%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT176^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 08:45:02 AM UTC 2026
% Result : Theorem 3.24s 1.82s
% Output : Refutation 3.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT176^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n018.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 06:09:16 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : DAT176^1 : TPTP v9.2.1. Released v7.0.0.
% 0.32/0.48 % Domain : Data Structures
% 0.32/0.48 % Problem : Lazy lists II 283
% 0.32/0.48 % Version : [Bla16] axioms : Especial.
% 0.32/0.48 % English :
% 0.32/0.48
% 0.32/0.48 % Refs : [Fri04] Friedrich (2004), Lazy Lists II
% 0.32/0.48 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.32/0.48 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.32/0.48 % Source : [Bla16]
% 0.32/0.48 % Names : llist2__283.p [Bla16]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.32/0.48 % Syntax : Number of formulae : 342 ( 140 unt; 43 typ; 0 def)
% 0.32/0.48 % Number of atoms : 590 ( 283 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 5 ( 1 avg)
% 0.32/0.48 % Number of connectives : 3667 ( 49 ~; 7 |; 23 &;3381 @)
% 0.32/0.48 % ( 0 <=>; 207 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 19 ( 6 avg)
% 0.32/0.48 % Number of types : 2 ( 1 usr)
% 0.32/0.48 % Number of type conns : 138 ( 138 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 43 ( 42 usr; 1 con; 0-5 aty)
% 0.32/0.48 % Number of variables : 908 ( 53 ^; 803 !; 13 ?; 908 :)
% 0.32/0.48 % ( 39 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.48 % SPC : TH1_THM_EQU_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.32/0.48 % 2016-07-13 14:45:22.261
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 %----Could-be-implicit typings (4)
% 0.32/0.48 thf(ty_t_Coinductive__List_Ollist,type,
% 0.32/0.48 coinductive_llist: $tType > $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_Set_Oset,type,
% 0.32/0.48 set: $tType > $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_itself,type,
% 0.32/0.48 itself: $tType > $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_tf_a,type,
% 0.32/0.48 a: $tType ).
% 0.32/0.48
% 0.32/0.48 %----Explicit typings (39)
% 0.32/0.48 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.32/0.48 bounded_lattice:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_HOL_Otype,type,
% 0.32/0.48 type:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Groups_Ominus,type,
% 0.32/0.48 minus:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Groups_Ouminus,type,
% 0.32/0.48 uminus:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Orderings_Obot,type,
% 0.32/0.48 bot:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Orderings_Otop,type,
% 0.32/0.48 top:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Groups_Ogroup__add,type,
% 0.32/0.48 group_add:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Olattice,type,
% 0.32/0.48 lattice:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Groups_Oab__group__add,type,
% 0.32/0.48 ab_group_add:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.32/0.48 boolean_algebra:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Odistrib__lattice,type,
% 0.32/0.48 distrib_lattice:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.32/0.48 semilattice_inf:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.32/0.48 semilattice_sup:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.32/0.48 bounded_lattice_bot:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.32/0.48 bounded_lattice_top:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.32/0.48 cancel146912293up_add:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Obounded__semilattice__inf__top,type,
% 0.32/0.48 bounde1561333602nf_top:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.32/0.48 bounde1808546759up_bot:
% 0.32/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.32/0.48 coinductive_LCons:
% 0.32/0.48 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.32/0.48 coinductive_LNil:
% 0.32/0.48 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.32/0.48 minus_minus:
% 0.32/0.48 !>[A: $tType] : ( A > A > A ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.32/0.48 uminus_uminus:
% 0.32/0.48 !>[A: $tType] : ( A > A ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 0.32/0.48 lList2435255213lllsts:
% 0.32/0.48 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.32/0.48 lList2236698231inlsts:
% 0.32/0.48 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.32/0.48 lList21916056377ts_rec:
% 0.32/0.48 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.32/0.48 lList22096119349pslsts:
% 0.32/0.48 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 0.32/0.48 lList21612149805nflsts:
% 0.32/0.48 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.32/0.48 lList21148268032oslsts:
% 0.32/0.48 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.32/0.48 inf_inf:
% 0.32/0.48 !>[A: $tType] : ( A > A > A ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.32/0.48 sup_sup:
% 0.32/0.48 !>[A: $tType] : ( A > A > A ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.32/0.48 bot_bot:
% 0.32/0.48 !>[A: $tType] : A ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.32/0.48 top_top:
% 0.32/0.48 !>[A: $tType] : A ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Pure_Otype,type,
% 0.32/0.48 type2:
% 0.32/0.48 !>[A: $tType] : ( itself @ A ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Set_OCollect,type,
% 0.32/0.48 collect:
% 0.32/0.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Set_Odisjnt,type,
% 0.32/0.48 disjnt:
% 0.32/0.48 !>[A: $tType] : ( ( set @ A ) > ( set @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Set_Oinsert,type,
% 0.32/0.48 insert:
% 0.32/0.48 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Set_Ois__empty,type,
% 0.32/0.48 is_empty:
% 0.32/0.48 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member,type,
% 0.32/0.48 member:
% 0.32/0.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_x,type,
% 0.32/0.48 x: coinductive_llist @ a ).
% 0.32/0.48
% 0.32/0.48 %----Relevant facts (256)
% 0.32/0.48 thf(fact_0_notfin__inf,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A] :
% 0.32/0.48 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.32/0.48 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % notfin_inf
% 0.32/0.48 thf(fact_1_finT__simp,axiom,
% 0.32/0.48 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finT_simp
% 0.32/0.48 thf(fact_2_infT__simp,axiom,
% 0.32/0.48 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % infT_simp
% 0.32/0.48 thf(fact_3_fin__finite,axiom,
% 0.32/0.48 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fin_finite
% 0.32/0.48 thf(fact_4_fin__inf__cases,axiom,
% 0.32/0.48 ! [A: $tType,R: coinductive_llist @ A] :
% 0.32/0.48 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fin_inf_cases
% 0.32/0.48 thf(fact_5_UNIV__I,axiom,
% 0.32/0.48 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % UNIV_I
% 0.32/0.48 thf(fact_6_iso__tuple__UNIV__I,axiom,
% 0.32/0.48 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % iso_tuple_UNIV_I
% 0.32/0.48 thf(fact_7_top__apply,axiom,
% 0.32/0.48 ! [C: $tType,D: $tType] :
% 0.32/0.48 ( ( top @ C @ ( type2 @ C ) )
% 0.32/0.48 => ( ( top_top @ ( D > C ) )
% 0.32/0.48 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % top_apply
% 0.32/0.48 thf(fact_8_inflstsI,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inflstsI
% 0.32/0.48 thf(fact_9_inflstsE,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.32/0.48 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inflstsE
% 0.32/0.48 thf(fact_10_alllstsE,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % alllstsE
% 0.32/0.48 thf(fact_11_UNIV__eq__I,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.32/0.48 => ( ( top_top @ ( set @ A ) )
% 0.32/0.48 = A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % UNIV_eq_I
% 0.32/0.48 thf(fact_12_UNIV__witness,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % UNIV_witness
% 0.32/0.48 thf(fact_13_alllsts__UNIV,axiom,
% 0.32/0.48 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % alllsts_UNIV
% 0.32/0.48 thf(fact_14_inflsts__def,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lList21612149805nflsts @ A )
% 0.32/0.48 = ( ^ [A3: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A3 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inflsts_def
% 0.32/0.48 thf(fact_15_infsubsetall,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % infsubsetall
% 0.32/0.48 thf(fact_16_finite__lemma,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_lemma
% 0.32/0.48 thf(fact_17_DiffI,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ A2 )
% 0.32/0.48 => ( ~ ( member @ A @ C2 @ B2 )
% 0.32/0.48 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % DiffI
% 0.32/0.48 thf(fact_18_Diff__iff,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( ( member @ A @ C2 @ A2 )
% 0.32/0.48 & ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_iff
% 0.32/0.48 thf(fact_19_Diff__idemp,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 0.32/0.48 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_idemp
% 0.32/0.48 thf(fact_20_DiffE,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 => ~ ( ( member @ A @ C2 @ A2 )
% 0.32/0.48 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % DiffE
% 0.32/0.48 thf(fact_21_DiffD1,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 => ( member @ A @ C2 @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % DiffD1
% 0.32/0.48 thf(fact_22_DiffD2,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 => ~ ( member @ A @ C2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % DiffD2
% 0.32/0.48 thf(fact_23_top__set__def,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( top_top @ ( set @ A ) )
% 0.32/0.48 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % top_set_def
% 0.32/0.48 thf(fact_24_finsubsetall,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finsubsetall
% 0.32/0.48 thf(fact_25_minus__apply,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( minus @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( minus_minus @ ( A > B ) )
% 0.32/0.48 = ( ^ [A3: A > B,B3: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B3 @ X2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % minus_apply
% 0.32/0.48 thf(fact_26_fin__Un__inf,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.32/0.48 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % fin_Un_inf
% 0.32/0.48 thf(fact_27_top__empty__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( top_top @ ( A > $o ) )
% 0.32/0.48 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % top_empty_eq
% 0.32/0.48 thf(fact_28_fun__diff__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( minus @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( minus_minus @ ( A > B ) )
% 0.32/0.48 = ( ^ [A3: A > B,B3: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B3 @ X2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fun_diff_def
% 0.32/0.48 thf(fact_29_diff__eq__diff__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A,C2: A,D2: A] :
% 0.32/0.48 ( ( ( minus_minus @ A @ A4 @ B4 )
% 0.32/0.48 = ( minus_minus @ A @ C2 @ D2 ) )
% 0.32/0.48 => ( ( A4 = B4 )
% 0.32/0.48 = ( C2 = D2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % diff_eq_diff_eq
% 0.32/0.48 thf(fact_30_diff__right__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,C2: A,B4: A] :
% 0.32/0.48 ( ( minus_minus @ A @ ( minus_minus @ A @ A4 @ C2 ) @ B4 )
% 0.32/0.48 = ( minus_minus @ A @ ( minus_minus @ A @ A4 @ B4 ) @ C2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % diff_right_commute
% 0.32/0.48 thf(fact_31_Diff__UNIV,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_UNIV
% 0.32/0.48 thf(fact_32_Compl__eq__Diff__UNIV,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( uminus_uminus @ ( set @ A ) )
% 0.32/0.48 = ( minus_minus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_eq_Diff_UNIV
% 0.32/0.48 thf(fact_33_LConsE,axiom,
% 0.32/0.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 = ( ( member @ A @ X @ A2 )
% 0.32/0.48 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % LConsE
% 0.32/0.48 thf(fact_34_Diff__empty,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = A2 ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_empty
% 0.32/0.48 thf(fact_35_bot__apply,axiom,
% 0.32/0.48 ! [C: $tType,D: $tType] :
% 0.32/0.48 ( ( bot @ C @ ( type2 @ C ) )
% 0.32/0.48 => ( ( bot_bot @ ( D > C ) )
% 0.32/0.48 = ( ^ [X2: D] : ( bot_bot @ C ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_apply
% 0.32/0.48 thf(fact_36_compl__eq__compl__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( ( uminus_uminus @ A @ X )
% 0.32/0.48 = ( uminus_uminus @ A @ Y ) )
% 0.32/0.48 = ( X = Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % compl_eq_compl_iff
% 0.32/0.48 thf(fact_37_double__compl,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % double_compl
% 0.32/0.48 thf(fact_38_neg__equal__iff__equal,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( ( uminus_uminus @ A @ A4 )
% 0.32/0.48 = ( uminus_uminus @ A @ B4 ) )
% 0.32/0.48 = ( A4 = B4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % neg_equal_iff_equal
% 0.32/0.48 thf(fact_39_add_Oinverse__inverse,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A] :
% 0.32/0.48 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A4 ) )
% 0.32/0.48 = A4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % add.inverse_inverse
% 0.32/0.48 thf(fact_40_uminus__apply,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( uminus @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( uminus_uminus @ ( A > B ) )
% 0.32/0.48 = ( ^ [A3: A > B,X2: A] : ( uminus_uminus @ B @ ( A3 @ X2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % uminus_apply
% 0.32/0.48 thf(fact_41_empty__iff,axiom,
% 0.32/0.48 ! [A: $tType,C2: A] :
% 0.32/0.48 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % empty_iff
% 0.32/0.48 thf(fact_42_all__not__in__conv,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( ! [X2: A] :
% 0.32/0.48 ~ ( member @ A @ X2 @ A2 ) )
% 0.32/0.48 = ( A2
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % all_not_in_conv
% 0.32/0.48 thf(fact_43_Collect__empty__eq,axiom,
% 0.32/0.48 ! [A: $tType,P: A > $o] :
% 0.32/0.48 ( ( ( collect @ A @ P )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( ! [X2: A] :
% 0.32/0.48 ~ ( P @ X2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Collect_empty_eq
% 0.32/0.48 thf(fact_44_empty__Collect__eq,axiom,
% 0.32/0.48 ! [A: $tType,P: A > $o] :
% 0.32/0.48 ( ( ( bot_bot @ ( set @ A ) )
% 0.32/0.48 = ( collect @ A @ P ) )
% 0.32/0.48 = ( ! [X2: A] :
% 0.32/0.48 ~ ( P @ X2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % empty_Collect_eq
% 0.32/0.48 thf(fact_45_mem__Collect__eq,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,P: A > $o] :
% 0.32/0.48 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.32/0.48 = ( P @ A4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % mem_Collect_eq
% 0.32/0.48 thf(fact_46_Collect__mem__eq,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( collect @ A
% 0.32/0.48 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.32/0.48 = A2 ) ).
% 0.32/0.48
% 0.32/0.48 % Collect_mem_eq
% 0.32/0.48 thf(fact_47_Collect__cong,axiom,
% 0.32/0.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.48 ( ! [X3: A] :
% 0.32/0.48 ( ( P @ X3 )
% 0.32/0.48 = ( Q @ X3 ) )
% 0.32/0.48 => ( ( collect @ A @ P )
% 0.32/0.48 = ( collect @ A @ Q ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Collect_cong
% 0.32/0.48 thf(fact_48_ext,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.32/0.48 ( ! [X3: A] :
% 0.32/0.48 ( ( F @ X3 )
% 0.32/0.48 = ( G @ X3 ) )
% 0.32/0.48 => ( F = G ) ) ).
