1.19 ! [Ys: list_a] : ( lexordp_eq_a @ less @ nil_a @ Ys ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_97_abel__semigroup_Oaxioms_I1_J,axiom,
% 1.95/1.19 ! [F: list_a > list_a > list_a] :
% 1.95/1.19 ( ( abel_s1075322906list_a @ F )
% 1.95/1.19 => ( semigroup_list_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_98_abel__semigroup_Oaxioms_I1_J,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ( abel_semigroup_a @ F )
% 1.95/1.19 => ( semigroup_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_99_semilattice__set_Oaxioms,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ( lattic1885654924_set_a @ F )
% 1.95/1.19 => ( semilattice_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_100_semilattice__set_Ointro,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ( semilattice_a @ F )
% 1.95/1.19 => ( lattic1885654924_set_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_101_semilattice__set__def,axiom,
% 1.95/1.19 lattic1885654924_set_a = semilattice_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_102_local_Olexordp__eq__simps_I1_J,axiom,
% 1.95/1.19 ! [Ys: list_a] : ( lexordp_eq_a @ less @ nil_a @ Ys ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_103_local_Olexordp__eq__simps_I2_J,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ( ( lexordp_eq_a @ less @ Xs @ nil_a )
% 1.95/1.19 = ( Xs = nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_104_abel__semigroup_Oleft__commute,axiom,
% 1.95/1.19 ! [F: a > a > a,B: a,A: a,C: a] :
% 1.95/1.19 ( ( abel_semigroup_a @ F )
% 1.95/1.19 => ( ( F @ B @ ( F @ A @ C ) )
% 1.95/1.19 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_105_abel__semigroup_Ocommute,axiom,
% 1.95/1.19 ! [F: a > a > a,A: a,B: a] :
% 1.95/1.19 ( ( abel_semigroup_a @ F )
% 1.95/1.19 => ( ( F @ A @ B )
% 1.95/1.19 = ( F @ B @ A ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_106_semigroup_Ointro,axiom,
% 1.95/1.19 ! [F: list_a > list_a > list_a] :
% 1.95/1.19 ( ! [A2: list_a,B2: list_a,C2: list_a] :
% 1.95/1.19 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 1.95/1.19 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 1.95/1.19 => ( semigroup_list_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_107_semigroup_Ointro,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ! [A2: a,B2: a,C2: a] :
% 1.95/1.19 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 1.95/1.19 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 1.95/1.19 => ( semigroup_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_108_semigroup_Oassoc,axiom,
% 1.95/1.19 ! [F: list_a > list_a > list_a,A: list_a,B: list_a,C: list_a] :
% 1.95/1.19 ( ( semigroup_list_a @ F )
% 1.95/1.19 => ( ( F @ ( F @ A @ B ) @ C )
% 1.95/1.19 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_109_semigroup_Oassoc,axiom,
% 1.95/1.19 ! [F: a > a > a,A: a,B: a,C: a] :
% 1.95/1.19 ( ( semigroup_a @ F )
% 1.95/1.19 => ( ( F @ ( F @ A @ B ) @ C )
% 1.95/1.19 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_110_semigroup__def,axiom,
% 1.95/1.19 ( semigroup_list_a
% 1.95/1.19 = ( ^ [F2: list_a > list_a > list_a] :
% 1.95/1.19 ! [A3: list_a,B3: list_a,C3: list_a] :
% 1.95/1.19 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 1.95/1.19 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_111_semigroup__def,axiom,
% 1.95/1.19 ( semigroup_a
% 1.95/1.19 = ( ^ [F2: a > a > a] :
% 1.95/1.19 ! [A3: a,B3: a,C3: a] :
% 1.95/1.19 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 1.95/1.19 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_112_ord_Olexordp__eq__simps_I2_J,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,Xs: list_list_a] :
% 1.95/1.19 ( ( lexordp_eq_list_a @ Less @ Xs @ nil_list_a )
% 1.95/1.19 = ( Xs = nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_113_ord_Olexordp__eq__simps_I2_J,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Xs: list_a] :
% 1.95/1.19 ( ( lexordp_eq_a @ Less @ Xs @ nil_a )
% 1.95/1.19 = ( Xs = nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_114_ord_Olexordp__eq__simps_I1_J,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,Ys: list_list_a] : ( lexordp_eq_list_a @ Less @ nil_list_a @ Ys ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_115_ord_Olexordp__eq__simps_I1_J,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Ys: list_a] : ( lexordp_eq_a @ Less @ nil_a @ Ys ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_116_local_Olexordp__eq_Osimps,axiom,
% 1.95/1.19 ! [A1: list_a,A22: list_a] :
% 1.95/1.19 ( ( lexordp_eq_a @ less @ A1 @ A22 )
% 1.95/1.19 = ( ? [Ys2: list_a] :
% 1.95/1.19 ( ( A1 = nil_a )
% 1.95/1.19 & ( A22 = Ys2 ) )
% 1.95/1.19 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A22
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ( less @ X3 @ Y3 ) )
% 1.95/1.19 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A22
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ~ ( less @ X3 @ Y3 )
% 1.95/1.19 & ~ ( less @ Y3 @ X3 )
% 1.95/1.19 & ( lexordp_eq_a @ less @ Xs2 @ Ys2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_117_local_Olexordp__eq_Oinducts,axiom,
% 1.95/1.19 ! [X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 1.95/1.19 ( ( lexordp_eq_a @ less @ X1 @ X22 )
% 1.95/1.19 => ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ( less @ X2 @ Y2 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ~ ( less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( less @ Y2 @ X2 )
% 1.95/1.19 => ( ( lexordp_eq_a @ less @ Xs3 @ Ys3 )
% 1.95/1.19 => ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 1.95/1.19 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_118_local_Olexordp__eq_Ocases,axiom,
% 1.95/1.19 ! [A1: list_a,A22: list_a] :
% 1.95/1.19 ( ( lexordp_eq_a @ less @ A1 @ A22 )
% 1.95/1.19 => ( ( A1 != nil_a )
% 1.95/1.19 => ( ! [X2: a] :
% 1.95/1.19 ( ? [Xs3: list_a] :
% 1.95/1.19 ( A1
% 1.95/1.19 = ( cons_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Y2: a] :
% 1.95/1.19 ( ? [Ys3: list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 = ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ~ ( less @ X2 @ Y2 ) ) )
% 1.95/1.19 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Ys3: list_a] :
% 1.95/1.19 ( ( A22
% 1.95/1.19 = ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ~ ( less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( less @ Y2 @ X2 )
% 1.95/1.19 => ~ ( lexordp_eq_a @ less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_119_local_Olexordp__eq_OCons__eq,axiom,
% 1.95/1.19 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ~ ( less @ X @ Y )
% 1.95/1.19 => ( ~ ( less @ Y @ X )
% 1.95/1.19 => ( ( lexordp_eq_a @ less @ Xs @ Ys )
% 1.95/1.19 => ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_120_local_Olexordp__eq_OCons,axiom,
% 1.95/1.19 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_121_list_Oinject,axiom,
% 1.95/1.19 ! [X21: list_a,X222: list_list_a,Y21: list_a,Y22: list_list_a] :
% 1.95/1.19 ( ( ( cons_list_a @ X21 @ X222 )
% 1.95/1.19 = ( cons_list_a @ Y21 @ Y22 ) )
% 1.95/1.19 = ( ( X21 = Y21 )
% 1.95/1.19 & ( X222 = Y22 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_122_list_Oinject,axiom,
% 1.95/1.19 ! [X21: a,X222: list_a,Y21: a,Y22: list_a] :
% 1.95/1.19 ( ( ( cons_a @ X21 @ X222 )
% 1.95/1.19 = ( cons_a @ Y21 @ Y22 ) )
% 1.95/1.19 = ( ( X21 = Y21 )
% 1.95/1.19 & ( X222 = Y22 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_123_ord_Olexordp__eq__simps_I4_J,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a,Y: list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) )
% 1.95/1.19 = ( ( Less @ X @ Y )
% 1.95/1.19 | ( ~ ( Less @ Y @ X )
% 1.95/1.19 & ( lexordp_eq_list_a @ Less @ Xs @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_124_ord_Olexordp__eq__simps_I4_J,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X: a,Xs: list_a,Y: a,Ys: list_a] :
% 1.95/1.19 ( ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 1.95/1.19 = ( ( Less @ X @ Y )
% 1.95/1.19 | ( ~ ( Less @ Y @ X )
% 1.95/1.19 & ( lexordp_eq_a @ Less @ Xs @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_125_ord_Olexordp__eq__simps_I3_J,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a] :
% 1.95/1.19 ~ ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_126_ord_Olexordp__eq__simps_I3_J,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X: a,Xs: list_a] :
% 1.95/1.19 ~ ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_127_local_Olexordp__eq__simps_I4_J,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a,Y: a,Ys: list_a] :
% 1.95/1.19 ( ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 1.95/1.19 = ( ( less @ X @ Y )
% 1.95/1.19 | ( ~ ( less @ Y @ X )
% 1.95/1.19 & ( lexordp_eq_a @ less @ Xs @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_128_local_Olexordp__eq__simps_I3_J,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a] :
% 1.95/1.19 ~ ( lexordp_eq_a @ less @ ( cons_a @ X @ Xs ) @ nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_129_map__tailrec__rev_Oinduct,axiom,
% 1.95/1.19 ! [P: ( list_a > a ) > list_list_a > list_a > $o,A0: list_a > a,A1: list_list_a,A22: list_a] :
% 1.95/1.19 ( ! [F3: list_a > a,X_1: list_a] : ( P @ F3 @ nil_list_a @ X_1 )
% 1.95/1.19 => ( ! [F3: list_a > a,A2: list_a,As: list_list_a,Bs: list_a] :
% 1.95/1.19 ( ( P @ F3 @ As @ ( cons_a @ ( F3 @ A2 ) @ Bs ) )
% 1.95/1.19 => ( P @ F3 @ ( cons_list_a @ A2 @ As ) @ Bs ) )
% 1.95/1.19 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_130_map__tailrec__rev_Oinduct,axiom,
% 1.95/1.19 ! [P: ( a > list_a ) > list_a > list_list_a > $o,A0: a > list_a,A1: list_a,A22: list_list_a] :
% 1.95/1.19 ( ! [F3: a > list_a,X_1: list_list_a] : ( P @ F3 @ nil_a @ X_1 )
% 1.95/1.19 => ( ! [F3: a > list_a,A2: a,As: list_a,Bs: list_list_a] :
% 1.95/1.19 ( ( P @ F3 @ As @ ( cons_list_a @ ( F3 @ A2 ) @ Bs ) )
% 1.95/1.19 => ( P @ F3 @ ( cons_a @ A2 @ As ) @ Bs ) )
% 1.95/1.19 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_131_map__tailrec__rev_Oinduct,axiom,
% 1.95/1.19 ! [P: ( list_a > list_a ) > list_list_a > list_list_a > $o,A0: list_a > list_a,A1: list_list_a,A22: list_list_a] :
% 1.95/1.19 ( ! [F3: list_a > list_a,X_1: list_list_a] : ( P @ F3 @ nil_list_a @ X_1 )
% 1.95/1.19 => ( ! [F3: list_a > list_a,A2: list_a,As: list_list_a,Bs: list_list_a] :
% 1.95/1.19 ( ( P @ F3 @ As @ ( cons_list_a @ ( F3 @ A2 ) @ Bs ) )
% 1.95/1.19 => ( P @ F3 @ ( cons_list_a @ A2 @ As ) @ Bs ) )
% 1.95/1.19 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_132_map__tailrec__rev_Oinduct,axiom,
% 1.95/1.19 ! [P: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A22: list_a] :
% 1.95/1.19 ( ! [F3: a > a,X_1: list_a] : ( P @ F3 @ nil_a @ X_1 )
% 1.95/1.19 => ( ! [F3: a > a,A2: a,As: list_a,Bs: list_a] :
% 1.95/1.19 ( ( P @ F3 @ As @ ( cons_a @ ( F3 @ A2 ) @ Bs ) )
% 1.95/1.19 => ( P @ F3 @ ( cons_a @ A2 @ As ) @ Bs ) )
% 1.95/1.19 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_133_list__nonempty__induct,axiom,
% 1.95/1.19 ! [Xs: list_list_a,P: list_list_a > $o] :
% 1.95/1.19 ( ( Xs != nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a] :
% 1.95/1.19 ( ( Xs3 != nil_list_a )
% 1.95/1.19 => ( ( P @ Xs3 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) ) ) )
% 1.95/1.19 => ( P @ Xs ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_134_list__nonempty__induct,axiom,
% 1.95/1.19 ! [Xs: list_a,P: list_a > $o] :
% 1.95/1.19 ( ( Xs != nil_a )
% 1.95/1.19 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a] :
% 1.95/1.19 ( ( Xs3 != nil_a )
% 1.95/1.19 => ( ( P @ Xs3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) ) ) )
% 1.95/1.19 => ( P @ Xs ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_135_successively_Oinduct,axiom,
% 1.95/1.19 ! [P: ( list_a > list_a > $o ) > list_list_a > $o,A0: list_a > list_a > $o,A1: list_list_a] :
% 1.95/1.19 ( ! [P2: list_a > list_a > $o] : ( P @ P2 @ nil_list_a )
% 1.95/1.19 => ( ! [P2: list_a > list_a > $o,X2: list_a] : ( P @ P2 @ ( cons_list_a @ X2 @ nil_list_a ) )
% 1.95/1.19 => ( ! [P2: list_a > list_a > $o,X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 1.95/1.19 ( ( P @ P2 @ ( cons_list_a @ Y2 @ Xs3 ) )
% 1.95/1.19 => ( P @ P2 @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) )
% 1.95/1.19 => ( P @ A0 @ A1 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_136_successively_Oinduct,axiom,