% 0.32/0.48
% 0.32/0.48 % ext
% 0.32/0.48 thf(fact_49_sup_Oright__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B4 ) @ B4 )
% 0.32/0.48 = ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup.right_idem
% 0.32/0.48 thf(fact_50_sup__left__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.32/0.48 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_left_idem
% 0.32/0.48 thf(fact_51_sup_Oleft__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( sup_sup @ A @ A4 @ ( sup_sup @ A @ A4 @ B4 ) )
% 0.32/0.48 = ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup.left_idem
% 0.32/0.48 thf(fact_52_sup__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ X )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_idem
% 0.32/0.48 thf(fact_53_sup_Oidem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A] :
% 0.32/0.48 ( ( sup_sup @ A @ A4 @ A4 )
% 0.32/0.48 = A4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup.idem
% 0.32/0.48 thf(fact_54_sup__apply,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( sup_sup @ ( A > B ) )
% 0.32/0.48 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_apply
% 0.32/0.48 thf(fact_55_UnCI,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.32/0.48 ( ( ~ ( member @ A @ C2 @ B2 )
% 0.32/0.48 => ( member @ A @ C2 @ A2 ) )
% 0.32/0.48 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % UnCI
% 0.32/0.48 thf(fact_56_Un__iff,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( ( member @ A @ C2 @ A2 )
% 0.32/0.48 | ( member @ A @ C2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_iff
% 0.32/0.48 thf(fact_57_ComplI,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A] :
% 0.32/0.48 ( ~ ( member @ A @ C2 @ A2 )
% 0.32/0.48 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ComplI
% 0.32/0.48 thf(fact_58_Compl__iff,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.32/0.48 = ( ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_iff
% 0.32/0.48 thf(fact_59_Compl__eq__Compl__iff,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( ( uminus_uminus @ ( set @ A ) @ A2 )
% 0.32/0.48 = ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.32/0.48 = ( A2 = B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_eq_Compl_iff
% 0.32/0.48 thf(fact_60_top1I,axiom,
% 0.32/0.48 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.32/0.48
% 0.32/0.48 % top1I
% 0.32/0.48 thf(fact_61_minus__diff__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( uminus_uminus @ A @ ( minus_minus @ A @ A4 @ B4 ) )
% 0.32/0.48 = ( minus_minus @ A @ B4 @ A4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % minus_diff_eq
% 0.32/0.48 thf(fact_62_sup__bot_Oright__neutral,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A] :
% 0.32/0.48 ( ( sup_sup @ A @ A4 @ ( bot_bot @ A ) )
% 0.32/0.48 = A4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_bot.right_neutral
% 0.32/0.48 thf(fact_63_sup__bot_Oleft__neutral,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A4 )
% 0.32/0.48 = A4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_bot.left_neutral
% 0.32/0.48 thf(fact_64_sup__eq__bot__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( ( sup_sup @ A @ X @ Y )
% 0.32/0.48 = ( bot_bot @ A ) )
% 0.32/0.48 = ( ( X
% 0.32/0.48 = ( bot_bot @ A ) )
% 0.32/0.48 & ( Y
% 0.32/0.48 = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_eq_bot_iff
% 0.32/0.48 thf(fact_65_bot__eq__sup__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( ( bot_bot @ A )
% 0.32/0.48 = ( sup_sup @ A @ X @ Y ) )
% 0.32/0.48 = ( ( X
% 0.32/0.48 = ( bot_bot @ A ) )
% 0.32/0.48 & ( Y
% 0.32/0.48 = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_eq_sup_iff
% 0.32/0.48 thf(fact_66_sup__top__left,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( top_top @ A ) @ X )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_top_left
% 0.32/0.48 thf(fact_67_sup__top__right,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( top_top @ A ) )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_top_right
% 0.32/0.48 thf(fact_68_Un__empty,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( ( A2
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 & ( B2
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_empty
% 0.32/0.48 thf(fact_69_Diff__cancel,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ A2 @ A2 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_cancel
% 0.32/0.48 thf(fact_70_empty__Diff,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % empty_Diff
% 0.32/0.48 thf(fact_71_Un__Diff__cancel2,axiom,
% 0.32/0.48 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) @ A2 )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_Diff_cancel2
% 0.32/0.48 thf(fact_72_Un__Diff__cancel,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_Diff_cancel
% 0.32/0.48 thf(fact_73_inflsts__empty,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lList21612149805nflsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inflsts_empty
% 0.32/0.48 thf(fact_74_compl__bot__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( uminus_uminus @ A @ ( bot_bot @ A ) )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % compl_bot_eq
% 0.32/0.48 thf(fact_75_compl__top__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( uminus_uminus @ A @ ( top_top @ A ) )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % compl_top_eq
% 0.32/0.48 thf(fact_76_compl__sup__top,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ X )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % compl_sup_top
% 0.32/0.48 thf(fact_77_sup__compl__top,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( uminus_uminus @ A @ X ) )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_compl_top
% 0.32/0.48 thf(fact_78_sup__compl__top__left1,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ ( sup_sup @ A @ X @ Y ) )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_compl_top_left1
% 0.32/0.48 thf(fact_79_sup__compl__top__left2,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ Y ) )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_compl_top_left2
% 0.32/0.48 thf(fact_80_Compl__Diff__eq,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( uminus_uminus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_Diff_eq
% 0.32/0.48 thf(fact_81_UnE,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 => ( ~ ( member @ A @ C2 @ A2 )
% 0.32/0.48 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % UnE
% 0.32/0.48 thf(fact_82_UnI1,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ A2 )
% 0.32/0.48 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % UnI1
% 0.32/0.48 thf(fact_83_UnI2,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ B2 )
% 0.32/0.48 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % UnI2
% 0.32/0.48 thf(fact_84_ComplD,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.32/0.48 => ~ ( member @ A @ C2 @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % ComplD
% 0.32/0.48 thf(fact_85_bex__Un,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.32/0.48 ( ( ? [X2: A] :
% 0.32/0.48 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 & ( P @ X2 ) ) )
% 0.32/0.48 = ( ? [X2: A] :
% 0.32/0.48 ( ( member @ A @ X2 @ A2 )
% 0.32/0.48 & ( P @ X2 ) )
% 0.32/0.48 | ? [X2: A] :
% 0.32/0.48 ( ( member @ A @ X2 @ B2 )
% 0.32/0.48 & ( P @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bex_Un
% 0.32/0.48 thf(fact_86_emptyE,axiom,
% 0.32/0.48 ! [A: $tType,A4: A] :
% 0.32/0.48 ~ ( member @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % emptyE
% 0.32/0.48 thf(fact_87_ball__Un,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.32/0.48 ( ( ! [X2: A] :
% 0.32/0.48 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 => ( P @ X2 ) ) )
% 0.32/0.48 = ( ! [X2: A] :
% 0.32/0.48 ( ( member @ A @ X2 @ A2 )
% 0.32/0.48 => ( P @ X2 ) )
% 0.32/0.48 & ! [X2: A] :
% 0.32/0.48 ( ( member @ A @ X2 @ B2 )
% 0.32/0.48 => ( P @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ball_Un
% 0.32/0.48 thf(fact_88_Un__assoc,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_assoc
% 0.32/0.48 thf(fact_89_equals0D,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,A4: A] :
% 0.32/0.48 ( ( A2
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 => ~ ( member @ A @ A4 @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0D
% 0.32/0.48 thf(fact_90_equals0I,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ! [Y2: A] :
% 0.32/0.48 ~ ( member @ A @ Y2 @ A2 )
% 0.32/0.48 => ( A2
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0I
% 0.32/0.48 thf(fact_91_Un__absorb,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.32/0.48 = A2 ) ).
% 0.32/0.48
% 0.32/0.48 % Un_absorb
% 0.32/0.48 thf(fact_92_Un__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) )
% 0.32/0.48 = ( ^ [A3: set @ A,B3: set @ A] : ( sup_sup @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_commute
% 0.32/0.48 thf(fact_93_ex__in__conv,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( ? [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.32/0.48 = ( A2
% 0.32/0.48 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ex_in_conv
% 0.32/0.48 thf(fact_94_Un__empty__left,axiom,
% 0.32/0.48 ! [A: $tType,B2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.32/0.48 = B2 ) ).
% 0.32/0.48
% 0.32/0.48 % Un_empty_left
% 0.32/0.48 thf(fact_95_Un__empty__right,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = A2 ) ).
% 0.32/0.48
% 0.32/0.48 % Un_empty_right
% 0.32/0.48 thf(fact_96_Un__left__absorb,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_left_absorb
% 0.32/0.48 thf(fact_97_Compl__partition,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.32/0.48 = ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_partition
% 0.32/0.48 thf(fact_98_Un__left__commute,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_left_commute
% 0.32/0.48 thf(fact_99_Compl__partition2,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ A2 )
% 0.32/0.48 = ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_partition2
% 0.32/0.48 thf(fact_100_bot__fun__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( bot @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( bot_bot @ ( A > B ) )
% 0.32/0.48 = ( ^ [X2: A] : ( bot_bot @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_fun_def
% 0.32/0.48 thf(fact_101_double__complement,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.32/0.48 = A2 ) ).
% 0.32/0.48
% 0.32/0.48 % double_complement
% 0.32/0.48 thf(fact_102_sup__cancel__left1,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,A4: A,B4: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ A4 ) @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ B4 ) )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_cancel_left1
% 0.32/0.48 thf(fact_103_sup__cancel__left2,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,A4: A,B4: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ A4 ) @ ( sup_sup @ A @ X @ B4 ) )
% 0.32/0.48 = ( top_top @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_cancel_left2
% 0.32/0.48 thf(fact_104_sup__bot__right,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_bot_right
% 0.32/0.48 thf(fact_105_sup__left__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.32/0.48 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_left_commute
% 0.32/0.48 thf(fact_106_sup_Oleft__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [B4: A,A4: A,C2: A] :
% 0.32/0.48 ( ( sup_sup @ A @ B4 @ ( sup_sup @ A @ A4 @ C2 ) )
% 0.32/0.48 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup.left_commute
% 0.32/0.48 thf(fact_107_sup__bot__left,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_bot_left
% 0.32/0.48 thf(fact_108_sup__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( sup_sup @ A )
% 0.32/0.48 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_commute
% 0.32/0.48 thf(fact_109_sup_Ocommute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( sup_sup @ A )
% 0.32/0.48 = ( ^ [A5: A,B5: A] : ( sup_sup @ A @ B5 @ A5 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup.commute
% 0.32/0.48 thf(fact_110_minus__equation__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( ( uminus_uminus @ A @ A4 )
% 0.32/0.48 = B4 )
% 0.32/0.48 = ( ( uminus_uminus @ A @ B4 )
% 0.32/0.48 = A4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % minus_equation_iff
% 0.32/0.48 thf(fact_111_equation__minus__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( A4
% 0.32/0.48 = ( uminus_uminus @ A @ B4 ) )
% 0.32/0.48 = ( B4
% 0.32/0.48 = ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % equation_minus_iff
% 0.32/0.48 thf(fact_112_sup__assoc,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.32/0.48 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_assoc
% 0.32/0.48 thf(fact_113_sup_Oassoc,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A,C2: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B4 ) @ C2 )
% 0.32/0.48 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup.assoc
% 0.32/0.48 thf(fact_114_fun__Compl__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( uminus @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( uminus_uminus @ ( A > B ) )
% 0.32/0.48 = ( ^ [A3: A > B,X2: A] : ( uminus_uminus @ B @ ( A3 @ X2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fun_Compl_def
% 0.32/0.48 thf(fact_115_sup__fun__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( sup_sup @ ( A > B ) )
% 0.32/0.48 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_fun_def
% 0.32/0.48 thf(fact_116_inf__sup__aci_I5_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( sup_sup @ A )
% 0.32/0.48 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_aci(5)
% 0.32/0.48 thf(fact_117_inf__sup__aci_I6_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.32/0.48 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_aci(6)
% 0.32/0.48 thf(fact_118_inf__sup__aci_I7_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.32/0.48 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_aci(7)
% 0.32/0.48 thf(fact_119_inf__sup__aci_I8_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.32/0.48 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_aci(8)
% 0.32/0.48 thf(fact_120_Compl__empty__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( uminus_uminus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_empty_eq
% 0.32/0.48 thf(fact_121_Compl__UNIV__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( uminus_uminus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_UNIV_eq
% 0.32/0.48 thf(fact_122_Un__UNIV__left,axiom,
% 0.32/0.48 ! [A: $tType,B2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.32/0.48 = ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_UNIV_left
% 0.32/0.48 thf(fact_123_Un__UNIV__right,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.32/0.48 = ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_UNIV_right
% 0.32/0.48 thf(fact_124_Un__Diff,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_Diff
% 0.32/0.48 thf(fact_125_empty__not__UNIV,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bot_bot @ ( set @ A ) )
% 0.32/0.48 != ( top_top @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % empty_not_UNIV
% 0.32/0.48 thf(fact_126_finlsts_OLCons__fin,axiom,
% 0.32/0.48 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ( member @ A @ A4 @ A2 )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts.LCons_fin
% 0.32/0.48 thf(fact_127_alllsts_OLCons__all,axiom,
% 0.32/0.48 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 => ( ( member @ A @ A4 @ A2 )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % alllsts.LCons_all
% 0.32/0.48 thf(fact_128_inflstsI2,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,A2: set @ A,T: coinductive_llist @ A] :
% 0.32/0.48 ( ( member @ A @ A4 @ A2 )
% 0.32/0.48 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inflstsI2
% 0.32/0.48 thf(fact_129_inflsts__cases,axiom,
% 0.32/0.48 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.32/0.48 => ~ ! [A6: A,L2: coinductive_llist @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.32/0.48 => ( ( member @ A @ A6 @ A2 )
% 0.32/0.48 => ( S
% 0.32/0.48 != ( coinductive_LCons @ A @ A6 @ L2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inflsts_cases
% 0.32/0.48 thf(fact_130_llist_Oinject,axiom,
% 0.32/0.48 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.32/0.48 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.32/0.48 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.32/0.48 = ( ( X21 = Y21 )
% 0.32/0.48 & ( X22 = Y22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % llist.inject
% 0.32/0.48 thf(fact_131_minus__diff__minus,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( minus_minus @ A @ ( uminus_uminus @ A @ A4 ) @ ( uminus_uminus @ A @ B4 ) )
% 0.32/0.48 = ( uminus_uminus @ A @ ( minus_minus @ A @ A4 @ B4 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % minus_diff_minus
% 0.32/0.48 thf(fact_132_fpslsts__cases,axiom,
% 0.32/0.48 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.32/0.48 => ~ ! [A6: A,Rs: coinductive_llist @ A] :
% 0.32/0.48 ( ( R
% 0.32/0.48 = ( coinductive_LCons @ A @ A6 @ Rs ) )
% 0.32/0.48 => ( ( member @ A @ A6 @ A2 )
% 0.32/0.48 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fpslsts_cases
% 0.32/0.48 thf(fact_133_finlsts__rec__LCons,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,A4: A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.32/0.48 = ( D2 @ A4 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ R ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts_rec_LCons
% 0.32/0.48 thf(fact_134_finlsts__rec__LCons__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.32/0.48 ( ( F
% 0.32/0.48 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.32/0.48 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ( F @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.32/0.48 = ( D2 @ A4 @ R @ ( F @ R ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts_rec_LCons_def
% 0.32/0.48 thf(fact_135_top__conj_I2_J,axiom,
% 0.32/0.48 ! [A: $tType,P: $o,X: A] :
% 0.32/0.48 ( ( P
% 0.32/0.48 & ( top_top @ ( A > $o ) @ X ) )
% 0.32/0.48 = P ) ).