% 1.95/1.19 ! [P: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 1.95/1.19 ( ! [P2: a > a > $o] : ( P @ P2 @ nil_a )
% 1.95/1.19 => ( ! [P2: a > a > $o,X2: a] : ( P @ P2 @ ( cons_a @ X2 @ nil_a ) )
% 1.95/1.19 => ( ! [P2: a > a > $o,X2: a,Y2: a,Xs3: list_a] :
% 1.95/1.19 ( ( P @ P2 @ ( cons_a @ Y2 @ Xs3 ) )
% 1.95/1.19 => ( P @ P2 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) )
% 1.95/1.19 => ( P @ A0 @ A1 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_137_remdups__adj_Oinduct,axiom,
% 1.95/1.19 ! [P: list_list_a > $o,A0: list_list_a] :
% 1.95/1.19 ( ( P @ nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 1.95/1.19 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 1.95/1.19 ( ( ( X2 = Y2 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) ) )
% 1.95/1.19 => ( ( ( X2 != Y2 )
% 1.95/1.19 => ( P @ ( cons_list_a @ Y2 @ Xs3 ) ) )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) ) )
% 1.95/1.19 => ( P @ A0 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_138_remdups__adj_Oinduct,axiom,
% 1.95/1.19 ! [P: list_a > $o,A0: list_a] :
% 1.95/1.19 ( ( P @ nil_a )
% 1.95/1.19 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a] :
% 1.95/1.19 ( ( ( X2 = Y2 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) ) )
% 1.95/1.19 => ( ( ( X2 != Y2 )
% 1.95/1.19 => ( P @ ( cons_a @ Y2 @ Xs3 ) ) )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) ) )
% 1.95/1.19 => ( P @ A0 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_139_sorted__wrt_Oinduct,axiom,
% 1.95/1.19 ! [P: ( list_a > list_a > $o ) > list_list_a > $o,A0: list_a > list_a > $o,A1: list_list_a] :
% 1.95/1.19 ( ! [P2: list_a > list_a > $o] : ( P @ P2 @ nil_list_a )
% 1.95/1.19 => ( ! [P2: list_a > list_a > $o,X2: list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ( P @ P2 @ Ys3 )
% 1.95/1.19 => ( P @ P2 @ ( cons_list_a @ X2 @ Ys3 ) ) )
% 1.95/1.19 => ( P @ A0 @ A1 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_140_sorted__wrt_Oinduct,axiom,
% 1.95/1.19 ! [P: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 1.95/1.19 ( ! [P2: a > a > $o] : ( P @ P2 @ nil_a )
% 1.95/1.19 => ( ! [P2: a > a > $o,X2: a,Ys3: list_a] :
% 1.95/1.19 ( ( P @ P2 @ Ys3 )
% 1.95/1.19 => ( P @ P2 @ ( cons_a @ X2 @ Ys3 ) ) )
% 1.95/1.19 => ( P @ A0 @ A1 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_141_remdups__adj_Ocases,axiom,
% 1.95/1.19 ! [X: list_list_a] :
% 1.95/1.19 ( ( X != nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a] :
% 1.95/1.19 ( X
% 1.95/1.19 != ( cons_list_a @ X2 @ nil_list_a ) )
% 1.95/1.19 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 1.95/1.19 ( X
% 1.95/1.19 != ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Xs3 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_142_remdups__adj_Ocases,axiom,
% 1.95/1.19 ! [X: list_a] :
% 1.95/1.19 ( ( X != nil_a )
% 1.95/1.19 => ( ! [X2: a] :
% 1.95/1.19 ( X
% 1.95/1.19 != ( cons_a @ X2 @ nil_a ) )
% 1.95/1.19 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 1.95/1.19 ( X
% 1.95/1.19 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs3 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_143_transpose_Ocases,axiom,
% 1.95/1.19 ! [X: list_list_list_a] :
% 1.95/1.19 ( ( X != nil_list_list_a )
% 1.95/1.19 => ( ! [Xss: list_list_list_a] :
% 1.95/1.19 ( X
% 1.95/1.19 != ( cons_list_list_a @ nil_list_a @ Xss ) )
% 1.95/1.19 => ~ ! [X2: list_a,Xs3: list_list_a,Xss: list_list_list_a] :
% 1.95/1.19 ( X
% 1.95/1.19 != ( cons_list_list_a @ ( cons_list_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_144_transpose_Ocases,axiom,
% 1.95/1.19 ! [X: list_list_a] :
% 1.95/1.19 ( ( X != nil_list_a )
% 1.95/1.19 => ( ! [Xss: list_list_a] :
% 1.95/1.19 ( X
% 1.95/1.19 != ( cons_list_a @ nil_a @ Xss ) )
% 1.95/1.19 => ~ ! [X2: a,Xs3: list_a,Xss: list_list_a] :
% 1.95/1.19 ( X
% 1.95/1.19 != ( cons_list_a @ ( cons_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_145_shuffles_Oinduct,axiom,
% 1.95/1.19 ! [P: list_list_a > list_list_a > $o,A0: list_list_a,A1: list_list_a] :
% 1.95/1.19 ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 1.95/1.19 => ( ! [Xs3: list_list_a] : ( P @ Xs3 @ nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a,Y2: list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ( P @ Xs3 @ ( cons_list_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ( P @ ( cons_list_a @ X2 @ Xs3 ) @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) )
% 1.95/1.19 => ( P @ A0 @ A1 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_146_shuffles_Oinduct,axiom,
% 1.95/1.19 ! [P: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 1.95/1.19 ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 1.95/1.19 => ( ! [Xs3: list_a] : ( P @ Xs3 @ nil_a )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a,Y2: a,Ys3: list_a] :
% 1.95/1.19 ( ( P @ Xs3 @ ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ( P @ ( cons_a @ X2 @ Xs3 ) @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) )
% 1.95/1.19 => ( P @ A0 @ A1 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_147_induct__list012,axiom,
% 1.95/1.19 ! [P: list_list_a > $o,Xs: list_list_a] :
% 1.95/1.19 ( ( P @ nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 1.95/1.19 => ( ! [X2: list_a,Y2: list_a,Zs: list_list_a] :
% 1.95/1.19 ( ( P @ Zs )
% 1.95/1.19 => ( ( P @ ( cons_list_a @ Y2 @ Zs ) )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ ( cons_list_a @ Y2 @ Zs ) ) ) ) )
% 1.95/1.19 => ( P @ Xs ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_148_induct__list012,axiom,
% 1.95/1.19 ! [P: list_a > $o,Xs: list_a] :
% 1.95/1.19 ( ( P @ nil_a )
% 1.95/1.19 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Zs: list_a] :
% 1.95/1.19 ( ( P @ Zs )
% 1.95/1.19 => ( ( P @ ( cons_a @ Y2 @ Zs ) )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Zs ) ) ) ) )
% 1.95/1.19 => ( P @ Xs ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_149_splice_Oinduct,axiom,
% 1.95/1.19 ! [P: list_list_a > list_list_a > $o,A0: list_list_a,A1: list_list_a] :
% 1.95/1.19 ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ( P @ Ys3 @ Xs3 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ Ys3 ) )
% 1.95/1.19 => ( P @ A0 @ A1 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_150_splice_Oinduct,axiom,
% 1.95/1.19 ! [P: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 1.95/1.19 ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ( P @ Ys3 @ Xs3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ Ys3 ) )
% 1.95/1.19 => ( P @ A0 @ A1 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_151_list__induct2_H,axiom,
% 1.95/1.19 ! [P: list_a > list_list_a > $o,Xs: list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( P @ nil_a @ nil_list_a )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a] : ( P @ ( cons_a @ X2 @ Xs3 ) @ nil_list_a )
% 1.95/1.19 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a,Y2: list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_152_list__induct2_H,axiom,
% 1.95/1.19 ! [P: list_list_a > list_a > $o,Xs: list_list_a,Ys: list_a] :
% 1.95/1.19 ( ( P @ nil_list_a @ nil_a )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a] : ( P @ ( cons_list_a @ X2 @ Xs3 ) @ nil_a )
% 1.95/1.19 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_list_a @ ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a,Y2: a,Ys3: list_a] :
% 1.95/1.19 ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_153_list__induct2_H,axiom,
% 1.95/1.19 ! [P: list_list_a > list_list_a > $o,Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( P @ nil_list_a @ nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a] : ( P @ ( cons_list_a @ X2 @ Xs3 ) @ nil_list_a )
% 1.95/1.19 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_list_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a,Y2: list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_154_list__induct2_H,axiom,
% 1.95/1.19 ! [P: list_a > list_a > $o,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( P @ nil_a @ nil_a )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a] : ( P @ ( cons_a @ X2 @ Xs3 ) @ nil_a )
% 1.95/1.19 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a,Y2: a,Ys3: list_a] :
% 1.95/1.19 ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_155_neq__Nil__conv,axiom,
% 1.95/1.19 ! [Xs: list_list_a] :
% 1.95/1.19 ( ( Xs != nil_list_a )
% 1.95/1.19 = ( ? [Y3: list_a,Ys2: list_list_a] :
% 1.95/1.19 ( Xs
% 1.95/1.19 = ( cons_list_a @ Y3 @ Ys2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_156_neq__Nil__conv,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ( ( Xs != nil_a )
% 1.95/1.19 = ( ? [Y3: a,Ys2: list_a] :
% 1.95/1.19 ( Xs
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_157_list_Oinducts,axiom,
% 1.95/1.19 ! [P: list_list_a > $o,List: list_list_a] :
% 1.95/1.19 ( ( P @ nil_list_a )
% 1.95/1.19 => ( ! [X12: list_a,X23: list_list_a] :
% 1.95/1.19 ( ( P @ X23 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X12 @ X23 ) ) )
% 1.95/1.19 => ( P @ List ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_158_list_Oinducts,axiom,
% 1.95/1.19 ! [P: list_a > $o,List: list_a] :
% 1.95/1.19 ( ( P @ nil_a )
% 1.95/1.19 => ( ! [X12: a,X23: list_a] :
% 1.95/1.19 ( ( P @ X23 )
% 1.95/1.19 => ( P @ ( cons_a @ X12 @ X23 ) ) )
% 1.95/1.19 => ( P @ List ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_159_list_Oexhaust,axiom,
% 1.95/1.19 ! [Y: list_list_a] :
% 1.95/1.19 ( ( Y != nil_list_a )
% 1.95/1.19 => ~ ! [X212: list_a,X223: list_list_a] :
% 1.95/1.19 ( Y
% 1.95/1.19 != ( cons_list_a @ X212 @ X223 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_160_list_Oexhaust,axiom,
% 1.95/1.19 ! [Y: list_a] :
% 1.95/1.19 ( ( Y != nil_a )
% 1.95/1.19 => ~ ! [X212: a,X223: list_a] :
% 1.95/1.19 ( Y
% 1.95/1.19 != ( cons_a @ X212 @ X223 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_161_list_OdiscI,axiom,
% 1.95/1.19 ! [List: list_list_a,X21: list_a,X222: list_list_a] :
% 1.95/1.19 ( ( List
% 1.95/1.19 = ( cons_list_a @ X21 @ X222 ) )
% 1.95/1.19 => ( List != nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_162_list_OdiscI,axiom,
% 1.95/1.19 ! [List: list_a,X21: a,X222: list_a] :
% 1.95/1.19 ( ( List
% 1.95/1.19 = ( cons_a @ X21 @ X222 ) )
% 1.95/1.19 => ( List != nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_163_list_Odistinct_I1_J,axiom,
% 1.95/1.19 ! [X21: list_a,X222: list_list_a] :
% 1.95/1.19 ( nil_list_a
% 1.95/1.19 != ( cons_list_a @ X21 @ X222 ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_164_list_Odistinct_I1_J,axiom,
% 1.95/1.19 ! [X21: a,X222: list_a] :
% 1.95/1.19 ( nil_a
% 1.95/1.19 != ( cons_a @ X21 @ X222 ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_165_not__Cons__self2,axiom,
% 1.95/1.19 ! [X: list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( cons_list_a @ X @ Xs )
% 1.95/1.19 != Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_166_not__Cons__self2,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a] :
% 1.95/1.19 ( ( cons_a @ X @ Xs )
% 1.95/1.19 != Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_167_ord_Olexordp__eq_OCons__eq,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ~ ( Less @ X @ Y )
% 1.95/1.19 => ( ~ ( Less @ Y @ X )
% 1.95/1.19 => ( ( lexordp_eq_list_a @ Less @ Xs @ Ys )
% 1.95/1.19 => ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_168_ord_Olexordp__eq_OCons__eq,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ~ ( Less @ X @ Y )
% 1.95/1.19 => ( ~ ( Less @ Y @ X )
% 1.95/1.19 => ( ( lexordp_eq_a @ Less @ Xs @ Ys )
% 1.95/1.19 => ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_169_ord_Olexordp__eq_OCons,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( Less @ X @ Y )
% 1.95/1.19 => ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_170_ord_Olexordp__eq_OCons,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( Less @ X @ Y )
% 1.95/1.19 => ( lexordp_eq_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_171_ord_Olexordp__eq_Oinducts,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X1: list_list_a,X22: list_list_a,P: list_list_a > list_list_a > $o] :
% 1.95/1.19 ( ( lexordp_eq_list_a @ Less @ X1 @ X22 )
% 1.95/1.19 => ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 1.95/1.19 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ~ ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( Less @ Y2 @ X2 )