% 0.32/0.48
% 0.32/0.48 % top_conj(2)
% 0.32/0.48 thf(fact_136_top__conj_I1_J,axiom,
% 0.32/0.48 ! [A: $tType,X: A,P: $o] :
% 0.32/0.48 ( ( ( top_top @ ( A > $o ) @ X )
% 0.32/0.48 & P )
% 0.32/0.48 = P ) ).
% 0.32/0.48
% 0.32/0.48 % top_conj(1)
% 0.32/0.48 thf(fact_137_Set_Ois__empty__def,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( is_empty @ A )
% 0.32/0.48 = ( ^ [A3: set @ A] :
% 0.32/0.48 ( A3
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Set.is_empty_def
% 0.32/0.48 thf(fact_138_poslsts__empty,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lList21148268032oslsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % poslsts_empty
% 0.32/0.48 thf(fact_139_fpslsts__empty,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lList22096119349pslsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fpslsts_empty
% 0.32/0.48 thf(fact_140_bot__empty__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bot_bot @ ( A > $o ) )
% 0.32/0.48 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_empty_eq
% 0.32/0.48 thf(fact_141_bot__set__def,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bot_bot @ ( set @ A ) )
% 0.32/0.48 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_set_def
% 0.32/0.48 thf(fact_142_compl__unique,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( ( inf_inf @ A @ X @ Y )
% 0.32/0.48 = ( bot_bot @ A ) )
% 0.32/0.48 => ( ( ( sup_sup @ A @ X @ Y )
% 0.32/0.48 = ( top_top @ A ) )
% 0.32/0.48 => ( ( uminus_uminus @ A @ X )
% 0.32/0.48 = Y ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % compl_unique
% 0.32/0.48 thf(fact_143_fin__Int__inf,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.32/0.48 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fin_Int_inf
% 0.32/0.48 thf(fact_144_poslsts__iff,axiom,
% 0.32/0.48 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.32/0.48 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 & ( S
% 0.32/0.48 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % poslsts_iff
% 0.32/0.48 thf(fact_145_fpslsts__iff,axiom,
% 0.32/0.48 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.32/0.48 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 & ( S
% 0.32/0.48 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fpslsts_iff
% 0.32/0.48 thf(fact_146_inf__apply,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( inf_inf @ ( A > B ) )
% 0.32/0.48 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( inf_inf @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_apply
% 0.32/0.48 thf(fact_147_inf_Oidem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A] :
% 0.32/0.48 ( ( inf_inf @ A @ A4 @ A4 )
% 0.32/0.48 = A4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.idem
% 0.32/0.48 thf(fact_148_inf__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ X )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_idem
% 0.32/0.48 thf(fact_149_inf_Oleft__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( inf_inf @ A @ A4 @ ( inf_inf @ A @ A4 @ B4 ) )
% 0.32/0.48 = ( inf_inf @ A @ A4 @ B4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.left_idem
% 0.32/0.48 thf(fact_150_inf__left__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.32/0.48 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_left_idem
% 0.32/0.48 thf(fact_151_inf_Oright__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ A4 @ B4 ) @ B4 )
% 0.32/0.48 = ( inf_inf @ A @ A4 @ B4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.right_idem
% 0.32/0.48 thf(fact_152_inf__right__idem,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 0.32/0.48 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_right_idem
% 0.32/0.48 thf(fact_153_IntI,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ A2 )
% 0.32/0.48 => ( ( member @ A @ C2 @ B2 )
% 0.32/0.48 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % IntI
% 0.32/0.48 thf(fact_154_Int__iff,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( ( member @ A @ C2 @ A2 )
% 0.32/0.48 & ( member @ A @ C2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_iff
% 0.32/0.48 thf(fact_155_inf__bot__left,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_bot_left
% 0.32/0.48 thf(fact_156_inf__bot__right,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_bot_right
% 0.32/0.48 thf(fact_157_inf__top_Oright__neutral,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounde1561333602nf_top @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A] :
% 0.32/0.48 ( ( inf_inf @ A @ A4 @ ( top_top @ A ) )
% 0.32/0.48 = A4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_top.right_neutral
% 0.32/0.48 thf(fact_158_inf__top_Oleft__neutral,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounde1561333602nf_top @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( top_top @ A ) @ A4 )
% 0.32/0.48 = A4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_top.left_neutral
% 0.32/0.48 thf(fact_159_inf__eq__top__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( ( inf_inf @ A @ X @ Y )
% 0.32/0.48 = ( top_top @ A ) )
% 0.32/0.48 = ( ( X
% 0.32/0.48 = ( top_top @ A ) )
% 0.32/0.48 & ( Y
% 0.32/0.48 = ( top_top @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_eq_top_iff
% 0.32/0.48 thf(fact_160_inf__sup__absorb,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_absorb
% 0.32/0.48 thf(fact_161_sup__inf__absorb,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_inf_absorb
% 0.32/0.48 thf(fact_162_Int__UNIV,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.32/0.48 = ( top_top @ ( set @ A ) ) )
% 0.32/0.48 = ( ( A2
% 0.32/0.48 = ( top_top @ ( set @ A ) ) )
% 0.32/0.48 & ( B2
% 0.32/0.48 = ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_UNIV
% 0.32/0.48 thf(fact_163_inf__compl__bot__right,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ ( uminus_uminus @ A @ X ) ) )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_compl_bot_right
% 0.32/0.48 thf(fact_164_inf__compl__bot__left2,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ Y ) )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_compl_bot_left2
% 0.32/0.48 thf(fact_165_inf__compl__bot__left1,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ ( inf_inf @ A @ X @ Y ) )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_compl_bot_left1
% 0.32/0.48 thf(fact_166_inf__compl__bot,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( uminus_uminus @ A @ X ) )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_compl_bot
% 0.32/0.48 thf(fact_167_compl__inf__bot,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ X )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % compl_inf_bot
% 0.32/0.48 thf(fact_168_compl__sup,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( uminus_uminus @ A @ ( sup_sup @ A @ X @ Y ) )
% 0.32/0.48 = ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % compl_sup
% 0.32/0.48 thf(fact_169_compl__inf,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( uminus_uminus @ A @ ( inf_inf @ A @ X @ Y ) )
% 0.32/0.48 = ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % compl_inf
% 0.32/0.48 thf(fact_170_Diff__disjoint,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_disjoint
% 0.32/0.48 thf(fact_171_Compl__disjoint,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_disjoint
% 0.32/0.48 thf(fact_172_Compl__disjoint2,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ A2 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_disjoint2
% 0.32/0.48 thf(fact_173_Diff__Compl,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_Compl
% 0.32/0.48 thf(fact_174_poslsts__UNIV,axiom,
% 0.32/0.48 ! [A: $tType,S: coinductive_llist @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.32/0.48 = ( S
% 0.32/0.48 != ( coinductive_LNil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % poslsts_UNIV
% 0.32/0.48 thf(fact_175_neq__LNil__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( coinductive_LNil @ A ) )
% 0.32/0.48 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.32/0.48 ( Xs
% 0.32/0.48 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % neq_LNil_conv
% 0.32/0.48 thf(fact_176_llist_Odistinct_I1_J,axiom,
% 0.32/0.48 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.32/0.48 ( ( coinductive_LNil @ A )
% 0.32/0.48 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % llist.distinct(1)
% 0.32/0.48 thf(fact_177_inf__top__right,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( top_top @ A ) )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_top_right
% 0.32/0.48 thf(fact_178_inf__top__left,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( top_top @ A ) @ X )
% 0.32/0.48 = X ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_top_left
% 0.32/0.48 thf(fact_179_distrib__imp1,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ! [X3: A,Y2: A,Z2: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) )
% 0.32/0.48 = ( sup_sup @ A @ ( inf_inf @ A @ X3 @ Y2 ) @ ( inf_inf @ A @ X3 @ Z2 ) ) )
% 0.32/0.48 => ( ( sup_sup @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.32/0.48 = ( inf_inf @ A @ ( sup_sup @ A @ X @ Y ) @ ( sup_sup @ A @ X @ Z ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % distrib_imp1
% 0.32/0.48 thf(fact_180_distrib__imp2,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ! [X3: A,Y2: A,Z2: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X3 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 0.32/0.48 = ( inf_inf @ A @ ( sup_sup @ A @ X3 @ Y2 ) @ ( sup_sup @ A @ X3 @ Z2 ) ) )
% 0.32/0.48 => ( ( inf_inf @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.32/0.48 = ( sup_sup @ A @ ( inf_inf @ A @ X @ Y ) @ ( inf_inf @ A @ X @ Z ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % distrib_imp2
% 0.32/0.48 thf(fact_181_inf__sup__distrib1,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( distrib_lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.32/0.48 = ( sup_sup @ A @ ( inf_inf @ A @ X @ Y ) @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_distrib1
% 0.32/0.48 thf(fact_182_inf__sup__distrib2,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( distrib_lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [Y: A,Z: A,X: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( sup_sup @ A @ Y @ Z ) @ X )
% 0.32/0.48 = ( sup_sup @ A @ ( inf_inf @ A @ Y @ X ) @ ( inf_inf @ A @ Z @ X ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_distrib2
% 0.32/0.48 thf(fact_183_sup__inf__distrib1,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( distrib_lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( sup_sup @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.32/0.48 = ( inf_inf @ A @ ( sup_sup @ A @ X @ Y ) @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_inf_distrib1
% 0.32/0.48 thf(fact_184_sup__inf__distrib2,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( distrib_lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [Y: A,Z: A,X: A] :
% 0.32/0.48 ( ( sup_sup @ A @ ( inf_inf @ A @ Y @ Z ) @ X )
% 0.32/0.48 = ( inf_inf @ A @ ( sup_sup @ A @ Y @ X ) @ ( sup_sup @ A @ Z @ X ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sup_inf_distrib2
% 0.32/0.48 thf(fact_185_disjoint__iff__not__equal,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( ! [X2: A] :
% 0.32/0.48 ( ( member @ A @ X2 @ A2 )
% 0.32/0.48 => ! [Y3: A] :
% 0.32/0.48 ( ( member @ A @ Y3 @ B2 )
% 0.32/0.48 => ( X2 != Y3 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % disjoint_iff_not_equal
% 0.32/0.48 thf(fact_186_Int__empty__right,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_empty_right
% 0.32/0.48 thf(fact_187_Int__empty__left,axiom,
% 0.32/0.48 ! [A: $tType,B2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_empty_left
% 0.32/0.48 thf(fact_188_Int__emptyI,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ! [X3: A] :
% 0.32/0.48 ( ( member @ A @ X3 @ A2 )
% 0.32/0.48 => ~ ( member @ A @ X3 @ B2 ) )
% 0.32/0.48 => ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_emptyI
% 0.32/0.48 thf(fact_189_Int__UNIV__right,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.32/0.48 = A2 ) ).
% 0.32/0.48
% 0.32/0.48 % Int_UNIV_right
% 0.32/0.48 thf(fact_190_Int__UNIV__left,axiom,
% 0.32/0.48 ! [A: $tType,B2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.32/0.48 = B2 ) ).
% 0.32/0.48
% 0.32/0.48 % Int_UNIV_left
% 0.32/0.48 thf(fact_191_Un__Int__distrib2,axiom,
% 0.32/0.48 ! [A: $tType,B2: set @ A,C3: set @ A,A2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) @ A2 )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ B2 @ A2 ) @ ( sup_sup @ ( set @ A ) @ C3 @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_Int_distrib2
% 0.32/0.48 thf(fact_192_Int__Un__distrib2,axiom,
% 0.32/0.48 ! [A: $tType,B2: set @ A,C3: set @ A,A2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) @ A2 )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B2 @ A2 ) @ ( inf_inf @ ( set @ A ) @ C3 @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_Un_distrib2
% 0.32/0.48 thf(fact_193_Un__Int__distrib,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_Int_distrib
% 0.32/0.48 thf(fact_194_Int__Un__distrib,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_Un_distrib
% 0.32/0.48 thf(fact_195_Un__Int__crazy,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) @ ( inf_inf @ ( set @ A ) @ C3 @ A2 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) @ ( sup_sup @ ( set @ A ) @ C3 @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_Int_crazy
% 0.32/0.48 thf(fact_196_Int__Diff,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_Diff
% 0.32/0.48 thf(fact_197_Diff__Int2,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,C3: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.32/0.48 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_Int2
% 0.32/0.48 thf(fact_198_Diff__Diff__Int,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_Diff_Int
% 0.32/0.48 thf(fact_199_Diff__Int__distrib,axiom,
% 0.32/0.48 ! [A: $tType,C3: set @ A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ C3 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ C3 @ A2 ) @ ( inf_inf @ ( set @ A ) @ C3 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_Int_distrib
% 0.32/0.48 thf(fact_200_Diff__Int__distrib2,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.32/0.48 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_Int_distrib2
% 0.32/0.48 thf(fact_201_llistE,axiom,
% 0.32/0.48 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.32/0.48 ( ( Y
% 0.32/0.48 != ( coinductive_LNil @ A ) )
% 0.32/0.48 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % llistE
% 0.32/0.48 thf(fact_202_finlsts_OLNil__fin,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts.LNil_fin
% 0.32/0.48 thf(fact_203_alllsts_OLNil__all,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % alllsts.LNil_all
% 0.32/0.48 thf(fact_204_IntE,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 => ~ ( ( member @ A @ C2 @ A2 )
% 0.32/0.48 => ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % IntE
% 0.32/0.48 thf(fact_205_IntD1,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 => ( member @ A @ C2 @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % IntD1
% 0.32/0.48 thf(fact_206_IntD2,axiom,
% 0.32/0.48 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 => ( member @ A @ C2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % IntD2
% 0.32/0.48 thf(fact_207_Int__assoc,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_assoc
% 0.32/0.48 thf(fact_208_Int__absorb,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A2 @ A2 )
% 0.32/0.48 = A2 ) ).