% 1.95/1.19 => ( ( lexordp_eq_list_a @ Less @ Xs3 @ Ys3 )
% 1.95/1.19 => ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) ) ) )
% 1.95/1.19 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_172_ord_Olexordp__eq_Oinducts,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 1.95/1.19 ( ( lexordp_eq_a @ Less @ X1 @ X22 )
% 1.95/1.19 => ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ~ ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( Less @ Y2 @ X2 )
% 1.95/1.19 => ( ( lexordp_eq_a @ Less @ Xs3 @ Ys3 )
% 1.95/1.19 => ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 1.95/1.19 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_173_ord_Olexordp__eq_Osimps,axiom,
% 1.95/1.19 ( lexordp_eq_list_a
% 1.95/1.19 = ( ^ [Less2: list_a > list_a > $o,A12: list_list_a,A23: list_list_a] :
% 1.95/1.19 ( ? [Ys2: list_list_a] :
% 1.95/1.19 ( ( A12 = nil_list_a )
% 1.95/1.19 & ( A23 = Ys2 ) )
% 1.95/1.19 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 1.95/1.19 ( ( A12
% 1.95/1.19 = ( cons_list_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_list_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ( Less2 @ X3 @ Y3 ) )
% 1.95/1.19 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 1.95/1.19 ( ( A12
% 1.95/1.19 = ( cons_list_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_list_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ~ ( Less2 @ X3 @ Y3 )
% 1.95/1.19 & ~ ( Less2 @ Y3 @ X3 )
% 1.95/1.19 & ( lexordp_eq_list_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_174_ord_Olexordp__eq_Osimps,axiom,
% 1.95/1.19 ( lexordp_eq_a
% 1.95/1.19 = ( ^ [Less2: a > a > $o,A12: list_a,A23: list_a] :
% 1.95/1.19 ( ? [Ys2: list_a] :
% 1.95/1.19 ( ( A12 = nil_a )
% 1.95/1.19 & ( A23 = Ys2 ) )
% 1.95/1.19 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 1.95/1.19 ( ( A12
% 1.95/1.19 = ( cons_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ( Less2 @ X3 @ Y3 ) )
% 1.95/1.19 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 1.95/1.19 ( ( A12
% 1.95/1.19 = ( cons_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ~ ( Less2 @ X3 @ Y3 )
% 1.95/1.19 & ~ ( Less2 @ Y3 @ X3 )
% 1.95/1.19 & ( lexordp_eq_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_175_ord_Olexordp__eq_Ocases,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,A1: list_list_a,A22: list_list_a] :
% 1.95/1.19 ( ( lexordp_eq_list_a @ Less @ A1 @ A22 )
% 1.95/1.19 => ( ( A1 != nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a] :
% 1.95/1.19 ( ? [Xs3: list_list_a] :
% 1.95/1.19 ( A1
% 1.95/1.19 = ( cons_list_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Y2: list_a] :
% 1.95/1.19 ( ? [Ys3: list_list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 = ( cons_list_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ~ ( Less @ X2 @ Y2 ) ) )
% 1.95/1.19 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_list_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Ys3: list_list_a] :
% 1.95/1.19 ( ( A22
% 1.95/1.19 = ( cons_list_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ~ ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( Less @ Y2 @ X2 )
% 1.95/1.19 => ~ ( lexordp_eq_list_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_176_ord_Olexordp__eq_Ocases,axiom,
% 1.95/1.19 ! [Less: a > a > $o,A1: list_a,A22: list_a] :
% 1.95/1.19 ( ( lexordp_eq_a @ Less @ A1 @ A22 )
% 1.95/1.19 => ( ( A1 != nil_a )
% 1.95/1.19 => ( ! [X2: a] :
% 1.95/1.19 ( ? [Xs3: list_a] :
% 1.95/1.19 ( A1
% 1.95/1.19 = ( cons_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Y2: a] :
% 1.95/1.19 ( ? [Ys3: list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 = ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ~ ( Less @ X2 @ Y2 ) ) )
% 1.95/1.19 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Ys3: list_a] :
% 1.95/1.19 ( ( A22
% 1.95/1.19 = ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ~ ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( Less @ Y2 @ X2 )
% 1.95/1.19 => ~ ( lexordp_eq_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_177_ord_Olexordp__eq_Ocong,axiom,
% 1.95/1.19 lexordp_eq_a = lexordp_eq_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_178_ord_Olexordp__eq__refl,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Xs: list_a] : ( lexordp_eq_a @ Less @ Xs @ Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_179_ord_Olexordp__eq_ONil,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,Ys: list_list_a] : ( lexordp_eq_list_a @ Less @ nil_list_a @ Ys ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_180_ord_Olexordp__eq_ONil,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Ys: list_a] : ( lexordp_eq_a @ Less @ nil_a @ Ys ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_181_local_Olexordp_ONil,axiom,
% 1.95/1.19 ! [Y: a,Ys: list_a] : ( lexordp_a @ less @ nil_a @ ( cons_a @ Y @ Ys ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_182_local_Olexordp_Ocases,axiom,
% 1.95/1.19 ! [A1: list_a,A22: list_a] :
% 1.95/1.19 ( ( lexordp_a @ less @ A1 @ A22 )
% 1.95/1.19 => ( ( ( A1 = nil_a )
% 1.95/1.19 => ! [Y2: a,Ys3: list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 != ( cons_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: a] :
% 1.95/1.19 ( ? [Xs3: list_a] :
% 1.95/1.19 ( A1
% 1.95/1.19 = ( cons_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Y2: a] :
% 1.95/1.19 ( ? [Ys3: list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 = ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ~ ( less @ X2 @ Y2 ) ) )
% 1.95/1.19 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Ys3: list_a] :
% 1.95/1.19 ( ( A22
% 1.95/1.19 = ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ~ ( less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( less @ Y2 @ X2 )
% 1.95/1.19 => ~ ( lexordp_a @ less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_183_local_Olexordp_Oinducts,axiom,
% 1.95/1.19 ! [X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 1.95/1.19 ( ( lexordp_a @ less @ X1 @ X22 )
% 1.95/1.19 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ( less @ X2 @ Y2 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ~ ( less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( less @ Y2 @ X2 )
% 1.95/1.19 => ( ( lexordp_a @ less @ Xs3 @ Ys3 )
% 1.95/1.19 => ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 1.95/1.19 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_184_local_Olexordp_Osimps,axiom,
% 1.95/1.19 ! [A1: list_a,A22: list_a] :
% 1.95/1.19 ( ( lexordp_a @ less @ A1 @ A22 )
% 1.95/1.19 = ( ? [Y3: a,Ys2: list_a] :
% 1.95/1.19 ( ( A1 = nil_a )
% 1.95/1.19 & ( A22
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) ) )
% 1.95/1.19 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A22
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ( less @ X3 @ Y3 ) )
% 1.95/1.19 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A22
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ~ ( less @ X3 @ Y3 )
% 1.95/1.19 & ~ ( less @ Y3 @ X3 )
% 1.95/1.19 & ( lexordp_a @ less @ Xs2 @ Ys2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_185_local_Olexordp__antisym,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( lexordp_a @ less @ Xs @ Ys )
% 1.95/1.19 => ~ ( lexordp_a @ less @ Ys @ Xs ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_186_local_Olexordp__irreflexive,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ( ! [X2: a] :
% 1.95/1.19 ~ ( less @ X2 @ X2 )
% 1.95/1.19 => ~ ( lexordp_a @ less @ Xs @ Xs ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_187_local_Olexordp__irreflexive_H,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ~ ( lexordp_a @ less @ Xs @ Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_188_local_Olexordp_OCons__eq,axiom,
% 1.95/1.19 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ~ ( less @ X @ Y )
% 1.95/1.19 => ( ~ ( less @ Y @ X )
% 1.95/1.19 => ( ( lexordp_a @ less @ Xs @ Ys )
% 1.95/1.19 => ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_189_local_Olexordp_OCons,axiom,
% 1.95/1.19 ! [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_190_local_Olexordp__into__lexordp__eq,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( lexordp_a @ less @ Xs @ Ys )
% 1.95/1.19 => ( lexordp_eq_a @ less @ Xs @ Ys ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_191_ord_Olexordp__simps_I3_J,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X: list_a,Xs: list_list_a,Y: list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) )
% 1.95/1.19 = ( ( Less @ X @ Y )
% 1.95/1.19 | ( ~ ( Less @ Y @ X )
% 1.95/1.19 & ( lexordp_list_a @ Less @ Xs @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_192_ord_Olexordp__simps_I3_J,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X: a,Xs: list_a,Y: a,Ys: list_a] :
% 1.95/1.19 ( ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 1.95/1.19 = ( ( Less @ X @ Y )
% 1.95/1.19 | ( ~ ( Less @ Y @ X )
% 1.95/1.19 & ( lexordp_a @ Less @ Xs @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_193_ord_Olexordp__simps_I2_J,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,Xs: list_list_a] :
% 1.95/1.19 ~ ( lexordp_list_a @ Less @ Xs @ nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_194_ord_Olexordp__simps_I2_J,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Xs: list_a] :
% 1.95/1.19 ~ ( lexordp_a @ Less @ Xs @ nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_195_ord_Olexordp__simps_I1_J,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,Ys: list_list_a] :
% 1.95/1.19 ( ( lexordp_list_a @ Less @ nil_list_a @ Ys )
% 1.95/1.19 = ( Ys != nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_196_ord_Olexordp__simps_I1_J,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Ys: list_a] :
% 1.95/1.19 ( ( lexordp_a @ Less @ nil_a @ Ys )
% 1.95/1.19 = ( Ys != nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_197_local_Olexordp__simps_I3_J,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a,Y: a,Ys: list_a] :
% 1.95/1.19 ( ( lexordp_a @ less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) )
% 1.95/1.19 = ( ( less @ X @ Y )
% 1.95/1.19 | ( ~ ( less @ Y @ X )
% 1.95/1.19 & ( lexordp_a @ less @ Xs @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_198_local_Olexordp__simps_I1_J,axiom,
% 1.95/1.19 ! [Ys: list_a] :
% 1.95/1.19 ( ( lexordp_a @ less @ nil_a @ Ys )
% 1.95/1.19 = ( Ys != nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_199_local_Olexordp__simps_I2_J,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ~ ( lexordp_a @ less @ Xs @ nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_200_ord_Olexordp_Ocong,axiom,
% 1.95/1.19 lexordp_a = lexordp_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_201_ord_Olexordp__irreflexive,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Xs: list_a] :
% 1.95/1.19 ( ! [X2: a] :
% 1.95/1.19 ~ ( Less @ X2 @ X2 )
% 1.95/1.19 => ~ ( lexordp_a @ Less @ Xs @ Xs ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_202_ord_Olexordp_OCons__eq,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ~ ( Less @ X @ Y )
% 1.95/1.19 => ( ~ ( Less @ Y @ X )
% 1.95/1.19 => ( ( lexordp_list_a @ Less @ Xs @ Ys )
% 1.95/1.19 => ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_203_ord_Olexordp_OCons__eq,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ~ ( Less @ X @ Y )
% 1.95/1.19 => ( ~ ( Less @ Y @ X )
% 1.95/1.19 => ( ( lexordp_a @ Less @ Xs @ Ys )
% 1.95/1.19 => ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_204_ord_Olexordp_OCons,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( Less @ X @ Y )
% 1.95/1.19 => ( lexordp_list_a @ Less @ ( cons_list_a @ X @ Xs ) @ ( cons_list_a @ Y @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_205_ord_Olexordp_OCons,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X: a,Y: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( Less @ X @ Y )
% 1.95/1.19 => ( lexordp_a @ Less @ ( cons_a @ X @ Xs ) @ ( cons_a @ Y @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_206_ord_Olexordp__into__lexordp__eq,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( lexordp_a @ Less @ Xs @ Ys )
% 1.95/1.19 => ( lexordp_eq_a @ Less @ Xs @ Ys ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_207_ord_Olexordp_ONil,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,Y: list_a,Ys: list_list_a] : ( lexordp_list_a @ Less @ nil_list_a @ ( cons_list_a @ Y @ Ys ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_208_ord_Olexordp_ONil,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Y: a,Ys: list_a] : ( lexordp_a @ Less @ nil_a @ ( cons_a @ Y @ Ys ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_209_ord_Olexordp_Ocases,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,A1: list_list_a,A22: list_list_a] :
% 1.95/1.19 ( ( lexordp_list_a @ Less @ A1 @ A22 )
% 1.95/1.19 => ( ( ( A1 = nil_list_a )
% 1.95/1.19 => ! [Y2: list_a,Ys3: list_list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 != ( cons_list_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: list_a] :
% 1.95/1.19 ( ? [Xs3: list_list_a] :
% 1.95/1.19 ( A1
% 1.95/1.19 = ( cons_list_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Y2: list_a] :
% 1.95/1.19 ( ? [Ys3: list_list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 = ( cons_list_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ~ ( Less @ X2 @ Y2 ) ) )
% 1.95/1.19 => ~ ! [X2: list_a,Y2: list_a,Xs3: list_list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_list_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Ys3: list_list_a] :
% 1.95/1.19 ( ( A22
% 1.95/1.19 = ( cons_list_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ~ ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( Less @ Y2 @ X2 )
% 1.95/1.19 => ~ ( lexordp_list_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_210_ord_Olexordp_Ocases,axiom,
% 1.95/1.19 ! [Less: a > a > $o,A1: list_a,A22: list_a] :
% 1.95/1.19 ( ( lexordp_a @ Less @ A1 @ A22 )
% 1.95/1.19 => ( ( ( A1 = nil_a )
% 1.95/1.19 => ! [Y2: a,Ys3: list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 != ( cons_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: a] :
% 1.95/1.19 ( ? [Xs3: list_a] :
% 1.95/1.19 ( A1
% 1.95/1.19 = ( cons_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Y2: a] :
% 1.95/1.19 ( ? [Ys3: list_a] :
% 1.95/1.19 ( A22
% 1.95/1.19 = ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ~ ( Less @ X2 @ Y2 ) ) )
% 1.95/1.19 => ~ ! [X2: a,Y2: a,Xs3: list_a] :
% 1.95/1.19 ( ( A1
% 1.95/1.19 = ( cons_a @ X2 @ Xs3 ) )
% 1.95/1.19 => ! [Ys3: list_a] :
% 1.95/1.19 ( ( A22
% 1.95/1.19 = ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ~ ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( Less @ Y2 @ X2 )
% 1.95/1.19 => ~ ( lexordp_a @ Less @ Xs3 @ Ys3 ) ) ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_211_ord_Olexordp_Osimps,axiom,
% 1.95/1.19 ( lexordp_list_a
% 1.95/1.19 = ( ^ [Less2: list_a > list_a > $o,A12: list_list_a,A23: list_list_a] :
% 1.95/1.19 ( ? [Y3: list_a,Ys2: list_list_a] :
% 1.95/1.19 ( ( A12 = nil_list_a )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_list_a @ Y3 @ Ys2 ) ) )
% 1.95/1.19 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 1.95/1.19 ( ( A12
% 1.95/1.19 = ( cons_list_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_list_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ( Less2 @ X3 @ Y3 ) )
% 1.95/1.19 | ? [X3: list_a,Y3: list_a,Xs2: list_list_a,Ys2: list_list_a] :
% 1.95/1.19 ( ( A12
% 1.95/1.19 = ( cons_list_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_list_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ~ ( Less2 @ X3 @ Y3 )
% 1.95/1.19 & ~ ( Less2 @ Y3 @ X3 )
% 1.95/1.19 & ( lexordp_list_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_212_ord_Olexordp_Osimps,axiom,
% 1.95/1.19 ( lexordp_a
% 1.95/1.19 = ( ^ [Less2: a > a > $o,A12: list_a,A23: list_a] :
% 1.95/1.19 ( ? [Y3: a,Ys2: list_a] :
% 1.95/1.19 ( ( A12 = nil_a )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) ) )
% 1.95/1.19 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 1.95/1.19 ( ( A12
% 1.95/1.19 = ( cons_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ( Less2 @ X3 @ Y3 ) )
% 1.95/1.19 | ? [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 1.95/1.19 ( ( A12
% 1.95/1.19 = ( cons_a @ X3 @ Xs2 ) )
% 1.95/1.19 & ( A23
% 1.95/1.19 = ( cons_a @ Y3 @ Ys2 ) )
% 1.95/1.19 & ~ ( Less2 @ X3 @ Y3 )
% 1.95/1.19 & ~ ( Less2 @ Y3 @ X3 )
% 1.95/1.19 & ( lexordp_a @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_213_ord_Olexordp_Oinducts,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X1: list_list_a,X22: list_list_a,P: list_list_a > list_list_a > $o] :
% 1.95/1.19 ( ( lexordp_list_a @ Less @ X1 @ X22 )
% 1.95/1.19 => ( ! [Y2: list_a,Ys3: list_list_a] : ( P @ nil_list_a @ ( cons_list_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: list_a,Y2: list_a,Xs3: list_list_a,Ys3: list_list_a] :
% 1.95/1.19 ( ~ ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( Less @ Y2 @ X2 )
% 1.95/1.19 => ( ( lexordp_list_a @ Less @ Xs3 @ Ys3 )
% 1.95/1.19 => ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_list_a @ X2 @ Xs3 ) @ ( cons_list_a @ Y2 @ Ys3 ) ) ) ) ) )
% 1.95/1.19 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_214_ord_Olexordp_Oinducts,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X1: list_a,X22: list_a,P: list_a > list_a > $o] :
% 1.95/1.19 ( ( lexordp_a @ Less @ X1 @ X22 )
% 1.95/1.19 => ( ! [Y2: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y2 @ Ys3 ) )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) )
% 1.95/1.19 => ( ! [X2: a,Y2: a,Xs3: list_a,Ys3: list_a] :
% 1.95/1.19 ( ~ ( Less @ X2 @ Y2 )
% 1.95/1.19 => ( ~ ( Less @ Y2 @ X2 )
% 1.95/1.19 => ( ( lexordp_a @ Less @ Xs3 @ Ys3 )
% 1.95/1.19 => ( ( P @ Xs3 @ Ys3 )
% 1.95/1.19 => ( P @ ( cons_a @ X2 @ Xs3 ) @ ( cons_a @ Y2 @ Ys3 ) ) ) ) ) )
% 1.95/1.19 => ( P @ X1 @ X22 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_215_local_Olexordp__append__rightI,axiom,
% 1.95/1.19 ! [Ys: list_a,Xs: list_a] :
% 1.95/1.19 ( ( Ys != nil_a )
% 1.95/1.19 => ( lexordp_a @ less @ Xs @ ( append_a @ Xs @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_216_local_Olexordp__append__left__rightI,axiom,
% 1.95/1.19 ! [X: a,Y: a,Us: list_a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( less @ X @ Y )
% 1.95/1.19 => ( lexordp_a @ less @ ( append_a @ Us @ ( cons_a @ X @ Xs ) ) @ ( append_a @ Us @ ( cons_a @ Y @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_217_semilattice_Oaxioms_I1_J,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ( semilattice_a @ F )
% 1.95/1.19 => ( abel_semigroup_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_218_local_Olexordp__append__leftD,axiom,
% 1.95/1.19 ! [Xs: list_a,Us: list_a,Vs: list_a] :
% 1.95/1.19 ( ( lexordp_a @ less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) )
% 1.95/1.19 => ( ! [A2: a] :
% 1.95/1.19 ~ ( less @ A2 @ A2 )
% 1.95/1.19 => ( lexordp_a @ less @ Us @ Vs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_219_local_Olexordp__append__leftI,axiom,
% 1.95/1.19 ! [Us: list_a,Vs: list_a,Xs: list_a] :
% 1.95/1.19 ( ( lexordp_a @ less @ Us @ Vs )
% 1.95/1.19 => ( lexordp_a @ less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_220_local_Olexordp__eq__pref,axiom,
% 1.95/1.19 ! [U: list_a,V: list_a] : ( lexordp_eq_a @ less @ U @ ( append_a @ U @ V ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_221_same__append__eq,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Xs @ Ys )
% 1.95/1.19 = ( append_list_a @ Xs @ Zs2 ) )
% 1.95/1.19 = ( Ys = Zs2 ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_222_same__append__eq,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a,Zs2: list_a] :
% 1.95/1.19 ( ( ( append_a @ Xs @ Ys )
% 1.95/1.19 = ( append_a @ Xs @ Zs2 ) )
% 1.95/1.19 = ( Ys = Zs2 ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_223_append__same__eq,axiom,
% 1.95/1.19 ! [Ys: list_list_a,Xs: list_list_a,Zs2: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Ys @ Xs )
% 1.95/1.19 = ( append_list_a @ Zs2 @ Xs ) )
% 1.95/1.19 = ( Ys = Zs2 ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_224_append__same__eq,axiom,
% 1.95/1.19 ! [Ys: list_a,Xs: list_a,Zs2: list_a] :
% 1.95/1.19 ( ( ( append_a @ Ys @ Xs )
% 1.95/1.19 = ( append_a @ Zs2 @ Xs ) )
% 1.95/1.19 = ( Ys = Zs2 ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_225_append__assoc,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 1.95/1.19 ( ( append_list_a @ ( append_list_a @ Xs @ Ys ) @ Zs2 )
% 1.95/1.19 = ( append_list_a @ Xs @ ( append_list_a @ Ys @ Zs2 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_226_append__assoc,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a,Zs2: list_a] :
% 1.95/1.19 ( ( append_a @ ( append_a @ Xs @ Ys ) @ Zs2 )
% 1.95/1.19 = ( append_a @ Xs @ ( append_a @ Ys @ Zs2 ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_227_append_Oassoc,axiom,
% 1.95/1.19 ! [A: list_list_a,B: list_list_a,C: list_list_a] :
% 1.95/1.19 ( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
% 1.95/1.19 = ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_228_append_Oassoc,axiom,
% 1.95/1.19 ! [A: list_a,B: list_a,C: list_a] :
% 1.95/1.19 ( ( append_a @ ( append_a @ A @ B ) @ C )
% 1.95/1.19 = ( append_a @ A @ ( append_a @ B @ C ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_229_append_Oright__neutral,axiom,
% 1.95/1.19 ! [A: list_list_a] :
% 1.95/1.19 ( ( append_list_a @ A @ nil_list_a )
% 1.95/1.19 = A ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_230_append_Oright__neutral,axiom,
% 1.95/1.19 ! [A: list_a] :
% 1.95/1.19 ( ( append_a @ A @ nil_a )
% 1.95/1.19 = A ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_231_append__is__Nil__conv,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Xs @ Ys )
% 1.95/1.19 = nil_list_a )
% 1.95/1.19 = ( ( Xs = nil_list_a )
% 1.95/1.19 & ( Ys = nil_list_a ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_232_append__is__Nil__conv,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( ( append_a @ Xs @ Ys )
% 1.95/1.19 = nil_a )
% 1.95/1.19 = ( ( Xs = nil_a )
% 1.95/1.19 & ( Ys = nil_a ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_233_Nil__is__append__conv,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( nil_list_a
% 1.95/1.19 = ( append_list_a @ Xs @ Ys ) )
% 1.95/1.19 = ( ( Xs = nil_list_a )
% 1.95/1.19 & ( Ys = nil_list_a ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_234_Nil__is__append__conv,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( nil_a
% 1.95/1.19 = ( append_a @ Xs @ Ys ) )
% 1.95/1.19 = ( ( Xs = nil_a )
% 1.95/1.19 & ( Ys = nil_a ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_235_self__append__conv2,axiom,
% 1.95/1.19 ! [Ys: list_list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( Ys
% 1.95/1.19 = ( append_list_a @ Xs @ Ys ) )
% 1.95/1.19 = ( Xs = nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_236_self__append__conv2,axiom,
% 1.95/1.19 ! [Ys: list_a,Xs: list_a] :
% 1.95/1.19 ( ( Ys
% 1.95/1.19 = ( append_a @ Xs @ Ys ) )
% 1.95/1.19 = ( Xs = nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_237_append__self__conv2,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Xs @ Ys )
% 1.95/1.19 = Ys )
% 1.95/1.19 = ( Xs = nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_238_append__self__conv2,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( ( append_a @ Xs @ Ys )
% 1.95/1.19 = Ys )
% 1.95/1.19 = ( Xs = nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_239_self__append__conv,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( Xs
% 1.95/1.19 = ( append_list_a @ Xs @ Ys ) )
% 1.95/1.19 = ( Ys = nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_240_self__append__conv,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( Xs
% 1.95/1.19 = ( append_a @ Xs @ Ys ) )
% 1.95/1.19 = ( Ys = nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_241_append__self__conv,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Xs @ Ys )
% 1.95/1.19 = Xs )
% 1.95/1.19 = ( Ys = nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_242_append__self__conv,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( ( append_a @ Xs @ Ys )
% 1.95/1.19 = Xs )
% 1.95/1.19 = ( Ys = nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_243_append__Nil2,axiom,
% 1.95/1.19 ! [Xs: list_list_a] :
% 1.95/1.19 ( ( append_list_a @ Xs @ nil_list_a )
% 1.95/1.19 = Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_244_append__Nil2,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ( ( append_a @ Xs @ nil_a )
% 1.95/1.19 = Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_245_append1__eq__conv,axiom,
% 1.95/1.19 ! [Xs: list_list_a,X: list_a,Ys: list_list_a,Y: list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) )