% 0.32/0.48
% 0.32/0.48 % Int_absorb
% 0.32/0.48 thf(fact_209_Int__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) )
% 0.32/0.48 = ( ^ [A3: set @ A,B3: set @ A] : ( inf_inf @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_commute
% 0.32/0.48 thf(fact_210_Int__left__absorb,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_left_absorb
% 0.32/0.48 thf(fact_211_Int__left__commute,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ B2 @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_left_commute
% 0.32/0.48 thf(fact_212_inf__sup__aci_I4_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.32/0.48 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_aci(4)
% 0.32/0.48 thf(fact_213_inf__sup__aci_I3_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.32/0.48 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_aci(3)
% 0.32/0.48 thf(fact_214_inf__sup__aci_I2_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Z )
% 0.32/0.48 = ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_aci(2)
% 0.32/0.48 thf(fact_215_inf__sup__aci_I1_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( inf_inf @ A )
% 0.32/0.48 = ( ^ [X2: A,Y3: A] : ( inf_inf @ A @ Y3 @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_aci(1)
% 0.32/0.48 thf(fact_216_inf__fun__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.32/0.48 => ( ( inf_inf @ ( A > B ) )
% 0.32/0.48 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( inf_inf @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_fun_def
% 0.32/0.48 thf(fact_217_inf_Oassoc,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [A4: A,B4: A,C2: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ A4 @ B4 ) @ C2 )
% 0.32/0.48 = ( inf_inf @ A @ A4 @ ( inf_inf @ A @ B4 @ C2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.assoc
% 0.32/0.48 thf(fact_218_inf__assoc,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Z )
% 0.32/0.48 = ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_assoc
% 0.32/0.48 thf(fact_219_inf_Ocommute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( inf_inf @ A )
% 0.32/0.48 = ( ^ [A5: A,B5: A] : ( inf_inf @ A @ B5 @ A5 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.commute
% 0.32/0.48 thf(fact_220_inf__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( inf_inf @ A )
% 0.32/0.48 = ( ^ [X2: A,Y3: A] : ( inf_inf @ A @ Y3 @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_commute
% 0.32/0.48 thf(fact_221_inf_Oleft__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [B4: A,A4: A,C2: A] :
% 0.32/0.48 ( ( inf_inf @ A @ B4 @ ( inf_inf @ A @ A4 @ C2 ) )
% 0.32/0.48 = ( inf_inf @ A @ A4 @ ( inf_inf @ A @ B4 @ C2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.left_commute
% 0.32/0.48 thf(fact_222_inf__left__commute,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,Y: A,Z: A] :
% 0.32/0.48 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.32/0.48 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_left_commute
% 0.32/0.48 thf(fact_223_finlsts__rec__LNil__def,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 0.32/0.48 ( ( F
% 0.32/0.48 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.32/0.48 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.32/0.48 = C2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts_rec_LNil_def
% 0.32/0.48 thf(fact_224_finlsts__rec__LNil,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,C2: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 0.32/0.48 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D2 @ ( coinductive_LNil @ B ) )
% 0.32/0.48 = C2 ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts_rec_LNil
% 0.32/0.48 thf(fact_225_diff__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ( ( minus_minus @ A )
% 0.32/0.48 = ( ^ [X2: A,Y3: A] : ( inf_inf @ A @ X2 @ ( uminus_uminus @ A @ Y3 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % diff_eq
% 0.32/0.48 thf(fact_226_inf__cancel__left2,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,A4: A,B4: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ A4 ) @ ( inf_inf @ A @ X @ B4 ) )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_cancel_left2
% 0.32/0.48 thf(fact_227_inf__cancel__left1,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/0.48 => ! [X: A,A4: A,B4: A] :
% 0.32/0.48 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ A4 ) @ ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ B4 ) )
% 0.32/0.48 = ( bot_bot @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_cancel_left1
% 0.32/0.48 thf(fact_228_Diff__triv,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 => ( ( minus_minus @ ( set @ A ) @ A2 @ B2 )
% 0.32/0.48 = A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_triv
% 0.32/0.48 thf(fact_229_Un__Diff__Int,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = A2 ) ).
% 0.32/0.48
% 0.32/0.48 % Un_Diff_Int
% 0.32/0.48 thf(fact_230_Diff__Int,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_Int
% 0.32/0.48 thf(fact_231_Diff__Un,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_Un
% 0.32/0.48 thf(fact_232_Compl__Un,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( uminus_uminus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_Un
% 0.32/0.48 thf(fact_233_Compl__Int,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( uminus_uminus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.32/0.48 = ( sup_sup @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Compl_Int
% 0.32/0.48 thf(fact_234_Diff__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( minus_minus @ ( set @ A ) )
% 0.32/0.48 = ( ^ [A3: set @ A,B3: set @ A] : ( inf_inf @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ B3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diff_eq
% 0.32/0.48 thf(fact_235_finlsts_Ocases,axiom,
% 0.32/0.48 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ( A4
% 0.32/0.48 != ( coinductive_LNil @ A ) )
% 0.32/0.48 => ~ ! [L2: coinductive_llist @ A,A6: A] :
% 0.32/0.48 ( ( A4
% 0.32/0.48 = ( coinductive_LCons @ A @ A6 @ L2 ) )
% 0.32/0.48 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ~ ( member @ A @ A6 @ A2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts.cases
% 0.32/0.48 thf(fact_236_finlsts_Osimps,axiom,
% 0.32/0.48 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 = ( ( A4
% 0.32/0.48 = ( coinductive_LNil @ A ) )
% 0.32/0.48 | ? [L3: coinductive_llist @ A,A5: A] :
% 0.32/0.48 ( ( A4
% 0.32/0.48 = ( coinductive_LCons @ A @ A5 @ L3 ) )
% 0.32/0.48 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts.simps
% 0.32/0.48 thf(fact_237_finlsts__induct,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ! [L2: coinductive_llist @ A] :
% 0.32/0.48 ( ( L2
% 0.32/0.48 = ( coinductive_LNil @ A ) )
% 0.32/0.48 => ( P @ L2 ) )
% 0.32/0.48 => ( ! [A6: A,L2: coinductive_llist @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ( P @ L2 )
% 0.32/0.48 => ( ( member @ A @ A6 @ A2 )
% 0.32/0.48 => ( P @ ( coinductive_LCons @ A @ A6 @ L2 ) ) ) ) )
% 0.32/0.48 => ( P @ X ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts_induct
% 0.32/0.48 thf(fact_238_finlsts_Oinducts,axiom,
% 0.32/0.48 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.32/0.48 => ( ! [L2: coinductive_llist @ A,A6: A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.32/0.48 => ( ( P @ L2 )
% 0.32/0.48 => ( ( member @ A @ A6 @ A2 )
% 0.32/0.48 => ( P @ ( coinductive_LCons @ A @ A6 @ L2 ) ) ) ) )
% 0.32/0.48 => ( P @ X ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finlsts.inducts
% 0.32/0.48 thf(fact_239_alllsts_Ocoinduct,axiom,
% 0.32/0.48 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( X4 @ X )
% 0.32/0.48 => ( ! [X3: coinductive_llist @ A] :
% 0.32/0.48 ( ( X4 @ X3 )
% 0.32/0.48 => ( ( X3
% 0.32/0.48 = ( coinductive_LNil @ A ) )
% 0.32/0.48 | ? [L4: coinductive_llist @ A,A7: A] :
% 0.32/0.48 ( ( X3
% 0.32/0.48 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 0.32/0.48 & ( ( X4 @ L4 )
% 0.32/0.48 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.32/0.48 & ( member @ A @ A7 @ A2 ) ) ) )
% 0.32/0.48 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % alllsts.coinduct
% 0.32/0.48 thf(fact_240_alllsts_Osimps,axiom,
% 0.32/0.48 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 = ( ( A4
% 0.32/0.48 = ( coinductive_LNil @ A ) )
% 0.32/0.48 | ? [L3: coinductive_llist @ A,A5: A] :
% 0.32/0.48 ( ( A4
% 0.32/0.48 = ( coinductive_LCons @ A @ A5 @ L3 ) )
% 0.32/0.48 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % alllsts.simps
% 0.32/0.48 thf(fact_241_alllsts_Ocases,axiom,
% 0.32/0.48 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.32/0.48 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 => ( ( A4
% 0.32/0.48 != ( coinductive_LNil @ A ) )
% 0.32/0.48 => ~ ! [L2: coinductive_llist @ A,A6: A] :
% 0.32/0.48 ( ( A4
% 0.32/0.48 = ( coinductive_LCons @ A @ A6 @ L2 ) )
% 0.32/0.48 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.32/0.48 => ~ ( member @ A @ A6 @ A2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % alllsts.cases
% 0.32/0.48 thf(fact_242_disjnt__def,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( disjnt @ A )
% 0.32/0.48 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ A3 @ B3 )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % disjnt_def
% 0.32/0.48 thf(fact_243_Collect__empty__eq__bot,axiom,
% 0.32/0.48 ! [A: $tType,P: A > $o] :
% 0.32/0.48 ( ( ( collect @ A @ P )
% 0.32/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48 = ( P
% 0.32/0.48 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Collect_empty_eq_bot
% 0.32/0.48 thf(fact_244_poslsts__def,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( lList21148268032oslsts @ A )
% 0.32/0.48 = ( ^ [A3: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A3 ) @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % poslsts_def
% 0.32/0.48 thf(fact_245_insert__absorb2,axiom,
% 0.32/0.48 ! [A: $tType,X: A,A2: set @ A] :
% 0.32/0.48 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 0.32/0.48 = ( insert @ A @ X @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_absorb2
% 0.32/0.48 thf(fact_246_insert__iff,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,B4: A,A2: set @ A] :
% 0.32/0.48 ( ( member @ A @ A4 @ ( insert @ A @ B4 @ A2 ) )
% 0.32/0.48 = ( ( A4 = B4 )
% 0.32/0.48 | ( member @ A @ A4 @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_iff
% 0.32/0.48 thf(fact_247_insertCI,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,B2: set @ A,B4: A] :
% 0.32/0.48 ( ( ~ ( member @ A @ A4 @ B2 )
% 0.32/0.48 => ( A4 = B4 ) )
% 0.32/0.48 => ( member @ A @ A4 @ ( insert @ A @ B4 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertCI
% 0.32/0.48 thf(fact_248_singletonI,axiom,
% 0.32/0.48 ! [A: $tType,A4: A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % singletonI
% 0.32/0.48 thf(fact_249_Int__insert__left__if0,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,C3: set @ A,B2: set @ A] :
% 0.32/0.48 ( ~ ( member @ A @ A4 @ C3 )
% 0.32/0.48 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A4 @ B2 ) @ C3 )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_insert_left_if0
% 0.32/0.48 thf(fact_250_Int__insert__left__if1,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,C3: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ A4 @ C3 )
% 0.32/0.48 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A4 @ B2 ) @ C3 )
% 0.32/0.48 = ( insert @ A @ A4 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_insert_left_if1
% 0.32/0.48 thf(fact_251_insert__inter__insert,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A4 @ A2 ) @ ( insert @ A @ A4 @ B2 ) )
% 0.32/0.48 = ( insert @ A @ A4 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_inter_insert
% 0.32/0.48 thf(fact_252_Int__insert__right__if0,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ~ ( member @ A @ A4 @ A2 )
% 0.32/0.48 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A4 @ B2 ) )
% 0.32/0.48 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_insert_right_if0
% 0.32/0.48 thf(fact_253_Int__insert__right__if1,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,A2: set @ A,B2: set @ A] :
% 0.32/0.48 ( ( member @ A @ A4 @ A2 )
% 0.32/0.48 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A4 @ B2 ) )
% 0.32/0.48 = ( insert @ A @ A4 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Int_insert_right_if1
% 0.32/0.48 thf(fact_254_Un__insert__left,axiom,
% 0.32/0.48 ! [A: $tType,A4: A,B2: set @ A,C3: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A4 @ B2 ) @ C3 )
% 0.32/0.48 = ( insert @ A @ A4 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_insert_left
% 0.32/0.48 thf(fact_255_Un__insert__right,axiom,
% 0.32/0.48 ! [A: $tType,A2: set @ A,A4: A,B2: set @ A] :
% 0.32/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A4 @ B2 ) )
% 0.32/0.48 = ( insert @ A @ A4 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Un_insert_right
% 0.32/0.48
% 0.32/0.48 %----Type constructors (42)
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.32/0.48 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.32/0.48 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( bounde1808546759up_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Obounded__semilattice__inf__top,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( bounde1561333602nf_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( bounded_lattice_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( semilattice_inf @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( semilattice_inf @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Odistrib__lattice,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( distrib_lattice @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( distrib_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( boolean_algebra @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( boolean_algebra @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Orderings_Otop,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Orderings_Obot,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( uminus @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( uminus @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Groups_Ominus,axiom,
% 0.32/0.48 ! [A8: $tType,A9: $tType] :
% 0.32/0.48 ( ( minus @ A9 @ ( type2 @ A9 ) )
% 0.32/0.48 => ( minus @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 0.32/0.48 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_4,axiom,
% 0.32/0.48 ! [A8: $tType] : ( bounde1561333602nf_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5,axiom,
% 0.32/0.48 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6,axiom,
% 0.32/0.48 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_7,axiom,
% 0.32/0.48 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_8,axiom,
% 0.32/0.48 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Odistrib__lattice_9,axiom,
% 0.32/0.48 ! [A8: $tType] : ( distrib_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_10,axiom,
% 0.32/0.48 ! [A8: $tType] : ( boolean_algebra @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Lattices_Olattice_11,axiom,
% 0.32/0.48 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Orderings_Otop_12,axiom,
% 0.32/0.48 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Orderings_Obot_13,axiom,
% 0.32/0.48 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Groups_Ouminus_14,axiom,
% 0.32/0.48 ! [A8: $tType] : ( uminus @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Groups_Ominus_15,axiom,
% 0.32/0.48 ! [A8: $tType] : ( minus @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_16,axiom,
% 0.32/0.48 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_17,axiom,
% 0.32/0.48 bounde1561333602nf_top @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_18,axiom,
% 0.32/0.48 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_19,axiom,
% 0.32/0.48 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_20,axiom,
% 0.32/0.48 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_21,axiom,
% 0.32/0.48 semilattice_inf @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Odistrib__lattice_22,axiom,
% 0.32/0.48 distrib_lattice @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_23,axiom,
% 0.32/0.48 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Lattices_Olattice_24,axiom,
% 0.32/0.48 lattice @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Otop_25,axiom,
% 0.32/0.48 top @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Obot_26,axiom,
% 0.32/0.48 bot @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Groups_Ouminus_27,axiom,
% 0.32/0.48 uminus @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Groups_Ominus_28,axiom,
% 0.32/0.48 minus @ $o @ ( type2 @ $o ) ).
% 0.32/0.48
% 0.32/0.48 %----Conjectures (1)
% 0.32/0.48 thf(conj_0,conjecture,
% 0.32/0.48 ( ( ~ ( member @ ( coinductive_llist @ a ) @ x @ ( lList21612149805nflsts @ a @ ( top_top @ ( set @ a ) ) ) ) )
% 0.32/0.48 = ( member @ ( coinductive_llist @ a ) @ x @ ( lList2236698231inlsts @ a @ ( top_top @ ( set @ a ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 0.34/1.70 ---- Embedded in THF ---
% 0.34/1.70 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.34/1.70 %%% Generated on Tue Feb 24 06:09:17 EST 2026
% 0.34/1.70 %%% using '$$dhol' embedding, version 1.3.0.
% 0.34/1.70 %%% Logic specification used:
% 0.34/1.70 %%% thf(spec, logic, $$dhol).
% 0.34/1.70
% 0.34/1.70 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dhScex8tFU/DTF2DTF5135.p
% 0.34/1.70 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 0.34/1.70 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.34/1.70 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.34/1.70 thf(ty_tf_a, type, a: $tType).
% 0.34/1.70 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Groups_Ouminus, type, uminus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Groups_Oab__group__add, type, ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Odistrib__lattice, type, distrib_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Obounded__semilattice__inf__top, type, bounde1561333602nf_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.34/1.70 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 0.34/1.70 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 0.34/1.70 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 0.34/1.70 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 0.34/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts, type, lList2435255213lllsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 0.34/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts, type, lList2236698231inlsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 0.34/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec, type, lList21916056377ts_rec: (!> [B:$tType,A:$tType]: ((B > ((A > ((coinductive_llist @ A) > (B > B))) > ((coinductive_llist @ A) > B)))))).
% 0.34/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts, type, lList22096119349pslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 0.34/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts, type, lList21612149805nflsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 0.34/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts, type, lList21148268032oslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 0.34/1.70 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 0.34/1.70 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 0.34/1.70 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 0.34/1.70 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 0.34/1.70 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 0.34/1.70 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.34/1.70 thf(sy_c_Set_Odisjnt, type, disjnt: (!> [A:$tType]: (((set @ A) > ((set @ A) > $o))))).
% 0.34/1.70 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 0.34/1.70 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.34/1.70 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.34/1.70 thf(sy_v_x, type, x: (coinductive_llist @ a)).
% 0.34/1.70 thf(fact_0_notfin__inf, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 0.34/1.70 thf(fact_1_finT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 0.34/1.70 thf(fact_2_infT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 0.34/1.70 thf(fact_3_fin__finite, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 0.34/1.70 thf(fact_4_fin__inf__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 0.34/1.70 thf(fact_5_UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 0.34/1.70 thf(fact_6_iso__tuple__UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 0.34/1.70 thf(fact_7_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X2:D]: ((top_top @ C)))))))).
% 0.34/1.70 thf(fact_8_inflstsI, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 0.34/1.70 thf(fact_9_inflstsE, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => (~ (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))))))).
% 0.34/1.70 thf(fact_10_alllstsE, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 0.34/1.70 thf(fact_11_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 0.34/1.70 thf(fact_12_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 0.34/1.70 thf(fact_13_alllsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ (top_top @ (set @ A))))))).
% 0.34/1.70 thf(fact_14_inflsts__def, axiom, (! [A:$tType]: (((lList21612149805nflsts @ A) = (^ [A3:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A3)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))))).
% 0.34/1.70 thf(fact_15_infsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 0.34/1.70 thf(fact_16_finite__lemma, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),B2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ B2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ B2))))))).
% 0.34/1.70 thf(fact_17_DiffI, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A2) => ((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2))))))).
% 0.34/1.70 thf(fact_18_Diff__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C2) @ A2) & (~ ((((member @ A) @ C2) @ B2)))))))).
% 0.34/1.70 thf(fact_19_Diff__idemp, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ B2) = (((minus_minus @ (set @ A)) @ A2) @ B2))))).
% 0.34/1.70 thf(fact_20_DiffE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B2)))))))).
% 0.34/1.70 thf(fact_21_DiffD1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C2) @ A2))))).
% 0.34/1.70 thf(fact_22_DiffD2, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ ((((member @ A) @ C2) @ B2))))))).
% 0.34/1.70 thf(fact_23_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 0.34/1.70 thf(fact_24_finsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 0.34/1.70 thf(fact_25_minus__apply, axiom, (! [B:$tType,A:$tType]: ((((minus @ B) @ (type2 @ B)) => ((minus_minus @ (A > B)) = (^ [A3:(A > B),B3:(A > B),X2:A]: ((((minus_minus @ B) @ (A3 @ X2)) @ (B3 @ X2))))))))).
% 0.34/1.70 thf(fact_26_fin__Un__inf, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A2)) @ ((lList21612149805nflsts @ A) @ A2)) = ((lList2435255213lllsts @ A) @ A2))))).
% 0.34/1.70 thf(fact_27_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A))))))))).
% 0.34/1.70 thf(fact_28_fun__diff__def, axiom, (! [B:$tType,A:$tType]: ((((minus @ B) @ (type2 @ B)) => ((minus_minus @ (A > B)) = (^ [A3:(A > B),B3:(A > B),X2:A]: ((((minus_minus @ B) @ (A3 @ X2)) @ (B3 @ X2))))))))).
% 0.34/1.70 thf(fact_29_diff__eq__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A,D2:A]: ((((((minus_minus @ A) @ A4) @ B4) = (((minus_minus @ A) @ C2) @ D2)) => ((A4 = B4) = (C2 = D2))))))))).
% 0.34/1.70 thf(fact_30_diff__right__commute, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A4:A,C2:A,B4:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ B4) = (((minus_minus @ A) @ (((minus_minus @ A) @ A4) @ B4)) @ C2)))))))).
% 0.34/1.70 thf(fact_31_Diff__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_32_Compl__eq__Diff__UNIV, axiom, (! [A:$tType]: (((uminus_uminus @ (set @ A)) = ((minus_minus @ (set @ A)) @ (top_top @ (set @ A))))))).
% 0.34/1.70 thf(fact_33_LConsE, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ ((lList2435255213lllsts @ A) @ A2)) = ((((member @ A) @ X) @ A2) & (((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 0.34/1.70 thf(fact_34_Diff__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 0.34/1.70 thf(fact_35_bot__apply, axiom, (! [C:$tType,D:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D > C)) = (^ [X2:D]: ((bot_bot @ C)))))))).
% 0.34/1.70 thf(fact_36_compl__eq__compl__iff, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((uminus_uminus @ A) @ X) = ((uminus_uminus @ A) @ Y)) = (X = Y)))))))).
% 0.34/1.70 thf(fact_37_double__compl, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ X)) = X))))))).
% 0.34/1.70 thf(fact_38_neg__equal__iff__equal, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((uminus_uminus @ A) @ A4) = ((uminus_uminus @ A) @ B4)) = (A4 = B4)))))))).
% 0.34/1.70 thf(fact_39_add_Oinverse__inverse, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A4)) = A4))))))).
% 0.34/1.70 thf(fact_40_uminus__apply, axiom, (! [B:$tType,A:$tType]: ((((uminus @ B) @ (type2 @ B)) => ((uminus_uminus @ (A > B)) = (^ [A3:(A > B),X2:A]: (((uminus_uminus @ B) @ (A3 @ X2))))))))).
% 0.34/1.70 thf(fact_41_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 0.34/1.70 thf(fact_42_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X2:A]: ((~ ((((member @ A) @ X2) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 0.34/1.70 thf(fact_43_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 0.34/1.70 thf(fact_44_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 0.34/1.70 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 0.34/1.70 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 0.34/1.70 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.34/1.70 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 0.34/1.70 thf(fact_49_sup_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A4) @ B4)) @ B4) = (((sup_sup @ A) @ A4) @ B4)))))))).
% 0.34/1.70 thf(fact_50_sup__left__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 0.34/1.70 thf(fact_51_sup_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ A4) @ B4)) = (((sup_sup @ A) @ A4) @ B4)))))))).
% 0.34/1.70 thf(fact_52_sup__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 0.34/1.70 thf(fact_53_sup_Oidem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A]: (((((sup_sup @ A) @ A4) @ A4) = A4))))))).
% 0.34/1.70 thf(fact_54_sup__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 0.34/1.70 thf(fact_55_UnCI, axiom, (! [A:$tType,C2:A,B2:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ A2)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 0.34/1.70 thf(fact_56_Un__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C2) @ A2) | (((member @ A) @ C2) @ B2)))))).
% 0.34/1.70 thf(fact_57_ComplI, axiom, (! [A:$tType,C2:A,A2:(set @ A)]: (((~ ((((member @ A) @ C2) @ A2))) => (((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A2)))))).
% 0.34/1.70 thf(fact_58_Compl__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A2)) = (~ ((((member @ A) @ C2) @ A2))))))).
% 0.34/1.70 thf(fact_59_Compl__eq__Compl__iff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A2) = ((uminus_uminus @ (set @ A)) @ B2)) = (A2 = B2))))).
% 0.34/1.70 thf(fact_60_top1I, axiom, (! [A:$tType,X:A]: (((top_top @ (A > $o)) @ X)))).
% 0.34/1.70 thf(fact_61_minus__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: ((((uminus_uminus @ A) @ (((minus_minus @ A) @ A4) @ B4)) = (((minus_minus @ A) @ B4) @ A4)))))))).
% 0.34/1.70 thf(fact_62_sup__bot_Oright__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A4:A]: (((((sup_sup @ A) @ A4) @ (bot_bot @ A)) = A4))))))).
% 0.34/1.70 thf(fact_63_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A4:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A4) = A4))))))).
% 0.34/1.70 thf(fact_64_sup__eq__bot__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((sup_sup @ A) @ X) @ Y) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 0.34/1.70 thf(fact_65_bot__eq__sup__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 0.34/1.70 thf(fact_66_sup__top__left, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (top_top @ A)) @ X) = (top_top @ A)))))))).
% 0.34/1.70 thf(fact_67_sup__top__right, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (top_top @ A)) = (top_top @ A)))))))).
% 0.34/1.70 thf(fact_68_Un__empty, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A))) = ((A2 = (bot_bot @ (set @ A))) & (B2 = (bot_bot @ (set @ A)))))))).
% 0.34/1.70 thf(fact_69_Diff__cancel, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ A2) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_70_empty__Diff, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_71_Un__Diff__cancel2, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) @ A2) = (((sup_sup @ (set @ A)) @ B2) @ A2))))).
% 0.34/1.70 thf(fact_72_Un__Diff__cancel, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 0.34/1.70 thf(fact_73_inflsts__empty, axiom, (! [A:$tType]: ((((lList21612149805nflsts @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ (coinductive_llist @ A))))))).
% 0.34/1.70 thf(fact_74_compl__bot__eq, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (((uminus_uminus @ A) @ (bot_bot @ A)) = (top_top @ A)))))).
% 0.34/1.70 thf(fact_75_compl__top__eq, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (((uminus_uminus @ A) @ (top_top @ A)) = (bot_bot @ A)))))).
% 0.34/1.70 thf(fact_76_compl__sup__top, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ X) = (top_top @ A)))))))).
% 0.34/1.70 thf(fact_77_sup__compl__top, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ ((uminus_uminus @ A) @ X)) = (top_top @ A)))))))).
% 0.34/1.70 thf(fact_78_sup__compl__top__left1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ (((sup_sup @ A) @ X) @ Y)) = (top_top @ A)))))))).
% 0.34/1.70 thf(fact_79_sup__compl__top__left2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ Y)) = (top_top @ A)))))))).
% 0.34/1.70 thf(fact_80_Compl__Diff__eq, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = (((sup_sup @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ B2))))).
% 0.34/1.70 thf(fact_81_UnE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => ((~ ((((member @ A) @ C2) @ A2))) => (((member @ A) @ C2) @ B2)))))).
% 0.34/1.70 thf(fact_82_UnI1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 0.34/1.70 thf(fact_83_UnI2, axiom, (! [A:$tType,C2:A,B2:(set @ A),A2:(set @ A)]: (((((member @ A) @ C2) @ B2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 0.34/1.70 thf(fact_84_ComplD, axiom, (! [A:$tType,C2:A,A2:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A2)) => (~ ((((member @ A) @ C2) @ A2))))))).
% 0.34/1.70 thf(fact_85_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B2) & (P @ X2))))))))).
% 0.34/1.70 thf(fact_86_emptyE, axiom, (! [A:$tType,A4:A]: ((~ ((((member @ A) @ A4) @ (bot_bot @ (set @ A)))))))).
% 0.34/1.70 thf(fact_87_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A2) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B2) => (P @ X2))))))))).
% 0.34/1.70 thf(fact_88_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C3) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C3)))))).
% 0.34/1.70 thf(fact_89_equals0D, axiom, (! [A:$tType,A2:(set @ A),A4:A]: (((A2 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A4) @ A2))))))).
% 0.34/1.70 thf(fact_90_equals0I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [Y2:A]: ((~ ((((member @ A) @ Y2) @ A2))))) => (A2 = (bot_bot @ (set @ A))))))).
% 0.34/1.70 thf(fact_91_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 0.34/1.70 thf(fact_92_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((((sup_sup @ (set @ A)) @ B3) @ A3))))))).
% 0.34/1.70 thf(fact_93_ex__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((? [X2:A]: ((((member @ A) @ X2) @ A2))) = (A2 != (bot_bot @ (set @ A))))))).
% 0.34/1.70 thf(fact_94_Un__empty__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B2) = B2)))).
% 0.34/1.70 thf(fact_95_Un__empty__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 0.34/1.70 thf(fact_96_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 0.34/1.70 thf(fact_97_Compl__partition, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ ((uminus_uminus @ (set @ A)) @ A2)) = (top_top @ (set @ A)))))).
% 0.34/1.70 thf(fact_98_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C3)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A2) @ C3)))))).
% 0.34/1.70 thf(fact_99_Compl__partition2, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ A2) = (top_top @ (set @ A)))))).
% 0.34/1.70 thf(fact_100_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X2:A]: ((bot_bot @ B)))))))).
% 0.34/1.70 thf(fact_101_double__complement, axiom, (! [A:$tType,A2:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) = A2)))).
% 0.34/1.70 thf(fact_102_sup__cancel__left1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,A4:A,B4:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ A4)) @ (((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ B4)) = (top_top @ A)))))))).