% 1.95/1.19 = ( append_list_a @ Ys @ ( cons_list_a @ Y @ nil_list_a ) ) )
% 1.95/1.19 = ( ( Xs = Ys )
% 1.95/1.19 & ( X = Y ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_246_append1__eq__conv,axiom,
% 1.95/1.19 ! [Xs: list_a,X: a,Ys: list_a,Y: a] :
% 1.95/1.19 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 1.95/1.19 = ( append_a @ Ys @ ( cons_a @ Y @ nil_a ) ) )
% 1.95/1.19 = ( ( Xs = Ys )
% 1.95/1.19 & ( X = Y ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_247_append_Oleft__neutral,axiom,
% 1.95/1.19 ! [A: list_list_a] :
% 1.95/1.19 ( ( append_list_a @ nil_list_a @ A )
% 1.95/1.19 = A ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_248_append_Oleft__neutral,axiom,
% 1.95/1.19 ! [A: list_a] :
% 1.95/1.19 ( ( append_a @ nil_a @ A )
% 1.95/1.19 = A ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_249_append__Nil,axiom,
% 1.95/1.19 ! [Ys: list_list_a] :
% 1.95/1.19 ( ( append_list_a @ nil_list_a @ Ys )
% 1.95/1.19 = Ys ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_250_append__Nil,axiom,
% 1.95/1.19 ! [Ys: list_a] :
% 1.95/1.19 ( ( append_a @ nil_a @ Ys )
% 1.95/1.19 = Ys ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_251_eq__Nil__appendI,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( Xs = Ys )
% 1.95/1.19 => ( Xs
% 1.95/1.19 = ( append_list_a @ nil_list_a @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_252_eq__Nil__appendI,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( Xs = Ys )
% 1.95/1.19 => ( Xs
% 1.95/1.19 = ( append_a @ nil_a @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_253_Cons__eq__appendI,axiom,
% 1.95/1.19 ! [X: list_a,Xs1: list_list_a,Ys: list_list_a,Xs: list_list_a,Zs2: list_list_a] :
% 1.95/1.19 ( ( ( cons_list_a @ X @ Xs1 )
% 1.95/1.19 = Ys )
% 1.95/1.19 => ( ( Xs
% 1.95/1.19 = ( append_list_a @ Xs1 @ Zs2 ) )
% 1.95/1.19 => ( ( cons_list_a @ X @ Xs )
% 1.95/1.19 = ( append_list_a @ Ys @ Zs2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_254_Cons__eq__appendI,axiom,
% 1.95/1.19 ! [X: a,Xs1: list_a,Ys: list_a,Xs: list_a,Zs2: list_a] :
% 1.95/1.19 ( ( ( cons_a @ X @ Xs1 )
% 1.95/1.19 = Ys )
% 1.95/1.19 => ( ( Xs
% 1.95/1.19 = ( append_a @ Xs1 @ Zs2 ) )
% 1.95/1.19 => ( ( cons_a @ X @ Xs )
% 1.95/1.19 = ( append_a @ Ys @ Zs2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_255_append__Cons,axiom,
% 1.95/1.19 ! [X: list_a,Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( append_list_a @ ( cons_list_a @ X @ Xs ) @ Ys )
% 1.95/1.19 = ( cons_list_a @ X @ ( append_list_a @ Xs @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_256_append__Cons,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( append_a @ ( cons_a @ X @ Xs ) @ Ys )
% 1.95/1.19 = ( cons_a @ X @ ( append_a @ Xs @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_257_ord_Olexordp__append__leftD,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,Xs: list_list_a,Us: list_list_a,Vs: list_list_a] :
% 1.95/1.19 ( ( lexordp_list_a @ Less @ ( append_list_a @ Xs @ Us ) @ ( append_list_a @ Xs @ Vs ) )
% 1.95/1.19 => ( ! [A2: list_a] :
% 1.95/1.19 ~ ( Less @ A2 @ A2 )
% 1.95/1.19 => ( lexordp_list_a @ Less @ Us @ Vs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_258_ord_Olexordp__append__leftD,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Xs: list_a,Us: list_a,Vs: list_a] :
% 1.95/1.19 ( ( lexordp_a @ Less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) )
% 1.95/1.19 => ( ! [A2: a] :
% 1.95/1.19 ~ ( Less @ A2 @ A2 )
% 1.95/1.19 => ( lexordp_a @ Less @ Us @ Vs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_259_ord_Olexordp__append__leftI,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,Us: list_list_a,Vs: list_list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( lexordp_list_a @ Less @ Us @ Vs )
% 1.95/1.19 => ( lexordp_list_a @ Less @ ( append_list_a @ Xs @ Us ) @ ( append_list_a @ Xs @ Vs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_260_ord_Olexordp__append__leftI,axiom,
% 1.95/1.19 ! [Less: a > a > $o,Us: list_a,Vs: list_a,Xs: list_a] :
% 1.95/1.19 ( ( lexordp_a @ Less @ Us @ Vs )
% 1.95/1.19 => ( lexordp_a @ Less @ ( append_a @ Xs @ Us ) @ ( append_a @ Xs @ Vs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_261_ord_Olexordp__eq__pref,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,U: list_list_a,V: list_list_a] : ( lexordp_eq_list_a @ Less @ U @ ( append_list_a @ U @ V ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_262_ord_Olexordp__eq__pref,axiom,
% 1.95/1.19 ! [Less: a > a > $o,U: list_a,V: list_a] : ( lexordp_eq_a @ Less @ U @ ( append_a @ U @ V ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_263_append__eq__append__conv2,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a,Ts: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Xs @ Ys )
% 1.95/1.19 = ( append_list_a @ Zs2 @ Ts ) )
% 1.95/1.19 = ( ? [Us2: list_list_a] :
% 1.95/1.19 ( ( ( Xs
% 1.95/1.19 = ( append_list_a @ Zs2 @ Us2 ) )
% 1.95/1.19 & ( ( append_list_a @ Us2 @ Ys )
% 1.95/1.19 = Ts ) )
% 1.95/1.19 | ( ( ( append_list_a @ Xs @ Us2 )
% 1.95/1.19 = Zs2 )
% 1.95/1.19 & ( Ys
% 1.95/1.19 = ( append_list_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_264_append__eq__append__conv2,axiom,
% 1.95/1.19 ! [Xs: list_a,Ys: list_a,Zs2: list_a,Ts: list_a] :
% 1.95/1.19 ( ( ( append_a @ Xs @ Ys )
% 1.95/1.19 = ( append_a @ Zs2 @ Ts ) )
% 1.95/1.19 = ( ? [Us2: list_a] :
% 1.95/1.19 ( ( ( Xs
% 1.95/1.19 = ( append_a @ Zs2 @ Us2 ) )
% 1.95/1.19 & ( ( append_a @ Us2 @ Ys )
% 1.95/1.19 = Ts ) )
% 1.95/1.19 | ( ( ( append_a @ Xs @ Us2 )
% 1.95/1.19 = Zs2 )
% 1.95/1.19 & ( Ys
% 1.95/1.19 = ( append_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_265_append__eq__appendI,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Xs1: list_list_a,Zs2: list_list_a,Ys: list_list_a,Us: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Xs @ Xs1 )
% 1.95/1.19 = Zs2 )
% 1.95/1.19 => ( ( Ys
% 1.95/1.19 = ( append_list_a @ Xs1 @ Us ) )
% 1.95/1.19 => ( ( append_list_a @ Xs @ Ys )
% 1.95/1.19 = ( append_list_a @ Zs2 @ Us ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_266_append__eq__appendI,axiom,
% 1.95/1.19 ! [Xs: list_a,Xs1: list_a,Zs2: list_a,Ys: list_a,Us: list_a] :
% 1.95/1.19 ( ( ( append_a @ Xs @ Xs1 )
% 1.95/1.19 = Zs2 )
% 1.95/1.19 => ( ( Ys
% 1.95/1.19 = ( append_a @ Xs1 @ Us ) )
% 1.95/1.19 => ( ( append_a @ Xs @ Ys )
% 1.95/1.19 = ( append_a @ Zs2 @ Us ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_267_append_Osemigroup__axioms,axiom,
% 1.95/1.19 semigr656274520list_a @ append_list_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_268_append_Osemigroup__axioms,axiom,
% 1.95/1.19 semigroup_list_a @ append_a ).
% 1.95/1.19
% 1.95/1.19 thf(fact_269_rev__nonempty__induct,axiom,
% 1.95/1.19 ! [Xs: list_list_a,P: list_list_a > $o] :
% 1.95/1.19 ( ( Xs != nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a] : ( P @ ( cons_list_a @ X2 @ nil_list_a ) )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a] :
% 1.95/1.19 ( ( Xs3 != nil_list_a )
% 1.95/1.19 => ( ( P @ Xs3 )
% 1.95/1.19 => ( P @ ( append_list_a @ Xs3 @ ( cons_list_a @ X2 @ nil_list_a ) ) ) ) )
% 1.95/1.19 => ( P @ Xs ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_270_rev__nonempty__induct,axiom,
% 1.95/1.19 ! [Xs: list_a,P: list_a > $o] :
% 1.95/1.19 ( ( Xs != nil_a )
% 1.95/1.19 => ( ! [X2: a] : ( P @ ( cons_a @ X2 @ nil_a ) )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a] :
% 1.95/1.19 ( ( Xs3 != nil_a )
% 1.95/1.19 => ( ( P @ Xs3 )
% 1.95/1.19 => ( P @ ( append_a @ Xs3 @ ( cons_a @ X2 @ nil_a ) ) ) ) )
% 1.95/1.19 => ( P @ Xs ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_271_append__eq__Cons__conv,axiom,
% 1.95/1.19 ! [Ys: list_list_a,Zs2: list_list_a,X: list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Ys @ Zs2 )
% 1.95/1.19 = ( cons_list_a @ X @ Xs ) )
% 1.95/1.19 = ( ( ( Ys = nil_list_a )
% 1.95/1.19 & ( Zs2
% 1.95/1.19 = ( cons_list_a @ X @ Xs ) ) )
% 1.95/1.19 | ? [Ys4: list_list_a] :
% 1.95/1.19 ( ( Ys
% 1.95/1.19 = ( cons_list_a @ X @ Ys4 ) )
% 1.95/1.19 & ( ( append_list_a @ Ys4 @ Zs2 )
% 1.95/1.19 = Xs ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_272_append__eq__Cons__conv,axiom,
% 1.95/1.19 ! [Ys: list_a,Zs2: list_a,X: a,Xs: list_a] :
% 1.95/1.19 ( ( ( append_a @ Ys @ Zs2 )
% 1.95/1.19 = ( cons_a @ X @ Xs ) )
% 1.95/1.19 = ( ( ( Ys = nil_a )
% 1.95/1.19 & ( Zs2
% 1.95/1.19 = ( cons_a @ X @ Xs ) ) )
% 1.95/1.19 | ? [Ys4: list_a] :
% 1.95/1.19 ( ( Ys
% 1.95/1.19 = ( cons_a @ X @ Ys4 ) )
% 1.95/1.19 & ( ( append_a @ Ys4 @ Zs2 )
% 1.95/1.19 = Xs ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_273_Cons__eq__append__conv,axiom,
% 1.95/1.19 ! [X: list_a,Xs: list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 1.95/1.19 ( ( ( cons_list_a @ X @ Xs )
% 1.95/1.19 = ( append_list_a @ Ys @ Zs2 ) )
% 1.95/1.19 = ( ( ( Ys = nil_list_a )
% 1.95/1.19 & ( ( cons_list_a @ X @ Xs )
% 1.95/1.19 = Zs2 ) )
% 1.95/1.19 | ? [Ys4: list_list_a] :
% 1.95/1.19 ( ( ( cons_list_a @ X @ Ys4 )
% 1.95/1.19 = Ys )
% 1.95/1.19 & ( Xs
% 1.95/1.19 = ( append_list_a @ Ys4 @ Zs2 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_274_Cons__eq__append__conv,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a,Ys: list_a,Zs2: list_a] :
% 1.95/1.19 ( ( ( cons_a @ X @ Xs )
% 1.95/1.19 = ( append_a @ Ys @ Zs2 ) )
% 1.95/1.19 = ( ( ( Ys = nil_a )
% 1.95/1.19 & ( ( cons_a @ X @ Xs )
% 1.95/1.19 = Zs2 ) )
% 1.95/1.19 | ? [Ys4: list_a] :
% 1.95/1.19 ( ( ( cons_a @ X @ Ys4 )
% 1.95/1.19 = Ys )
% 1.95/1.19 & ( Xs
% 1.95/1.19 = ( append_a @ Ys4 @ Zs2 ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_275_rev__exhaust,axiom,
% 1.95/1.19 ! [Xs: list_list_a] :
% 1.95/1.19 ( ( Xs != nil_list_a )
% 1.95/1.19 => ~ ! [Ys3: list_list_a,Y2: list_a] :
% 1.95/1.19 ( Xs
% 1.95/1.19 != ( append_list_a @ Ys3 @ ( cons_list_a @ Y2 @ nil_list_a ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_276_rev__exhaust,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ( ( Xs != nil_a )
% 1.95/1.19 => ~ ! [Ys3: list_a,Y2: a] :
% 1.95/1.19 ( Xs
% 1.95/1.19 != ( append_a @ Ys3 @ ( cons_a @ Y2 @ nil_a ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_277_rev__induct,axiom,
% 1.95/1.19 ! [P: list_list_a > $o,Xs: list_list_a] :
% 1.95/1.19 ( ( P @ nil_list_a )
% 1.95/1.19 => ( ! [X2: list_a,Xs3: list_list_a] :
% 1.95/1.19 ( ( P @ Xs3 )
% 1.95/1.19 => ( P @ ( append_list_a @ Xs3 @ ( cons_list_a @ X2 @ nil_list_a ) ) ) )
% 1.95/1.19 => ( P @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_278_rev__induct,axiom,
% 1.95/1.19 ! [P: list_a > $o,Xs: list_a] :
% 1.95/1.19 ( ( P @ nil_a )
% 1.95/1.19 => ( ! [X2: a,Xs3: list_a] :
% 1.95/1.19 ( ( P @ Xs3 )
% 1.95/1.19 => ( P @ ( append_a @ Xs3 @ ( cons_a @ X2 @ nil_a ) ) ) )
% 1.95/1.19 => ( P @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_279_ord_Olexordp__append__left__rightI,axiom,
% 1.95/1.19 ! [Less: list_a > list_a > $o,X: list_a,Y: list_a,Us: list_list_a,Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( Less @ X @ Y )
% 1.95/1.19 => ( lexordp_list_a @ Less @ ( append_list_a @ Us @ ( cons_list_a @ X @ Xs ) ) @ ( append_list_a @ Us @ ( cons_list_a @ Y @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_280_ord_Olexordp__append__left__rightI,axiom,
% 1.95/1.19 ! [Less: a > a > $o,X: a,Y: a,Us: list_a,Xs: list_a,Ys: list_a] :
% 1.95/1.19 ( ( Less @ X @ Y )
% 1.95/1.19 => ( lexordp_a @ Less @ ( append_a @ Us @ ( cons_a @ X @ Xs ) ) @ ( append_a @ Us @ ( cons_a @ Y @ Ys ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_281_ord_Olexordp__append__rightI,axiom,
% 1.95/1.19 ! [Ys: list_list_a,Less: list_a > list_a > $o,Xs: list_list_a] :
% 1.95/1.19 ( ( Ys != nil_list_a )
% 1.95/1.19 => ( lexordp_list_a @ Less @ Xs @ ( append_list_a @ Xs @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_282_ord_Olexordp__append__rightI,axiom,
% 1.95/1.19 ! [Ys: list_a,Less: a > a > $o,Xs: list_a] :
% 1.95/1.19 ( ( Ys != nil_a )
% 1.95/1.19 => ( lexordp_a @ Less @ Xs @ ( append_a @ Xs @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_283_semilattice_Oidem,axiom,
% 1.95/1.19 ! [F: a > a > a,A: a] :
% 1.95/1.19 ( ( semilattice_a @ F )
% 1.95/1.19 => ( ( F @ A @ A )
% 1.95/1.19 = A ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_284_semilattice_Oleft__idem,axiom,
% 1.95/1.19 ! [F: a > a > a,A: a,B: a] :
% 1.95/1.19 ( ( semilattice_a @ F )
% 1.95/1.19 => ( ( F @ A @ ( F @ A @ B ) )
% 1.95/1.19 = ( F @ A @ B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_285_semilattice_Oright__idem,axiom,
% 1.95/1.19 ! [F: a > a > a,A: a,B: a] :
% 1.95/1.19 ( ( semilattice_a @ F )
% 1.95/1.19 => ( ( F @ ( F @ A @ B ) @ B )
% 1.95/1.19 = ( F @ A @ B ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_286_product__lists_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( product_lists_list_a @ nil_list_list_a )
% 1.95/1.19 = ( cons_list_list_a @ nil_list_a @ nil_list_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_287_product__lists_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( product_lists_a @ nil_list_a )
% 1.95/1.19 = ( cons_list_a @ nil_a @ nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_288_bind__simps_I2_J,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a,F: a > list_list_a] :
% 1.95/1.19 ( ( bind_a_list_a @ ( cons_a @ X @ Xs ) @ F )
% 1.95/1.19 = ( append_list_a @ ( F @ X ) @ ( bind_a_list_a @ Xs @ F ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_289_bind__simps_I2_J,axiom,
% 1.95/1.19 ! [X: list_a,Xs: list_list_a,F: list_a > list_a] :
% 1.95/1.19 ( ( bind_list_a_a @ ( cons_list_a @ X @ Xs ) @ F )
% 1.95/1.19 = ( append_a @ ( F @ X ) @ ( bind_list_a_a @ Xs @ F ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_290_bind__simps_I2_J,axiom,
% 1.95/1.19 ! [X: list_a,Xs: list_list_a,F: list_a > list_list_a] :
% 1.95/1.19 ( ( bind_list_a_list_a @ ( cons_list_a @ X @ Xs ) @ F )
% 1.95/1.19 = ( append_list_a @ ( F @ X ) @ ( bind_list_a_list_a @ Xs @ F ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_291_bind__simps_I2_J,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a,F: a > list_a] :
% 1.95/1.19 ( ( bind_a_a @ ( cons_a @ X @ Xs ) @ F )
% 1.95/1.19 = ( append_a @ ( F @ X ) @ ( bind_a_a @ Xs @ F ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_292_bind__simps_I1_J,axiom,
% 1.95/1.19 ! [F: a > list_list_a] :
% 1.95/1.19 ( ( bind_a_list_a @ nil_a @ F )
% 1.95/1.19 = nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_293_bind__simps_I1_J,axiom,
% 1.95/1.19 ! [F: list_a > list_a] :
% 1.95/1.19 ( ( bind_list_a_a @ nil_list_a @ F )
% 1.95/1.19 = nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_294_bind__simps_I1_J,axiom,
% 1.95/1.19 ! [F: list_a > list_list_a] :
% 1.95/1.19 ( ( bind_list_a_list_a @ nil_list_a @ F )
% 1.95/1.19 = nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_295_bind__simps_I1_J,axiom,
% 1.95/1.19 ! [F: a > list_a] :
% 1.95/1.19 ( ( bind_a_a @ nil_a @ F )
% 1.95/1.19 = nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_296_abel__semigroup__def,axiom,
% 1.95/1.19 ( abel_s1075322906list_a
% 1.95/1.19 = ( ^ [F2: list_a > list_a > list_a] :
% 1.95/1.19 ( ( semigroup_list_a @ F2 )
% 1.95/1.19 & ( abel_s374399671list_a @ F2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_297_abel__semigroup__def,axiom,
% 1.95/1.19 ( abel_semigroup_a
% 1.95/1.19 = ( ^ [F2: a > a > a] :
% 1.95/1.19 ( ( semigroup_a @ F2 )
% 1.95/1.19 & ( abel_s2117090225ioms_a @ F2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_298_abel__semigroup_Ointro,axiom,
% 1.95/1.19 ! [F: list_a > list_a > list_a] :
% 1.95/1.19 ( ( semigroup_list_a @ F )
% 1.95/1.19 => ( ( abel_s374399671list_a @ F )
% 1.95/1.19 => ( abel_s1075322906list_a @ F ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_299_abel__semigroup_Ointro,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ( semigroup_a @ F )
% 1.95/1.19 => ( ( abel_s2117090225ioms_a @ F )
% 1.95/1.19 => ( abel_semigroup_a @ F ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_300_abel__semigroup__axioms_Ointro,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ! [A2: a,B2: a] :
% 1.95/1.19 ( ( F @ A2 @ B2 )
% 1.95/1.19 = ( F @ B2 @ A2 ) )
% 1.95/1.19 => ( abel_s2117090225ioms_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_301_abel__semigroup__axioms__def,axiom,
% 1.95/1.19 ( abel_s2117090225ioms_a
% 1.95/1.19 = ( ^ [F2: a > a > a] :
% 1.95/1.19 ! [A3: a,B3: a] :
% 1.95/1.19 ( ( F2 @ A3 @ B3 )
% 1.95/1.19 = ( F2 @ B3 @ A3 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_302_abel__semigroup_Oaxioms_I2_J,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ( abel_semigroup_a @ F )
% 1.95/1.19 => ( abel_s2117090225ioms_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_303_semilattice_Ointro,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ( abel_semigroup_a @ F )
% 1.95/1.19 => ( ( semilattice_axioms_a @ F )
% 1.95/1.19 => ( semilattice_a @ F ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_304_semilattice__def,axiom,
% 1.95/1.19 ( semilattice_a
% 1.95/1.19 = ( ^ [F2: a > a > a] :
% 1.95/1.19 ( ( abel_semigroup_a @ F2 )
% 1.95/1.19 & ( semilattice_axioms_a @ F2 ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_305_semilattice_Oaxioms_I2_J,axiom,
% 1.95/1.19 ! [F: a > a > a] :
% 1.95/1.19 ( ( semilattice_a @ F )
% 1.95/1.19 => ( semilattice_axioms_a @ F ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_306_subseqs_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( subseqs_list_a @ nil_list_a )
% 1.95/1.19 = ( cons_list_list_a @ nil_list_a @ nil_list_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_307_subseqs_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( subseqs_a @ nil_a )
% 1.95/1.19 = ( cons_list_a @ nil_a @ nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_308_maps__simps_I1_J,axiom,
% 1.95/1.19 ! [F: a > list_list_a,X: a,Xs: list_a] :
% 1.95/1.19 ( ( maps_a_list_a @ F @ ( cons_a @ X @ Xs ) )
% 1.95/1.19 = ( append_list_a @ ( F @ X ) @ ( maps_a_list_a @ F @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_309_maps__simps_I1_J,axiom,
% 1.95/1.19 ! [F: list_a > list_a,X: list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( maps_list_a_a @ F @ ( cons_list_a @ X @ Xs ) )
% 1.95/1.19 = ( append_a @ ( F @ X ) @ ( maps_list_a_a @ F @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_310_maps__simps_I1_J,axiom,
% 1.95/1.19 ! [F: list_a > list_list_a,X: list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( maps_list_a_list_a @ F @ ( cons_list_a @ X @ Xs ) )
% 1.95/1.19 = ( append_list_a @ ( F @ X ) @ ( maps_list_a_list_a @ F @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_311_maps__simps_I1_J,axiom,
% 1.95/1.19 ! [F: a > list_a,X: a,Xs: list_a] :
% 1.95/1.19 ( ( maps_a_a @ F @ ( cons_a @ X @ Xs ) )
% 1.95/1.19 = ( append_a @ ( F @ X ) @ ( maps_a_a @ F @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_312_maps__simps_I2_J,axiom,
% 1.95/1.19 ! [F: a > list_list_a] :
% 1.95/1.19 ( ( maps_a_list_a @ F @ nil_a )
% 1.95/1.19 = nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_313_maps__simps_I2_J,axiom,
% 1.95/1.19 ! [F: list_a > list_a] :
% 1.95/1.19 ( ( maps_list_a_a @ F @ nil_list_a )
% 1.95/1.19 = nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_314_maps__simps_I2_J,axiom,
% 1.95/1.19 ! [F: list_a > list_list_a] :
% 1.95/1.19 ( ( maps_list_a_list_a @ F @ nil_list_a )
% 1.95/1.19 = nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_315_maps__simps_I2_J,axiom,
% 1.95/1.19 ! [F: a > list_a] :
% 1.95/1.19 ( ( maps_a_a @ F @ nil_a )
% 1.95/1.19 = nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_316_local_Otransp__less,axiom,
% 1.95/1.19 transp_a @ less ).
% 1.95/1.19
% 1.95/1.19 thf(fact_317_insert__Nil,axiom,
% 1.95/1.19 ! [X: list_a] :
% 1.95/1.19 ( ( insert_list_a @ X @ nil_list_a )
% 1.95/1.19 = ( cons_list_a @ X @ nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_318_insert__Nil,axiom,
% 1.95/1.19 ! [X: a] :
% 1.95/1.19 ( ( insert_a @ X @ nil_a )
% 1.95/1.19 = ( cons_a @ X @ nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_319_concat__eq__append__conv,axiom,
% 1.95/1.19 ! [Xss2: list_list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 1.95/1.19 ( ( ( concat_list_a @ Xss2 )
% 1.95/1.19 = ( append_list_a @ Ys @ Zs2 ) )
% 1.95/1.19 = ( ( ( Xss2 = nil_list_list_a )
% 1.95/1.19 => ( ( Ys = nil_list_a )
% 1.95/1.19 & ( Zs2 = nil_list_a ) ) )
% 1.95/1.19 & ( ( Xss2 != nil_list_list_a )
% 1.95/1.19 => ? [Xss1: list_list_list_a,Xs2: list_list_a,Xs4: list_list_a,Xss22: list_list_list_a] :
% 1.95/1.19 ( ( Xss2
% 1.95/1.19 = ( append_list_list_a @ Xss1 @ ( cons_list_list_a @ ( append_list_a @ Xs2 @ Xs4 ) @ Xss22 ) ) )
% 1.95/1.19 & ( Ys
% 1.95/1.19 = ( append_list_a @ ( concat_list_a @ Xss1 ) @ Xs2 ) )
% 1.95/1.19 & ( Zs2
% 1.95/1.19 = ( append_list_a @ Xs4 @ ( concat_list_a @ Xss22 ) ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_320_concat__eq__append__conv,axiom,
% 1.95/1.19 ! [Xss2: list_list_a,Ys: list_a,Zs2: list_a] :
% 1.95/1.19 ( ( ( concat_a @ Xss2 )
% 1.95/1.19 = ( append_a @ Ys @ Zs2 ) )
% 1.95/1.19 = ( ( ( Xss2 = nil_list_a )
% 1.95/1.19 => ( ( Ys = nil_a )
% 1.95/1.19 & ( Zs2 = nil_a ) ) )
% 1.95/1.19 & ( ( Xss2 != nil_list_a )
% 1.95/1.19 => ? [Xss1: list_list_a,Xs2: list_a,Xs4: list_a,Xss22: list_list_a] :
% 1.95/1.19 ( ( Xss2
% 1.95/1.19 = ( append_list_a @ Xss1 @ ( cons_list_a @ ( append_a @ Xs2 @ Xs4 ) @ Xss22 ) ) )
% 1.95/1.19 & ( Ys
% 1.95/1.19 = ( append_a @ ( concat_a @ Xss1 ) @ Xs2 ) )
% 1.95/1.19 & ( Zs2
% 1.95/1.19 = ( append_a @ Xs4 @ ( concat_a @ Xss22 ) ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_321_rotate1_Osimps_I2_J,axiom,
% 1.95/1.19 ! [X: list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( rotate1_list_a @ ( cons_list_a @ X @ Xs ) )
% 1.95/1.19 = ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_322_rotate1_Osimps_I2_J,axiom,
% 1.95/1.19 ! [X: a,Xs: list_a] :
% 1.95/1.19 ( ( rotate1_a @ ( cons_a @ X @ Xs ) )
% 1.95/1.19 = ( append_a @ Xs @ ( cons_a @ X @ nil_a ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_323_rotate1__is__Nil__conv,axiom,
% 1.95/1.19 ! [Xs: list_list_a] :
% 1.95/1.19 ( ( ( rotate1_list_a @ Xs )
% 1.95/1.19 = nil_list_a )
% 1.95/1.19 = ( Xs = nil_list_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_324_rotate1__is__Nil__conv,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ( ( ( rotate1_a @ Xs )
% 1.95/1.19 = nil_a )
% 1.95/1.19 = ( Xs = nil_a ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_325_concat__append,axiom,
% 1.95/1.19 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 1.95/1.19 ( ( concat_list_a @ ( append_list_list_a @ Xs @ Ys ) )
% 1.95/1.19 = ( append_list_a @ ( concat_list_a @ Xs ) @ ( concat_list_a @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_326_concat__append,axiom,
% 1.95/1.19 ! [Xs: list_list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( concat_a @ ( append_list_a @ Xs @ Ys ) )
% 1.95/1.19 = ( append_a @ ( concat_a @ Xs ) @ ( concat_a @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_327_concat_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( concat_list_a @ nil_list_list_a )
% 1.95/1.19 = nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_328_concat_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( concat_a @ nil_list_a )
% 1.95/1.19 = nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_329_concat_Osimps_I2_J,axiom,
% 1.95/1.19 ! [X: list_list_a,Xs: list_list_list_a] :
% 1.95/1.19 ( ( concat_list_a @ ( cons_list_list_a @ X @ Xs ) )
% 1.95/1.19 = ( append_list_a @ X @ ( concat_list_a @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_330_concat_Osimps_I2_J,axiom,
% 1.95/1.19 ! [X: list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( concat_a @ ( cons_list_a @ X @ Xs ) )
% 1.95/1.19 = ( append_a @ X @ ( concat_a @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_331_rotate1_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( rotate1_list_a @ nil_list_a )
% 1.95/1.19 = nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_332_rotate1_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( rotate1_a @ nil_a )
% 1.95/1.19 = nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_333_concat__eq__appendD,axiom,
% 1.95/1.19 ! [Xss2: list_list_list_a,Ys: list_list_a,Zs2: list_list_a] :
% 1.95/1.19 ( ( ( concat_list_a @ Xss2 )
% 1.95/1.19 = ( append_list_a @ Ys @ Zs2 ) )
% 1.95/1.19 => ( ( Xss2 != nil_list_list_a )
% 1.95/1.19 => ? [Xss12: list_list_list_a,Xs3: list_list_a,Xs5: list_list_a,Xss23: list_list_list_a] :
% 1.95/1.19 ( ( Xss2
% 1.95/1.19 = ( append_list_list_a @ Xss12 @ ( cons_list_list_a @ ( append_list_a @ Xs3 @ Xs5 ) @ Xss23 ) ) )
% 1.95/1.19 & ( Ys