% 0.34/1.70 thf(fact_103_sup__cancel__left2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,A4:A,B4:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ A4)) @ (((sup_sup @ A) @ X) @ B4)) = (top_top @ A)))))))).
% 0.34/1.70 thf(fact_104_sup__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 0.34/1.70 thf(fact_105_sup__left__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 0.34/1.70 thf(fact_106_sup_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B4:A,A4:A,C2:A]: (((((sup_sup @ A) @ B4) @ (((sup_sup @ A) @ A4) @ C2)) = (((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ B4) @ C2))))))))).
% 0.34/1.70 thf(fact_107_sup__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 0.34/1.70 thf(fact_108_sup__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X2)))))))).
% 0.34/1.70 thf(fact_109_sup_Ocommute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [A5:A,B5:A]: ((((sup_sup @ A) @ B5) @ A5)))))))).
% 0.34/1.70 thf(fact_110_minus__equation__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((uminus_uminus @ A) @ A4) = B4) = (((uminus_uminus @ A) @ B4) = A4)))))))).
% 0.34/1.70 thf(fact_111_equation__minus__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((A4 = ((uminus_uminus @ A) @ B4)) = (B4 = ((uminus_uminus @ A) @ A4))))))))).
% 0.34/1.70 thf(fact_112_sup__assoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 0.34/1.70 thf(fact_113_sup_Oassoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A4) @ B4)) @ C2) = (((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ B4) @ C2))))))))).
% 0.34/1.70 thf(fact_114_fun__Compl__def, axiom, (! [B:$tType,A:$tType]: ((((uminus @ B) @ (type2 @ B)) => ((uminus_uminus @ (A > B)) = (^ [A3:(A > B),X2:A]: (((uminus_uminus @ B) @ (A3 @ X2))))))))).
% 0.34/1.70 thf(fact_115_sup__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 0.34/1.70 thf(fact_116_inf__sup__aci_I5_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X2)))))))).
% 0.34/1.70 thf(fact_117_inf__sup__aci_I6_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 0.34/1.70 thf(fact_118_inf__sup__aci_I7_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 0.34/1.70 thf(fact_119_inf__sup__aci_I8_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 0.34/1.70 thf(fact_120_Compl__empty__eq, axiom, (! [A:$tType]: ((((uminus_uminus @ (set @ A)) @ (bot_bot @ (set @ A))) = (top_top @ (set @ A)))))).
% 0.34/1.70 thf(fact_121_Compl__UNIV__eq, axiom, (! [A:$tType]: ((((uminus_uminus @ (set @ A)) @ (top_top @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_122_Un__UNIV__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (top_top @ (set @ A))) @ B2) = (top_top @ (set @ A)))))).
% 0.34/1.70 thf(fact_123_Un__UNIV__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 0.34/1.70 thf(fact_124_Un__Diff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C3) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ C3)) @ (((minus_minus @ (set @ A)) @ B2) @ C3)))))).
% 0.34/1.70 thf(fact_125_empty__not__UNIV, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) != (top_top @ (set @ A)))))).
% 0.34/1.70 thf(fact_126_finlsts_OLCons__fin, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A4) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ L)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 0.34/1.70 thf(fact_127_alllsts_OLCons__all, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ A) @ A4) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ L)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 0.34/1.70 thf(fact_128_inflstsI2, axiom, (! [A:$tType,A4:A,A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ A) @ A4) @ A2) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 0.34/1.70 thf(fact_129_inflsts__cases, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => (~ ((! [A6:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ A) @ A6) @ A2) => (S != (((coinductive_LCons @ A) @ A6) @ L2)))))))))))).
% 0.34/1.70 thf(fact_130_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X22) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 0.34/1.70 thf(fact_131_minus__diff__minus, axiom, (! [A:$tType]: ((((ab_group_add @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((minus_minus @ A) @ ((uminus_uminus @ A) @ A4)) @ ((uminus_uminus @ A) @ B4)) = ((uminus_uminus @ A) @ (((minus_minus @ A) @ A4) @ B4))))))))).
% 0.34/1.70 thf(fact_132_fpslsts__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList22096119349pslsts @ A) @ A2)) => (~ ((! [A6:A,Rs:(coinductive_llist @ A)]: (((R = (((coinductive_LCons @ A) @ A6) @ Rs)) => ((((member @ A) @ A6) @ A2) => (~ ((((member @ (coinductive_llist @ A)) @ Rs) @ ((lList2236698231inlsts @ A) @ A2)))))))))))))).
% 0.34/1.70 thf(fact_133_finlsts__rec__LCons, axiom, (! [B:$tType,A:$tType,R:(coinductive_llist @ A),A2:(set @ A),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B))),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2) @ (((coinductive_LCons @ A) @ A4) @ R)) = (((D2 @ A4) @ R) @ (((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2) @ R))))))).
% 0.34/1.70 thf(fact_134_finlsts__rec__LCons__def, axiom, (! [B:$tType,A:$tType,F:((coinductive_llist @ A) > B),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B))),R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((F @ (((coinductive_LCons @ A) @ A4) @ R)) = (((D2 @ A4) @ R) @ (F @ R)))))))).
% 0.34/1.70 thf(fact_135_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X:A]: (((P & ((top_top @ (A > $o)) @ X)) = P)))).
% 0.34/1.70 thf(fact_136_top__conj_I1_J, axiom, (! [A:$tType,X:A,P:$o]: (((((top_top @ (A > $o)) @ X) & P) = P)))).
% 0.34/1.70 thf(fact_137_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A3:(set @ A)]: ((A3 = (bot_bot @ (set @ A))))))))).
% 0.34/1.70 thf(fact_138_poslsts__empty, axiom, (! [A:$tType]: ((((lList21148268032oslsts @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ (coinductive_llist @ A))))))).
% 0.34/1.70 thf(fact_139_fpslsts__empty, axiom, (! [A:$tType]: ((((lList22096119349pslsts @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ (coinductive_llist @ A))))))).
% 0.34/1.70 thf(fact_140_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (bot_bot @ (set @ A))))))))).
% 0.34/1.70 thf(fact_141_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 0.34/1.70 thf(fact_142_compl__unique, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((inf_inf @ A) @ X) @ Y) = (bot_bot @ A)) => (((((sup_sup @ A) @ X) @ Y) = (top_top @ A)) => (((uminus_uminus @ A) @ X) = Y))))))))).
% 0.34/1.70 thf(fact_143_fin__Int__inf, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A2)) @ ((lList21612149805nflsts @ A) @ A2)) = (bot_bot @ (set @ (coinductive_llist @ A))))))).
% 0.34/1.70 thf(fact_144_poslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2)) & (S != (coinductive_LNil @ A))))))).
% 0.34/1.70 thf(fact_145_fpslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList22096119349pslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) & (S != (coinductive_LNil @ A))))))).
% 0.34/1.70 thf(fact_146_inf__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_inf @ B) @ (type2 @ B)) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((inf_inf @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 0.34/1.70 thf(fact_147_inf_Oidem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A4:A]: (((((inf_inf @ A) @ A4) @ A4) = A4))))))).
% 0.34/1.70 thf(fact_148_inf__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ X) = X))))))).
% 0.34/1.70 thf(fact_149_inf_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((inf_inf @ A) @ A4) @ (((inf_inf @ A) @ A4) @ B4)) = (((inf_inf @ A) @ A4) @ B4)))))))).
% 0.34/1.70 thf(fact_150_inf__left__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = (((inf_inf @ A) @ X) @ Y)))))))).
% 0.34/1.70 thf(fact_151_inf_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A4:A,B4:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A4) @ B4)) @ B4) = (((inf_inf @ A) @ A4) @ B4)))))))).
% 0.34/1.70 thf(fact_152_inf__right__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Y) = (((inf_inf @ A) @ X) @ Y)))))))).
% 0.34/1.70 thf(fact_153_IntI, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A2) => ((((member @ A) @ C2) @ B2) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A2) @ B2))))))).
% 0.34/1.70 thf(fact_154_Int__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C2) @ A2) & (((member @ A) @ C2) @ B2)))))).
% 0.34/1.70 thf(fact_155_inf__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_156_inf__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_157_inf__top_Oright__neutral, axiom, (! [A:$tType]: ((((bounde1561333602nf_top @ A) @ (type2 @ A)) => (! [A4:A]: (((((inf_inf @ A) @ A4) @ (top_top @ A)) = A4))))))).
% 0.34/1.70 thf(fact_158_inf__top_Oleft__neutral, axiom, (! [A:$tType]: ((((bounde1561333602nf_top @ A) @ (type2 @ A)) => (! [A4:A]: (((((inf_inf @ A) @ (top_top @ A)) @ A4) = A4))))))).
% 0.34/1.70 thf(fact_159_inf__eq__top__iff, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((inf_inf @ A) @ X) @ Y) = (top_top @ A)) = ((X = (top_top @ A)) & (Y = (top_top @ A)))))))))).
% 0.34/1.70 thf(fact_160_inf__sup__absorb, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = X))))))).
% 0.34/1.70 thf(fact_161_sup__inf__absorb, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = X))))))).
% 0.34/1.70 thf(fact_162_Int__UNIV, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A2) @ B2) = (top_top @ (set @ A))) = ((A2 = (top_top @ (set @ A))) & (B2 = (top_top @ (set @ A)))))))).
% 0.34/1.70 thf(fact_163_inf__compl__bot__right, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ ((uminus_uminus @ A) @ X))) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_164_inf__compl__bot__left2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ Y)) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_165_inf__compl__bot__left1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ (((inf_inf @ A) @ X) @ Y)) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_166_inf__compl__bot, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ ((uminus_uminus @ A) @ X)) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_167_compl__inf__bot, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ X) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_168_compl__sup, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((uminus_uminus @ A) @ (((sup_sup @ A) @ X) @ Y)) = (((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ ((uminus_uminus @ A) @ Y))))))))).
% 0.34/1.70 thf(fact_169_compl__inf, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((uminus_uminus @ A) @ (((inf_inf @ A) @ X) @ Y)) = (((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ ((uminus_uminus @ A) @ Y))))))))).
% 0.34/1.70 thf(fact_170_Diff__disjoint, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_171_Compl__disjoint, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ ((uminus_uminus @ (set @ A)) @ A2)) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_172_Compl__disjoint2, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ A2) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_173_Diff__Compl, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ ((uminus_uminus @ (set @ A)) @ B2)) = (((inf_inf @ (set @ A)) @ A2) @ B2))))).
% 0.34/1.70 thf(fact_174_poslsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ (top_top @ (set @ A)))) = (S != (coinductive_LNil @ A)))))).
% 0.34/1.70 thf(fact_175_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X2:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs2)))))))).
% 0.34/1.70 thf(fact_176_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X21) @ X22))))).
% 0.34/1.70 thf(fact_177_inf__top__right, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ (top_top @ A)) = X))))))).
% 0.34/1.70 thf(fact_178_inf__top__left, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ (top_top @ A)) @ X) = X))))))).
% 0.34/1.70 thf(fact_179_distrib__imp1, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((! [X3:A,Y2:A,Z2:A]: (((((inf_inf @ A) @ X3) @ (((sup_sup @ A) @ Y2) @ Z2)) = (((sup_sup @ A) @ (((inf_inf @ A) @ X3) @ Y2)) @ (((inf_inf @ A) @ X3) @ Z2))))) => ((((sup_sup @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = (((inf_inf @ A) @ (((sup_sup @ A) @ X) @ Y)) @ (((sup_sup @ A) @ X) @ Z)))))))))).
% 0.34/1.70 thf(fact_180_distrib__imp2, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((! [X3:A,Y2:A,Z2:A]: (((((sup_sup @ A) @ X3) @ (((inf_inf @ A) @ Y2) @ Z2)) = (((inf_inf @ A) @ (((sup_sup @ A) @ X3) @ Y2)) @ (((sup_sup @ A) @ X3) @ Z2))))) => ((((inf_inf @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ (((inf_inf @ A) @ X) @ Y)) @ (((inf_inf @ A) @ X) @ Z)))))))))).
% 0.34/1.70 thf(fact_181_inf__sup__distrib1, axiom, (! [A:$tType]: ((((distrib_lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ (((inf_inf @ A) @ X) @ Y)) @ (((inf_inf @ A) @ X) @ Z))))))))).
% 0.34/1.70 thf(fact_182_inf__sup__distrib2, axiom, (! [A:$tType]: ((((distrib_lattice @ A) @ (type2 @ A)) => (! [Y:A,Z:A,X:A]: (((((inf_inf @ A) @ (((sup_sup @ A) @ Y) @ Z)) @ X) = (((sup_sup @ A) @ (((inf_inf @ A) @ Y) @ X)) @ (((inf_inf @ A) @ Z) @ X))))))))).
% 0.34/1.70 thf(fact_183_sup__inf__distrib1, axiom, (! [A:$tType]: ((((distrib_lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = (((inf_inf @ A) @ (((sup_sup @ A) @ X) @ Y)) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 0.34/1.70 thf(fact_184_sup__inf__distrib2, axiom, (! [A:$tType]: ((((distrib_lattice @ A) @ (type2 @ A)) => (! [Y:A,Z:A,X:A]: (((((sup_sup @ A) @ (((inf_inf @ A) @ Y) @ Z)) @ X) = (((inf_inf @ A) @ (((sup_sup @ A) @ Y) @ X)) @ (((sup_sup @ A) @ Z) @ X))))))))).
% 0.34/1.70 thf(fact_185_disjoint__iff__not__equal, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A))) = (! [X2:A]: (((((member @ A) @ X2) @ A2) => (! [Y3:A]: (((((member @ A) @ Y3) @ B2) => (X2 != Y3))))))))))).
% 0.34/1.70 thf(fact_186_Int__empty__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_187_Int__empty__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (bot_bot @ (set @ A))) @ B2) = (bot_bot @ (set @ A)))))).
% 0.34/1.70 thf(fact_188_Int__emptyI, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A2) => (~ ((((member @ A) @ X3) @ B2)))))) => ((((inf_inf @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A))))))).
% 0.34/1.70 thf(fact_189_Int__UNIV__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = A2)))).
% 0.34/1.70 thf(fact_190_Int__UNIV__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (top_top @ (set @ A))) @ B2) = B2)))).
% 0.34/1.70 thf(fact_191_Un__Int__distrib2, axiom, (! [A:$tType,B2:(set @ A),C3:(set @ A),A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((inf_inf @ (set @ A)) @ B2) @ C3)) @ A2) = (((inf_inf @ (set @ A)) @ (((sup_sup @ (set @ A)) @ B2) @ A2)) @ (((sup_sup @ (set @ A)) @ C3) @ A2)))))).