% 1.95/1.19 = ( append_list_a @ ( concat_list_a @ Xss12 ) @ Xs3 ) )
% 1.95/1.19 & ( Zs2
% 1.95/1.19 = ( append_list_a @ Xs5 @ ( concat_list_a @ Xss23 ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_334_concat__eq__appendD,axiom,
% 1.95/1.19 ! [Xss2: list_list_a,Ys: list_a,Zs2: list_a] :
% 1.95/1.19 ( ( ( concat_a @ Xss2 )
% 1.95/1.19 = ( append_a @ Ys @ Zs2 ) )
% 1.95/1.19 => ( ( Xss2 != nil_list_a )
% 1.95/1.19 => ? [Xss12: list_list_a,Xs3: list_a,Xs5: list_a,Xss23: list_list_a] :
% 1.95/1.19 ( ( Xss2
% 1.95/1.19 = ( append_list_a @ Xss12 @ ( cons_list_a @ ( append_a @ Xs3 @ Xs5 ) @ Xss23 ) ) )
% 1.95/1.19 & ( Ys
% 1.95/1.19 = ( append_a @ ( concat_a @ Xss12 ) @ Xs3 ) )
% 1.95/1.19 & ( Zs2
% 1.95/1.19 = ( append_a @ Xs5 @ ( concat_a @ Xss23 ) ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_335_butlast__snoc,axiom,
% 1.95/1.19 ! [Xs: list_list_a,X: list_a] :
% 1.95/1.19 ( ( butlast_list_a @ ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) ) )
% 1.95/1.19 = Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_336_butlast__snoc,axiom,
% 1.95/1.19 ! [Xs: list_a,X: a] :
% 1.95/1.19 ( ( butlast_a @ ( append_a @ Xs @ ( cons_a @ X @ nil_a ) ) )
% 1.95/1.19 = Xs ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_337_list__ex1__simps_I1_J,axiom,
% 1.95/1.19 ! [P: list_a > $o] :
% 1.95/1.19 ~ ( list_ex1_list_a @ P @ nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_338_list__ex1__simps_I1_J,axiom,
% 1.95/1.19 ! [P: a > $o] :
% 1.95/1.19 ~ ( list_ex1_a @ P @ nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_339_butlast__append,axiom,
% 1.95/1.19 ! [Ys: list_list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( ( Ys = nil_list_a )
% 1.95/1.19 => ( ( butlast_list_a @ ( append_list_a @ Xs @ Ys ) )
% 1.95/1.19 = ( butlast_list_a @ Xs ) ) )
% 1.95/1.19 & ( ( Ys != nil_list_a )
% 1.95/1.19 => ( ( butlast_list_a @ ( append_list_a @ Xs @ Ys ) )
% 1.95/1.19 = ( append_list_a @ Xs @ ( butlast_list_a @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_340_butlast__append,axiom,
% 1.95/1.19 ! [Ys: list_a,Xs: list_a] :
% 1.95/1.19 ( ( ( Ys = nil_a )
% 1.95/1.19 => ( ( butlast_a @ ( append_a @ Xs @ Ys ) )
% 1.95/1.19 = ( butlast_a @ Xs ) ) )
% 1.95/1.19 & ( ( Ys != nil_a )
% 1.95/1.19 => ( ( butlast_a @ ( append_a @ Xs @ Ys ) )
% 1.95/1.19 = ( append_a @ Xs @ ( butlast_a @ Ys ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_341_butlast_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( butlast_list_a @ nil_list_a )
% 1.95/1.19 = nil_list_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_342_butlast_Osimps_I1_J,axiom,
% 1.95/1.19 ( ( butlast_a @ nil_a )
% 1.95/1.19 = nil_a ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_343_butlast_Osimps_I2_J,axiom,
% 1.95/1.19 ! [Xs: list_list_a,X: list_a] :
% 1.95/1.19 ( ( ( Xs = nil_list_a )
% 1.95/1.19 => ( ( butlast_list_a @ ( cons_list_a @ X @ Xs ) )
% 1.95/1.19 = nil_list_a ) )
% 1.95/1.19 & ( ( Xs != nil_list_a )
% 1.95/1.19 => ( ( butlast_list_a @ ( cons_list_a @ X @ Xs ) )
% 1.95/1.19 = ( cons_list_a @ X @ ( butlast_list_a @ Xs ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_344_butlast_Osimps_I2_J,axiom,
% 1.95/1.19 ! [Xs: list_a,X: a] :
% 1.95/1.19 ( ( ( Xs = nil_a )
% 1.95/1.19 => ( ( butlast_a @ ( cons_a @ X @ Xs ) )
% 1.95/1.19 = nil_a ) )
% 1.95/1.19 & ( ( Xs != nil_a )
% 1.95/1.19 => ( ( butlast_a @ ( cons_a @ X @ Xs ) )
% 1.95/1.19 = ( cons_a @ X @ ( butlast_a @ Xs ) ) ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_345_append__butlast__last__id,axiom,
% 1.95/1.19 ! [Xs: list_list_a] :
% 1.95/1.19 ( ( Xs != nil_list_a )
% 1.95/1.19 => ( ( append_list_a @ ( butlast_list_a @ Xs ) @ ( cons_list_a @ ( last_list_a @ Xs ) @ nil_list_a ) )
% 1.95/1.19 = Xs ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_346_append__butlast__last__id,axiom,
% 1.95/1.19 ! [Xs: list_a] :
% 1.95/1.19 ( ( Xs != nil_a )
% 1.95/1.19 => ( ( append_a @ ( butlast_a @ Xs ) @ ( cons_a @ ( last_a @ Xs ) @ nil_a ) )
% 1.95/1.19 = Xs ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_347_snoc__eq__iff__butlast,axiom,
% 1.95/1.19 ! [Xs: list_list_a,X: list_a,Ys: list_list_a] :
% 1.95/1.19 ( ( ( append_list_a @ Xs @ ( cons_list_a @ X @ nil_list_a ) )
% 1.95/1.19 = Ys )
% 1.95/1.19 = ( ( Ys != nil_list_a )
% 1.95/1.19 & ( ( butlast_list_a @ Ys )
% 1.95/1.19 = Xs )
% 1.95/1.19 & ( ( last_list_a @ Ys )
% 1.95/1.19 = X ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_348_snoc__eq__iff__butlast,axiom,
% 1.95/1.19 ! [Xs: list_a,X: a,Ys: list_a] :
% 1.95/1.19 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 1.95/1.19 = Ys )
% 1.95/1.19 = ( ( Ys != nil_a )
% 1.95/1.19 & ( ( butlast_a @ Ys )
% 1.95/1.19 = Xs )
% 1.95/1.19 & ( ( last_a @ Ys )
% 1.95/1.19 = X ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_349_last__appendR,axiom,
% 1.95/1.19 ! [Ys: list_list_a,Xs: list_list_a] :
% 1.95/1.19 ( ( Ys != nil_list_a )
% 1.95/1.19 => ( ( last_list_a @ ( append_list_a @ Xs @ Ys ) )
% 1.95/1.19 = ( last_list_a @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_350_last__appendR,axiom,
% 1.95/1.19 ! [Ys: list_a,Xs: list_a] :
% 1.95/1.19 ( ( Ys != nil_a )
% 1.95/1.19 => ( ( last_a @ ( append_a @ Xs @ Ys ) )
% 1.95/1.19 = ( last_a @ Ys ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(fact_351_last__appendL,axiom,
% 1.95/1.19 ! [Ys: list_a,Xs: list_a] :
% 1.95/1.19 ( ( Ys = nil_a )
% 1.95/1.19 => ( ( last_a @ ( append_a @ Xs @ Ys ) )
% 1.95/1.19 = ( last_a @ Xs ) ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(conj_0,hypothesis,
% 1.95/1.19 ( b
% 1.95/1.19 = ( inf @ b @ c ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(conj_1,hypothesis,
% 1.95/1.19 ( ( inf @ c @ ( sup @ b @ c ) )
% 1.95/1.19 = b ) ).
% 1.95/1.19
% 1.95/1.19 thf(conj_2,hypothesis,
% 1.95/1.19 ( a2
% 1.95/1.19 = ( sup @ b @ c ) ) ).
% 1.95/1.19
% 1.95/1.19 thf(conj_3,hypothesis,
% 1.95/1.19 less @ b @ ( sup @ b @ c ) ).
% 1.95/1.19
% 1.95/1.19 thf(conj_4,hypothesis,
% 1.95/1.19 ( ( inf @ c @ ( sup @ b @ c ) )
% 1.95/1.19 = c ) ).
% 1.95/1.19
% 1.95/1.19 thf(conj_5,conjecture,
% 1.95/1.19 $false ).
% 1.95/1.19 ------------------------
% 2.07/1.21 % (2770)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/27Mi)
% 2.07/1.21 % (2769)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/4Mi)
% 2.07/1.21 % (2771)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/2Mi)
% 2.07/1.21 % (2773)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/275Mi)
% 2.07/1.21 % (2768)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/183Mi)
% 2.07/1.21 % (2772)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/2Mi)
% 2.07/1.21 % (2774)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/18Mi)
% 2.07/1.22 % (2771)Instruction limit reached!
% 2.07/1.22 % (2771)------------------------------
% 2.07/1.22 % (2771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.22 % (2771)Termination reason: Unknown
% 2.07/1.22 % (2771)Termination phase: shuffling
% 2.07/1.22
% 2.07/1.22 % (2772)Instruction limit reached!
% 2.07/1.22 % (2772)------------------------------
% 2.07/1.22 % (2772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.22 % (2772)Termination reason: Unknown
% 2.07/1.22 % (2772)Termination phase: shuffling
% 2.07/1.22
% 2.07/1.22 % (2772)Memory used [KB]: 1407
% 2.07/1.22 % (2772)Time elapsed: 0.002 s
% 2.07/1.22 % (2772)Instructions burned: 2 (million)
% 2.07/1.22 % (2772)------------------------------
% 2.07/1.22 % (2772)------------------------------
% 2.07/1.22 % (2771)Memory used [KB]: 1407
% 2.07/1.22 % (2771)Time elapsed: 0.002 s
% 2.07/1.22 % (2771)Instructions burned: 2 (million)
% 2.07/1.22 % (2771)------------------------------
% 2.07/1.22 % (2771)------------------------------
% 2.07/1.22 % (2769)Instruction limit reached!
% 2.07/1.22 % (2769)------------------------------
% 2.07/1.22 % (2769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.22 % (2769)Termination reason: Unknown
% 2.07/1.22 % (2769)Termination phase: shuffling
% 2.07/1.22
% 2.07/1.22 % (2769)Memory used [KB]: 1535
% 2.07/1.22 % (2769)Time elapsed: 0.003 s
% 2.07/1.22 % (2769)Instructions burned: 6 (million)
% 2.07/1.22 % (2769)------------------------------
% 2.07/1.22 % (2769)------------------------------
% 2.07/1.22 % (2774)Instruction limit reached!
% 2.07/1.22 % (2774)------------------------------
% 2.07/1.22 % (2774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.22 % (2774)Termination reason: Unknown
% 2.07/1.22 % (2774)Termination phase: shuffling
% 2.07/1.22
% 2.07/1.22 % (2774)Memory used [KB]: 1791
% 2.07/1.22 % (2774)Time elapsed: 0.007 s
% 2.07/1.22 % (2774)Instructions burned: 18 (million)
% 2.07/1.22 % (2774)------------------------------
% 2.07/1.22 % (2774)------------------------------
% 2.07/1.22 % (2770)Instruction limit reached!
% 2.07/1.22 % (2770)------------------------------
% 2.07/1.22 % (2770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.22 % (2770)Termination reason: Unknown
% 2.07/1.22 % (2770)Termination phase: Property scanning
% 2.07/1.22
% 2.07/1.22 % (2770)Memory used [KB]: 1918
% 2.07/1.22 % (2770)Time elapsed: 0.010 s
% 2.07/1.22 % (2770)Instructions burned: 28 (million)
% 2.07/1.22 % (2770)------------------------------
% 2.07/1.22 % (2770)------------------------------
% 2.07/1.22 % (2775)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/3Mi)
% 2.07/1.22 % (2776)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/37Mi)
% 2.07/1.23 % (2775)Instruction limit reached!
% 2.07/1.23 % (2775)------------------------------
% 2.07/1.23 % (2775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.23 % (2775)Termination reason: Unknown
% 2.07/1.23 % (2775)Termination phase: shuffling
% 2.07/1.23
% 2.07/1.23 % (2775)Memory used [KB]: 1535
% 2.07/1.23 % (2775)Time elapsed: 0.002 s
% 2.07/1.23 % (2775)Instructions burned: 3 (million)
% 2.07/1.23 % (2775)------------------------------
% 2.07/1.23 % (2775)------------------------------
% 2.07/1.23 % (2777)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/15Mi)
% 2.07/1.23 % (2778)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/3Mi)
% 2.07/1.23 % (2778)Instruction limit reached!
% 2.07/1.23 % (2778)------------------------------
% 2.07/1.23 % (2778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.23 % (2778)Termination reason: Unknown
% 2.07/1.23 % (2778)Termination phase: shuffling
% 2.07/1.23
% 2.07/1.23 % (2778)Memory used [KB]: 1535
% 2.07/1.23 % (2778)Time elapsed: 0.002 s
% 2.07/1.23 % (2778)Instructions burned: 3 (million)
% 2.07/1.23 % (2778)------------------------------
% 2.07/1.23 % (2778)------------------------------
% 2.07/1.23 % (2779)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/1041Mi)
% 2.07/1.23 % (2777)Instruction limit reached!
% 2.07/1.23 % (2777)------------------------------
% 2.07/1.23 % (2777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.23 % (2777)Termination reason: Unknown
% 2.07/1.23 % (2777)Termination phase: shuffling
% 2.07/1.23
% 2.07/1.23 % (2777)Memory used [KB]: 1791
% 2.07/1.23 % (2777)Time elapsed: 0.006 s
% 2.07/1.23 % (2777)Instructions burned: 16 (million)
% 2.07/1.23 % (2777)------------------------------
% 2.07/1.23 % (2777)------------------------------
% 2.07/1.23 % (2776)Instruction limit reached!
% 2.07/1.23 % (2776)------------------------------
% 2.07/1.23 % (2776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.23 % (2776)Termination reason: Unknown
% 2.07/1.23 % (2776)Termination phase: shuffling
% 2.07/1.23
% 2.07/1.23 % (2776)Memory used [KB]: 2174
% 2.07/1.23 % (2776)Time elapsed: 0.011 s
% 2.07/1.23 % (2776)Instructions burned: 38 (million)
% 2.07/1.23 % (2776)------------------------------
% 2.07/1.23 % (2776)------------------------------
% 2.07/1.23 % (2780)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/7Mi)
% 2.07/1.24 % (2780)Instruction limit reached!
% 2.07/1.24 % (2780)------------------------------
% 2.07/1.24 % (2780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.24 % (2780)Termination reason: Unknown
% 2.07/1.24 % (2780)Termination phase: shuffling
% 2.07/1.24
% 2.07/1.24 % (2780)Memory used [KB]: 1535
% 2.07/1.24 % (2780)Time elapsed: 0.003 s
% 2.07/1.24 % (2780)Instructions burned: 7 (million)
% 2.07/1.24 % (2780)------------------------------
% 2.07/1.24 % (2780)------------------------------
% 2.07/1.24 % (2773)First to succeed.