% 0.34/1.70 thf(fact_192_Int__Un__distrib2, axiom, (! [A:$tType,B2:(set @ A),C3:(set @ A),A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((sup_sup @ (set @ A)) @ B2) @ C3)) @ A2) = (((sup_sup @ (set @ A)) @ (((inf_inf @ (set @ A)) @ B2) @ A2)) @ (((inf_inf @ (set @ A)) @ C3) @ A2)))))).
% 0.34/1.70 thf(fact_193_Un__Int__distrib, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ B2) @ C3)) = (((inf_inf @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ (((sup_sup @ (set @ A)) @ A2) @ C3)))))).
% 0.34/1.70 thf(fact_194_Int__Un__distrib, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C3)) = (((sup_sup @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ (((inf_inf @ (set @ A)) @ A2) @ C3)))))).
% 0.34/1.70 thf(fact_195_Un__Int__crazy, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ (((inf_inf @ (set @ A)) @ B2) @ C3))) @ (((inf_inf @ (set @ A)) @ C3) @ A2)) = (((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ (((sup_sup @ (set @ A)) @ B2) @ C3))) @ (((sup_sup @ (set @ A)) @ C3) @ A2)))))).
% 0.34/1.70 thf(fact_196_Int__Diff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ C3) = (((inf_inf @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B2) @ C3)))))).
% 0.34/1.70 thf(fact_197_Diff__Int2, axiom, (! [A:$tType,A2:(set @ A),C3:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ C3)) @ (((inf_inf @ (set @ A)) @ B2) @ C3)) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ C3)) @ B2))))).
% 0.34/1.70 thf(fact_198_Diff__Diff__Int, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = (((inf_inf @ (set @ A)) @ A2) @ B2))))).
% 0.34/1.70 thf(fact_199_Diff__Int__distrib, axiom, (! [A:$tType,C3:(set @ A),A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ C3) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ C3) @ A2)) @ (((inf_inf @ (set @ A)) @ C3) @ B2)))))).
% 0.34/1.70 thf(fact_200_Diff__Int__distrib2, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ C3) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ C3)) @ (((inf_inf @ (set @ A)) @ B2) @ C3)))))).
% 0.34/1.70 thf(fact_201_llistE, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X212:A,X222:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X212) @ X222)))))))))).
% 0.34/1.70 thf(fact_202_finlsts_OLNil__fin, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2236698231inlsts @ A) @ A2))))).
% 0.34/1.70 thf(fact_203_alllsts_OLNil__all, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2435255213lllsts @ A) @ A2))))).
% 0.34/1.70 thf(fact_204_IntE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) => (~ (((((member @ A) @ C2) @ A2) => (~ ((((member @ A) @ C2) @ B2)))))))))).
% 0.34/1.70 thf(fact_205_IntD1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C2) @ A2))))).
% 0.34/1.70 thf(fact_206_IntD2, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C2) @ B2))))).
% 0.34/1.70 thf(fact_207_Int__assoc, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ C3) = (((inf_inf @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ B2) @ C3)))))).
% 0.34/1.70 thf(fact_208_Int__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ A2) = A2)))).
% 0.34/1.70 thf(fact_209_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((((inf_inf @ (set @ A)) @ B3) @ A3))))))).
% 0.34/1.70 thf(fact_210_Int__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) = (((inf_inf @ (set @ A)) @ A2) @ B2))))).
% 0.34/1.70 thf(fact_211_Int__left__commute, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ B2) @ C3)) = (((inf_inf @ (set @ A)) @ B2) @ (((inf_inf @ (set @ A)) @ A2) @ C3)))))).
% 0.34/1.70 thf(fact_212_inf__sup__aci_I4_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = (((inf_inf @ A) @ X) @ Y)))))))).
% 0.34/1.70 thf(fact_213_inf__sup__aci_I3_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = (((inf_inf @ A) @ Y) @ (((inf_inf @ A) @ X) @ Z))))))))).
% 0.34/1.70 thf(fact_214_inf__sup__aci_I2_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Z) = (((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z))))))))).
% 0.34/1.70 thf(fact_215_inf__sup__aci_I1_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [X2:A,Y3:A]: ((((inf_inf @ A) @ Y3) @ X2)))))))).
% 0.34/1.70 thf(fact_216_inf__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_inf @ B) @ (type2 @ B)) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((inf_inf @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 0.34/1.70 thf(fact_217_inf_Oassoc, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A4:A,B4:A,C2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A4) @ B4)) @ C2) = (((inf_inf @ A) @ A4) @ (((inf_inf @ A) @ B4) @ C2))))))))).
% 0.34/1.70 thf(fact_218_inf__assoc, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Z) = (((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z))))))))).
% 0.34/1.70 thf(fact_219_inf_Ocommute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [A5:A,B5:A]: ((((inf_inf @ A) @ B5) @ A5)))))))).
% 0.34/1.70 thf(fact_220_inf__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [X2:A,Y3:A]: ((((inf_inf @ A) @ Y3) @ X2)))))))).
% 0.34/1.70 thf(fact_221_inf_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [B4:A,A4:A,C2:A]: (((((inf_inf @ A) @ B4) @ (((inf_inf @ A) @ A4) @ C2)) = (((inf_inf @ A) @ A4) @ (((inf_inf @ A) @ B4) @ C2))))))))).
% 0.34/1.70 thf(fact_222_inf__left__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = (((inf_inf @ A) @ Y) @ (((inf_inf @ A) @ X) @ Z))))))))).
% 0.34/1.70 thf(fact_223_finlsts__rec__LNil__def, axiom, (! [A:$tType,B:$tType,F:((coinductive_llist @ A) > B),C2:B,D2:(A > ((coinductive_llist @ A) > (B > B)))]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C2) @ D2)) => ((F @ (coinductive_LNil @ A)) = C2))))).
% 0.34/1.70 thf(fact_224_finlsts__rec__LNil, axiom, (! [B:$tType,A:$tType,C2:A,D2:(B > ((coinductive_llist @ B) > (A > A)))]: (((((((lList21916056377ts_rec @ A) @ B) @ C2) @ D2) @ (coinductive_LNil @ B)) = C2)))).
% 0.34/1.70 thf(fact_225_diff__eq, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => ((minus_minus @ A) = (^ [X2:A,Y3:A]: ((((inf_inf @ A) @ X2) @ ((uminus_uminus @ A) @ Y3))))))))).
% 0.34/1.70 thf(fact_226_inf__cancel__left2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,A4:A,B4:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ A4)) @ (((inf_inf @ A) @ X) @ B4)) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_227_inf__cancel__left1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,A4:A,B4:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ A4)) @ (((inf_inf @ A) @ ((uminus_uminus @ A) @ X)) @ B4)) = (bot_bot @ A)))))))).
% 0.34/1.70 thf(fact_228_Diff__triv, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A))) => ((((minus_minus @ (set @ A)) @ A2) @ B2) = A2))))).
% 0.34/1.70 thf(fact_229_Un__Diff__Int, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) = A2)))).
% 0.34/1.70 thf(fact_230_Diff__Int, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ B2) @ C3)) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ (((minus_minus @ (set @ A)) @ A2) @ C3)))))).
% 0.34/1.70 thf(fact_231_Diff__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C3)) = (((inf_inf @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ (((minus_minus @ (set @ A)) @ A2) @ C3)))))).
% 0.34/1.70 thf(fact_232_Compl__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((inf_inf @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ ((uminus_uminus @ (set @ A)) @ B2)))))).
% 0.34/1.70 thf(fact_233_Compl__Int, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) = (((sup_sup @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ ((uminus_uminus @ (set @ A)) @ B2)))))).
% 0.34/1.70 thf(fact_234_Diff__eq, axiom, (! [A:$tType]: (((minus_minus @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((((inf_inf @ (set @ A)) @ A3) @ ((uminus_uminus @ (set @ A)) @ B3)))))))).
% 0.34/1.70 thf(fact_235_finlsts_Ocases, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2236698231inlsts @ A) @ A2)) => ((A4 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A6:A]: (((A4 = (((coinductive_LCons @ A) @ A6) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => (~ ((((member @ A) @ A6) @ A2)))))))))))))).
% 0.34/1.70 thf(fact_236_finlsts_Osimps, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2236698231inlsts @ A) @ A2)) = ((A4 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A5:A]: (((A4 = (((coinductive_LCons @ A) @ A5) @ L3)) & ((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ A) @ A5) @ A2)))))))))).
% 0.34/1.70 thf(fact_237_finlsts__induct, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((! [L2:(coinductive_llist @ A)]: (((L2 = (coinductive_LNil @ A)) => (P @ L2)))) => ((! [A6:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A6) @ A2) => (P @ (((coinductive_LCons @ A) @ A6) @ L2))))))) => (P @ X))))))).
% 0.34/1.70 thf(fact_238_finlsts_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [L2:(coinductive_llist @ A),A6:A]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A6) @ A2) => (P @ (((coinductive_LCons @ A) @ A6) @ L2))))))) => (P @ X))))))).
% 0.34/1.70 thf(fact_239_alllsts_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A),A2:(set @ A)]: (((X4 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X4 @ X3) => ((X3 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A7:A]: (((X3 = (((coinductive_LCons @ A) @ A7) @ L4)) & (((X4 @ L4) | (((member @ (coinductive_llist @ A)) @ L4) @ ((lList2435255213lllsts @ A) @ A2))) & (((member @ A) @ A7) @ A2))))))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 0.34/1.70 thf(fact_240_alllsts_Osimps, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2435255213lllsts @ A) @ A2)) = ((A4 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A5:A]: (((A4 = (((coinductive_LCons @ A) @ A5) @ L3)) & ((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ A) @ A5) @ A2)))))))))).
% 0.34/1.70 thf(fact_241_alllsts_Ocases, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2435255213lllsts @ A) @ A2)) => ((A4 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A6:A]: (((A4 = (((coinductive_LCons @ A) @ A6) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2435255213lllsts @ A) @ A2)) => (~ ((((member @ A) @ A6) @ A2)))))))))))))).
% 0.34/1.70 thf(fact_242_disjnt__def, axiom, (! [A:$tType]: (((disjnt @ A) = (^ [A3:(set @ A),B3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ B3) = (bot_bot @ (set @ A))))))))).
% 0.34/1.70 thf(fact_243_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 0.34/1.70 thf(fact_244_poslsts__def, axiom, (! [A:$tType]: (((lList21148268032oslsts @ A) = (^ [A3:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A3)) @ (((insert @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (bot_bot @ (set @ (coinductive_llist @ A))))))))))).
% 0.34/1.70 thf(fact_245_insert__absorb2, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A2)) = (((insert @ A) @ X) @ A2))))).
% 0.34/1.70 thf(fact_246_insert__iff, axiom, (! [A:$tType,A4:A,B4:A,A2:(set @ A)]: (((((member @ A) @ A4) @ (((insert @ A) @ B4) @ A2)) = ((A4 = B4) | (((member @ A) @ A4) @ A2)))))).
% 0.34/1.70 thf(fact_247_insertCI, axiom, (! [A:$tType,A4:A,B2:(set @ A),B4:A]: ((((~ ((((member @ A) @ A4) @ B2))) => (A4 = B4)) => (((member @ A) @ A4) @ (((insert @ A) @ B4) @ B2)))))).
% 0.34/1.70 thf(fact_248_singletonI, axiom, (! [A:$tType,A4:A]: ((((member @ A) @ A4) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))))).
% 0.34/1.70 thf(fact_249_Int__insert__left__if0, axiom, (! [A:$tType,A4:A,C3:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ A4) @ C3))) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A4) @ B2)) @ C3) = (((inf_inf @ (set @ A)) @ B2) @ C3)))))).
% 0.34/1.70 thf(fact_250_Int__insert__left__if1, axiom, (! [A:$tType,A4:A,C3:(set @ A),B2:(set @ A)]: (((((member @ A) @ A4) @ C3) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A4) @ B2)) @ C3) = (((insert @ A) @ A4) @ (((inf_inf @ (set @ A)) @ B2) @ C3))))))).
% 0.34/1.70 thf(fact_251_insert__inter__insert, axiom, (! [A:$tType,A4:A,A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((insert @ A) @ A4) @ A2)) @ (((insert @ A) @ A4) @ B2)) = (((insert @ A) @ A4) @ (((inf_inf @ (set @ A)) @ A2) @ B2)))))).
% 0.34/1.70 thf(fact_252_Int__insert__right__if0, axiom, (! [A:$tType,A4:A,A2:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ A4) @ A2))) => ((((inf_inf @ (set @ A)) @ A2) @ (((insert @ A) @ A4) @ B2)) = (((inf_inf @ (set @ A)) @ A2) @ B2)))))).
% 0.34/1.70 thf(fact_253_Int__insert__right__if1, axiom, (! [A:$tType,A4:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ A4) @ A2) => ((((inf_inf @ (set @ A)) @ A2) @ (((insert @ A) @ A4) @ B2)) = (((insert @ A) @ A4) @ (((inf_inf @ (set @ A)) @ A2) @ B2))))))).
% 0.34/1.70 thf(fact_254_Un__insert__left, axiom, (! [A:$tType,A4:A,B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A4) @ B2)) @ C3) = (((insert @ A) @ A4) @ (((sup_sup @ (set @ A)) @ B2) @ C3)))))).