% 2.07/1.24 % (2781)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2662 for (2999ds/16Mi)
% 2.07/1.24 % (2773)Refutation found. Thanks to Tanya!
% 2.07/1.24 % SZS status Theorem for DTF2THF_2662
% 2.07/1.24 % SZS output start Proof for DTF2THF_2662
% 2.07/1.24 thf(type_def_5, type, a: $tType).
% 2.07/1.24 thf(type_def_7, type, list_a: $tType).
% 2.07/1.24 thf(type_def_8, type, list_list_a: $tType).
% 2.07/1.24 thf(type_def_9, type, list_list_list_a: $tType).
% 2.07/1.24 thf(func_def_0, type, list_list_list_a: $tType).
% 2.07/1.24 thf(func_def_1, type, list_list_a: $tType).
% 2.07/1.24 thf(func_def_2, type, list_a: $tType).
% 2.07/1.24 thf(func_def_3, type, a: $tType).
% 2.07/1.24 thf(func_def_4, type, finite40241356em_a_a: (a > a > a) > $o).
% 2.07/1.24 thf(func_def_5, type, abel_s1075322906list_a: (list_a > list_a > list_a) > $o).
% 2.07/1.24 thf(func_def_6, type, abel_semigroup_a: (a > a > a) > $o).
% 2.07/1.24 thf(func_def_7, type, abel_s374399671list_a: (list_a > list_a > list_a) > $o).
% 2.07/1.24 thf(func_def_8, type, abel_s2117090225ioms_a: (a > a > a) > $o).
% 2.07/1.24 thf(func_def_9, type, semigr656274520list_a: (list_list_a > list_list_a > list_list_a) > $o).
% 2.07/1.24 thf(func_def_10, type, semigroup_list_a: (list_a > list_a > list_a) > $o).
% 2.07/1.24 thf(func_def_11, type, semigroup_a: (a > a > a) > $o).
% 2.07/1.24 thf(func_def_12, type, semilattice_a: (a > a > a) > $o).
% 2.07/1.24 thf(func_def_13, type, semilattice_axioms_a: (a > a > a) > $o).
% 2.07/1.24 thf(func_def_14, type, lattic1885654924_set_a: (a > a > a) > $o).
% 2.07/1.24 thf(func_def_15, type, append_list_list_a: list_list_list_a > list_list_list_a > list_list_list_a).
% 2.07/1.24 thf(func_def_16, type, append_list_a: list_list_a > list_list_a > list_list_a).
% 2.07/1.24 thf(func_def_17, type, append_a: list_a > list_a > list_a).
% 2.07/1.24 thf(func_def_18, type, bind_list_a_list_a: list_list_a > (list_a > list_list_a) > list_list_a).
% 2.07/1.24 thf(func_def_19, type, bind_list_a_a: list_list_a > (list_a > list_a) > list_a).
% 2.07/1.24 thf(func_def_20, type, bind_a_list_a: list_a > (a > list_list_a) > list_list_a).
% 2.07/1.24 thf(func_def_21, type, bind_a_a: list_a > (a > list_a) > list_a).
% 2.07/1.24 thf(func_def_22, type, butlast_list_a: list_list_a > list_list_a).
% 2.07/1.24 thf(func_def_23, type, butlast_a: list_a > list_a).
% 2.07/1.24 thf(func_def_24, type, concat_list_a: list_list_list_a > list_list_a).
% 2.07/1.24 thf(func_def_25, type, concat_a: list_list_a > list_a).
% 2.07/1.24 thf(func_def_26, type, insert_list_a: list_a > list_list_a > list_list_a).
% 2.07/1.24 thf(func_def_27, type, insert_a: a > list_a > list_a).
% 2.07/1.24 thf(func_def_28, type, last_list_a: list_list_a > list_a).
% 2.07/1.24 thf(func_def_29, type, last_a: list_a > a).
% 2.07/1.24 thf(func_def_30, type, cons_list_list_a: list_list_a > list_list_list_a > list_list_list_a).
% 2.07/1.24 thf(func_def_31, type, cons_list_a: list_a > list_list_a > list_list_a).
% 2.07/1.24 thf(func_def_32, type, cons_a: a > list_a > list_a).
% 2.07/1.24 thf(func_def_33, type, nil_list_list_a: list_list_list_a).
% 2.07/1.24 thf(func_def_34, type, nil_list_a: list_list_a).
% 2.07/1.24 thf(func_def_35, type, nil_a: list_a).
% 2.07/1.24 thf(func_def_36, type, list_ex1_list_a: (list_a > $o) > list_list_a > $o).
% 2.07/1.24 thf(func_def_37, type, list_ex1_a: (a > $o) > list_a > $o).
% 2.07/1.24 thf(func_def_38, type, maps_list_a_list_a: (list_a > list_list_a) > list_list_a > list_list_a).
% 2.07/1.24 thf(func_def_39, type, maps_list_a_a: (list_a > list_a) > list_list_a > list_a).
% 2.07/1.24 thf(func_def_40, type, maps_a_list_a: (a > list_list_a) > list_a > list_list_a).
% 2.07/1.24 thf(func_def_41, type, maps_a_a: (a > list_a) > list_a > list_a).
% 2.07/1.24 thf(func_def_42, type, lexordp_list_a: (list_a > list_a > $o) > list_list_a > list_list_a > $o).
% 2.07/1.24 thf(func_def_43, type, lexordp_a: (a > a > $o) > list_a > list_a > $o).
% 2.07/1.24 thf(func_def_44, type, lexordp_eq_list_a: (list_a > list_a > $o) > list_list_a > list_list_a > $o).
% 2.07/1.24 thf(func_def_45, type, lexordp_eq_a: (a > a > $o) > list_a > list_a > $o).
% 2.07/1.24 thf(func_def_46, type, product_lists_list_a: list_list_list_a > list_list_list_a).
% 2.07/1.24 thf(func_def_47, type, product_lists_a: list_list_a > list_list_a).
% 2.07/1.24 thf(func_def_48, type, rotate1_list_a: list_list_a > list_list_a).
% 2.07/1.24 thf(func_def_49, type, rotate1_a: list_a > list_a).
% 2.07/1.24 thf(func_def_50, type, subseqs_list_a: list_list_a > list_list_list_a).
% 2.07/1.24 thf(func_def_51, type, subseqs_a: list_a > list_list_a).
% 2.07/1.24 thf(func_def_52, type, modula1376131916tice_a: (a > a > a) > (a > a > $o) > (a > a > a) > a > a > a > $o).
% 2.07/1.24 thf(func_def_53, type, modula397570059tice_a: (a > a > a) > (a > a > $o) > (a > a > a) > a > a > a > $o).
% 2.07/1.24 thf(func_def_54, type, modula17988509_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.07/1.24 thf(func_def_55, type, modula1373251614_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.07/1.24 thf(func_def_56, type, modula581031071_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.07/1.24 thf(func_def_57, type, modula1936294176_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.07/1.24 thf(func_def_58, type, modula1144073633_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.07/1.24 thf(func_def_59, type, modula1962211574trib_a: (a > a > a) > (a > a > $o) > (a > a > a) > a > a > a > $o).
% 2.07/1.24 thf(func_def_60, type, transp_a: (a > a > $o) > $o).
% 2.07/1.24 thf(func_def_61, type, a2: a).
% 2.07/1.24 thf(func_def_62, type, b: a).
% 2.07/1.24 thf(func_def_63, type, c: a).
% 2.07/1.24 thf(func_def_64, type, inf: a > a > a).
% 2.07/1.24 thf(func_def_65, type, less: a > a > $o).
% 2.07/1.24 thf(func_def_66, type, sup: a > a > a).
% 2.07/1.24 thf(func_def_84, type, sK0: a).
% 2.07/1.24 thf(func_def_85, type, sK1: a).
% 2.07/1.24 thf(func_def_86, type, sK2: a).
% 2.07/1.24 thf(func_def_87, type, sK3: a).
% 2.07/1.24 thf(func_def_88, type, sK4: a).
% 2.07/1.24 thf(func_def_89, type, sK5: a).
% 2.07/1.24 thf(f1084,plain,(
% 2.07/1.24 $false),
% 2.07/1.24 inference(avatar_sat_refutation,[status(thm)],[f1068,f1083])).
% 2.07/1.24 thf(f1083,plain,(
% 2.07/1.24 ~spl6_5),
% 2.07/1.24 inference(avatar_contradiction_clause,[status(thm)],[f1082])).
% 2.07/1.24 thf(f1082,plain,(
% 2.07/1.24 $false | ~spl6_5),
% 2.07/1.24 inference(subsumption_resolution,[status(thm)],[f1081,f903])).
% 2.07/1.24 thf(f903,plain,(
% 2.07/1.24 ( ! [X0 : a] : (($true != (less @ X0 @ X0))) )),
% 2.07/1.24 inference(cnf_transformation,[status(thm)],[f822])).
% 2.07/1.24 thf(f822,plain,(
% 2.07/1.24 ! [X0 : a] : ($true != (less @ X0 @ X0))),
% 2.07/1.24 inference(flattening,[status(thm)],[f658])).
% 2.07/1.24 thf(f658,plain,(
% 2.07/1.24 ! [X0 : a] : ~($true = (less @ X0 @ X0))),
% 2.07/1.24 inference(fool_elimination,[status(thm)],[f657])).
% 2.07/1.24 thf(f657,plain,(
% 2.07/1.24 ! [X0 : a] : ~(less @ X0 @ X0)),
% 2.07/1.24 inference(rectify,[status(thm)],[f11])).
% 2.07/1.24 thf(f11,axiom,(
% 2.07/1.24 ! [X3 : a] : ~(less @ X3 @ X3)),
% 2.07/1.24 file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',fact_10_local_Oless__irrefl)).
% 2.07/1.24 thf(f1081,plain,(
% 2.07/1.24 ($true = (less @ b @ b)) | ~spl6_5),
% 2.07/1.24 inference(forward_demodulation,[status(thm)],[f1079,f936])).
% 2.07/1.24 thf(f936,plain,(
% 2.07/1.24 ( ! [X0 : a] : (((sup @ X0 @ X0) = X0)) )),
% 2.07/1.24 inference(cnf_transformation,[status(thm)],[f817])).
% 2.07/1.24 thf(f817,plain,(
% 2.07/1.24 ! [X0 : a] : ((sup @ X0 @ X0) = X0)),
% 2.07/1.24 inference(rectify,[status(thm)],[f55])).
% 2.07/1.24 thf(f55,axiom,(
% 2.07/1.24 ! [X3 : a] : ((sup @ X3 @ X3) = X3)),
% 2.07/1.24 file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',fact_54_local_Osup__idem)).
% 2.07/1.24 thf(f1079,plain,(
% 2.07/1.24 ($true = (less @ b @ (sup @ b @ b))) | ~spl6_5),
% 2.07/1.24 inference(superposition,[status(thm)],[f889,f1029])).
% 2.07/1.24 thf(f1029,plain,(
% 2.07/1.24 (b = c) | ~spl6_5),
% 2.07/1.24 inference(avatar_component_clause,[status(thm)],[f1027])).
% 2.07/1.24 thf(f1027,definition,(
% 2.07/1.24 spl6_5 <=> (b = c)),
% 2.07/1.24 introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition])).
% 2.07/1.24 thf(f889,plain,(
% 2.07/1.24 ((less @ b @ (sup @ b @ c)) = $true)),
% 2.07/1.24 inference(cnf_transformation,[status(thm)],[f708])).
% 2.07/1.24 thf(f708,plain,(
% 2.07/1.24 ((less @ b @ (sup @ b @ c)) = $true)),
% 2.07/1.24 inference(fool_elimination,[status(thm)],[f707])).
% 2.07/1.24 thf(f707,plain,(
% 2.07/1.24 (less @ b @ (sup @ b @ c))),
% 2.07/1.24 inference(rectify,[status(thm)],[f356])).
% 2.07/1.24 thf(f356,axiom,(
% 2.07/1.24 (less @ b @ (sup @ b @ c))),
% 2.07/1.24 file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',conj_3)).
% 2.07/1.24 thf(f1068,plain,(
% 2.07/1.24 spl6_5),
% 2.07/1.24 inference(avatar_split_clause,[status(thm)],[f1046,f1027])).
% 2.07/1.24 thf(f1046,plain,(
% 2.07/1.24 (b = c)),
% 2.07/1.24 inference(superposition,[status(thm)],[f911,f927])).
% 2.07/1.24 thf(f927,plain,(
% 2.07/1.24 (c = (inf @ c @ (sup @ b @ c)))),
% 2.07/1.24 inference(cnf_transformation,[status(thm)],[f357])).
% 2.07/1.24 thf(f357,axiom,(
% 2.07/1.24 (c = (inf @ c @ (sup @ b @ c)))),
% 2.07/1.24 file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',conj_4)).
% 2.07/1.24 thf(f911,plain,(
% 2.07/1.24 (b = (inf @ c @ (sup @ b @ c)))),
% 2.07/1.24 inference(cnf_transformation,[status(thm)],[f354])).
% 2.07/1.24 thf(f354,axiom,(
% 2.07/1.24 (b = (inf @ c @ (sup @ b @ c)))),
% 2.07/1.24 file('/export/starexec/sandbox/tmp/tmp.QCj81cxWHB/DTF2THF_2662.p',conj_1)).
% 2.07/1.24 % SZS output end Proof for DTF2THF_2662
% 2.07/1.24 % (2773)------------------------------
% 2.07/1.24 % (2773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.24 % (2773)Termination reason: Refutation
% 2.07/1.24
% 2.07/1.24 % (2773)Memory used [KB]: 6524
% 2.07/1.24 % (2773)Time elapsed: 0.026 s
% 2.07/1.24 % (2773)Instructions burned: 84 (million)
% 2.07/1.24 % (2773)------------------------------
% 2.07/1.24 % (2773)------------------------------
% 2.07/1.24 % (2767)Success in time 0.043 s
%------------------------------------------------------------------------------