% 0.34/1.70 thf(fact_255_Un__insert__right, axiom, (! [A:$tType,A2:(set @ A),A4:A,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((insert @ A) @ A4) @ B2)) = (((insert @ A) @ A4) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: (((bounded_lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounde1808546759up_bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Obounded__semilattice__inf__top, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounde1561333602nf_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Obounded__lattice__top, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice_bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: ((((semilattice_sup @ A9) @ (type2 @ A9)) => ((semilattice_sup @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A8:$tType,A9:$tType]: ((((semilattice_inf @ A9) @ (type2 @ A9)) => ((semilattice_inf @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Odistrib__lattice, axiom, (! [A8:$tType,A9:$tType]: ((((distrib_lattice @ A9) @ (type2 @ A9)) => ((distrib_lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A8:$tType,A9:$tType]: ((((boolean_algebra @ A9) @ (type2 @ A9)) => ((boolean_algebra @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: ((((lattice @ A9) @ (type2 @ A9)) => ((lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: ((((bot @ A9) @ (type2 @ A9)) => ((bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Groups_Ouminus, axiom, (! [A8:$tType,A9:$tType]: ((((uminus @ A9) @ (type2 @ A9)) => ((uminus @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_fun___Groups_Ominus, axiom, (! [A8:$tType,A9:$tType]: ((((minus @ A9) @ (type2 @ A9)) => ((minus @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3, axiom, (! [A8:$tType]: (((bounde1808546759up_bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_4, axiom, (! [A8:$tType]: (((bounde1561333602nf_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5, axiom, (! [A8:$tType]: (((bounded_lattice_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6, axiom, (! [A8:$tType]: (((bounded_lattice_bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_7, axiom, (! [A8:$tType]: (((semilattice_sup @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_8, axiom, (! [A8:$tType]: (((semilattice_inf @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Odistrib__lattice_9, axiom, (! [A8:$tType]: (((distrib_lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_10, axiom, (! [A8:$tType]: (((boolean_algebra @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Lattices_Olattice_11, axiom, (! [A8:$tType]: (((lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Orderings_Otop_12, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Orderings_Obot_13, axiom, (! [A8:$tType]: (((bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Groups_Ouminus_14, axiom, (! [A8:$tType]: (((uminus @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_Set_Oset___Groups_Ominus_15, axiom, (! [A8:$tType]: (((minus @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_16, axiom, ((bounde1808546759up_bot @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_17, axiom, ((bounde1561333602nf_top @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_18, axiom, ((bounded_lattice_top @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_19, axiom, ((bounded_lattice_bot @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_20, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_21, axiom, ((semilattice_inf @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Odistrib__lattice_22, axiom, ((distrib_lattice @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_23, axiom, ((boolean_algebra @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Lattices_Olattice_24, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Orderings_Otop_25, axiom, ((top @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Orderings_Obot_26, axiom, ((bot @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Groups_Ouminus_27, axiom, ((uminus @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(tcon_HOL_Obool___Groups_Ominus_28, axiom, ((minus @ $o) @ (type2 @ $o))).
% 0.34/1.70 thf(conj_0, conjecture, ((~ ((((member @ (coinductive_llist @ a)) @ x) @ ((lList21612149805nflsts @ a) @ (top_top @ (set @ a)))))) = (((member @ (coinductive_llist @ a)) @ x) @ ((lList2236698231inlsts @ a) @ (top_top @ (set @ a)))))).
% 0.34/1.70 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.dhScex8tFU/DTF2DTF5135.p
% 0.34/1.70 ------------------------
% 0.34/1.74 ---- Cleaned THF ---
% 0.34/1.75 thf(ty_t_Coinductive__List_Ollist,type,
% 0.34/1.75 coinductive_llist: $tType > $tType ).
% 0.34/1.75
% 0.34/1.75 thf(ty_t_Set_Oset,type,
% 0.34/1.75 set: $tType > $tType ).
% 0.34/1.75
% 0.34/1.75 thf(ty_t_itself,type,
% 0.34/1.75 itself: $tType > $tType ).
% 0.34/1.75
% 0.34/1.75 thf(ty_tf_a,type,
% 0.34/1.75 a: $tType ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.34/1.75 bounded_lattice:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_HOL_Otype,type,
% 0.34/1.75 type:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Groups_Ominus,type,
% 0.34/1.75 minus:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Groups_Ouminus,type,
% 0.34/1.75 uminus:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Orderings_Obot,type,
% 0.34/1.75 bot:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Orderings_Otop,type,
% 0.34/1.75 top:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Groups_Ogroup__add,type,
% 0.34/1.75 group_add:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Olattice,type,
% 0.34/1.75 lattice:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Groups_Oab__group__add,type,
% 0.34/1.75 ab_group_add:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.34/1.75 boolean_algebra:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Odistrib__lattice,type,
% 0.34/1.75 distrib_lattice:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.34/1.75 semilattice_inf:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.34/1.75 semilattice_sup:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.34/1.75 bounded_lattice_bot:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.34/1.75 bounded_lattice_top:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.34/1.75 cancel146912293up_add:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Obounded__semilattice__inf__top,type,
% 0.34/1.75 bounde1561333602nf_top:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.34/1.75 bounde1808546759up_bot:
% 0.34/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.34/1.75 coinductive_LCons:
% 0.34/1.75 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.34/1.75 coinductive_LNil:
% 0.34/1.75 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.34/1.75 minus_minus:
% 0.34/1.75 !>[A: $tType] : ( A > A > A ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.34/1.75 uminus_uminus:
% 0.34/1.75 !>[A: $tType] : ( A > A ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 0.34/1.75 lList2435255213lllsts:
% 0.34/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.34/1.75 lList2236698231inlsts:
% 0.34/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.34/1.75 lList21916056377ts_rec:
% 0.34/1.75 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.34/1.75 lList22096119349pslsts:
% 0.34/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 0.34/1.75 lList21612149805nflsts:
% 0.34/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.34/1.75 lList21148268032oslsts:
% 0.34/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.34/1.75 inf_inf:
% 0.34/1.75 !>[A: $tType] : ( A > A > A ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.34/1.75 sup_sup:
% 0.34/1.75 !>[A: $tType] : ( A > A > A ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.34/1.75 bot_bot:
% 0.34/1.75 !>[A: $tType] : A ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.34/1.75 top_top:
% 0.34/1.75 !>[A: $tType] : A ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Pure_Otype,type,
% 0.34/1.75 type2:
% 0.34/1.75 !>[A: $tType] : ( itself @ A ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Set_OCollect,type,
% 0.34/1.75 collect:
% 0.34/1.75 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Set_Odisjnt,type,
% 0.34/1.75 disjnt:
% 0.34/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Set_Oinsert,type,
% 0.34/1.75 insert:
% 0.34/1.75 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_Set_Ois__empty,type,
% 0.34/1.75 is_empty:
% 0.34/1.75 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_c_member,type,
% 0.34/1.75 member:
% 0.34/1.75 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(sy_v_x,type,
% 0.34/1.75 x: coinductive_llist @ a ).
% 0.34/1.75
% 0.34/1.75 thf(fact_0_notfin__inf,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A] :
% 0.34/1.75 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.34/1.75 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_1_finT__simp,axiom,
% 0.34/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_2_infT__simp,axiom,
% 0.34/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_3_fin__finite,axiom,
% 0.34/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_4_fin__inf__cases,axiom,
% 0.34/1.75 ! [A: $tType,R: coinductive_llist @ A] :
% 0.34/1.75 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_5_UNIV__I,axiom,
% 0.34/1.75 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_6_iso__tuple__UNIV__I,axiom,
% 0.34/1.75 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_7_top__apply,axiom,
% 0.34/1.75 ! [C: $tType,D: $tType] :
% 0.34/1.75 ( ( top @ C @ ( type2 @ C ) )
% 0.34/1.75 => ( ( top_top @ ( D > C ) )
% 0.34/1.75 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_8_inflstsI,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_9_inflstsE,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.34/1.75 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_10_alllstsE,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_11_UNIV__eq__I,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.34/1.75 => ( ( top_top @ ( set @ A ) )
% 0.34/1.75 = A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_12_UNIV__witness,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_13_alllsts__UNIV,axiom,
% 0.34/1.75 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_14_inflsts__def,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lList21612149805nflsts @ A )
% 0.34/1.75 = ( ^ [A3: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A3 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_15_infsubsetall,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_16_finite__lemma,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_17_DiffI,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ A2 )
% 0.34/1.75 => ( ~ ( member @ A @ C2 @ B2 )
% 0.34/1.75 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_18_Diff__iff,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( ( member @ A @ C2 @ A2 )
% 0.34/1.75 & ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_19_Diff__idemp,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 0.34/1.75 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_20_DiffE,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 => ~ ( ( member @ A @ C2 @ A2 )
% 0.34/1.75 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_21_DiffD1,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 => ( member @ A @ C2 @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_22_DiffD2,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 => ~ ( member @ A @ C2 @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_23_top__set__def,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( top_top @ ( set @ A ) )
% 0.34/1.75 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_24_finsubsetall,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_25_minus__apply,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( minus @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( minus_minus @ ( A > B ) )
% 0.34/1.75 = ( ^ [A3: A > B,B3: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B3 @ X2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_26_fin__Un__inf,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.34/1.75 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_27_top__empty__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( top_top @ ( A > $o ) )
% 0.34/1.75 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_28_fun__diff__def,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( minus @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( minus_minus @ ( A > B ) )
% 0.34/1.75 = ( ^ [A3: A > B,B3: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B3 @ X2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_29_diff__eq__diff__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A,C2: A,D2: A] :
% 0.34/1.75 ( ( ( minus_minus @ A @ A4 @ B4 )
% 0.34/1.75 = ( minus_minus @ A @ C2 @ D2 ) )
% 0.34/1.75 => ( ( A4 = B4 )
% 0.34/1.75 = ( C2 = D2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_30_diff__right__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,C2: A,B4: A] :
% 0.34/1.75 ( ( minus_minus @ A @ ( minus_minus @ A @ A4 @ C2 ) @ B4 )
% 0.34/1.75 = ( minus_minus @ A @ ( minus_minus @ A @ A4 @ B4 ) @ C2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_31_Diff__UNIV,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_32_Compl__eq__Diff__UNIV,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( uminus_uminus @ ( set @ A ) )
% 0.34/1.75 = ( minus_minus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_33_LConsE,axiom,
% 0.34/1.75 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 = ( ( member @ A @ X @ A2 )
% 0.34/1.75 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_34_Diff__empty,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = A2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_35_bot__apply,axiom,
% 0.34/1.75 ! [C: $tType,D: $tType] :
% 0.34/1.75 ( ( bot @ C @ ( type2 @ C ) )
% 0.34/1.75 => ( ( bot_bot @ ( D > C ) )
% 0.34/1.75 = ( ^ [X2: D] : ( bot_bot @ C ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_36_compl__eq__compl__iff,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( ( uminus_uminus @ A @ X )
% 0.34/1.75 = ( uminus_uminus @ A @ Y ) )
% 0.34/1.75 = ( X = Y ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_37_double__compl,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_38_neg__equal__iff__equal,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( ( uminus_uminus @ A @ A4 )
% 0.34/1.75 = ( uminus_uminus @ A @ B4 ) )
% 0.34/1.75 = ( A4 = B4 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_39_add_Oinverse__inverse,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A] :
% 0.34/1.75 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A4 ) )
% 0.34/1.75 = A4 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_40_uminus__apply,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( uminus @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( uminus_uminus @ ( A > B ) )
% 0.34/1.75 = ( ^ [A3: A > B,X2: A] : ( uminus_uminus @ B @ ( A3 @ X2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_41_empty__iff,axiom,
% 0.34/1.75 ! [A: $tType,C2: A] :
% 0.34/1.75 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_42_all__not__in__conv,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( ! [X2: A] :
% 0.34/1.75 ~ ( member @ A @ X2 @ A2 ) )
% 0.34/1.75 = ( A2
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_43_Collect__empty__eq,axiom,
% 0.34/1.75 ! [A: $tType,P: A > $o] :
% 0.34/1.75 ( ( ( collect @ A @ P )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( ! [X2: A] :
% 0.34/1.75 ~ ( P @ X2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_44_empty__Collect__eq,axiom,
% 0.34/1.75 ! [A: $tType,P: A > $o] :
% 0.34/1.75 ( ( ( bot_bot @ ( set @ A ) )
% 0.34/1.75 = ( collect @ A @ P ) )
% 0.34/1.75 = ( ! [X2: A] :
% 0.34/1.75 ~ ( P @ X2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_45_mem__Collect__eq,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,P: A > $o] :
% 0.34/1.75 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.34/1.75 = ( P @ A4 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_46_Collect__mem__eq,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( collect @ A
% 0.34/1.75 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.34/1.75 = A2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_47_Collect__cong,axiom,
% 0.34/1.75 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.34/1.75 ( ! [X3: A] :
% 0.34/1.75 ( ( P @ X3 )
% 0.34/1.75 = ( Q @ X3 ) )
% 0.34/1.75 => ( ( collect @ A @ P )
% 0.34/1.75 = ( collect @ A @ Q ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_48_ext,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.34/1.75 ( ! [X3: A] :
% 0.34/1.75 ( ( F @ X3 )
% 0.34/1.75 = ( G @ X3 ) )
% 0.34/1.75 => ( F = G ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_49_sup_Oright__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B4 ) @ B4 )
% 0.34/1.75 = ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_50_sup__left__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.34/1.75 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_51_sup_Oleft__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( sup_sup @ A @ A4 @ ( sup_sup @ A @ A4 @ B4 ) )
% 0.34/1.75 = ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_52_sup__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ X )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_53_sup_Oidem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A] :
% 0.34/1.75 ( ( sup_sup @ A @ A4 @ A4 )
% 0.34/1.75 = A4 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_54_sup__apply,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( sup_sup @ ( A > B ) )
% 0.34/1.75 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_55_UnCI,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.34/1.75 ( ( ~ ( member @ A @ C2 @ B2 )
% 0.34/1.75 => ( member @ A @ C2 @ A2 ) )
% 0.34/1.75 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_56_Un__iff,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( ( member @ A @ C2 @ A2 )
% 0.34/1.75 | ( member @ A @ C2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_57_ComplI,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A] :
% 0.34/1.75 ( ~ ( member @ A @ C2 @ A2 )
% 0.34/1.75 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_58_Compl__iff,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.34/1.75 = ( ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_59_Compl__eq__Compl__iff,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( ( uminus_uminus @ ( set @ A ) @ A2 )
% 0.34/1.75 = ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.34/1.75 = ( A2 = B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_60_top1I,axiom,
% 0.34/1.75 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_61_minus__diff__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( uminus_uminus @ A @ ( minus_minus @ A @ A4 @ B4 ) )
% 0.34/1.75 = ( minus_minus @ A @ B4 @ A4 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_62_sup__bot_Oright__neutral,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A] :
% 0.34/1.75 ( ( sup_sup @ A @ A4 @ ( bot_bot @ A ) )
% 0.34/1.75 = A4 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_63_sup__bot_Oleft__neutral,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A4 )
% 0.34/1.75 = A4 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_64_sup__eq__bot__iff,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( ( sup_sup @ A @ X @ Y )
% 0.34/1.75 = ( bot_bot @ A ) )
% 0.34/1.75 = ( ( X
% 0.34/1.75 = ( bot_bot @ A ) )
% 0.34/1.75 & ( Y
% 0.34/1.75 = ( bot_bot @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_65_bot__eq__sup__iff,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( ( bot_bot @ A )
% 0.34/1.75 = ( sup_sup @ A @ X @ Y ) )
% 0.34/1.75 = ( ( X
% 0.34/1.75 = ( bot_bot @ A ) )
% 0.34/1.75 & ( Y
% 0.34/1.75 = ( bot_bot @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_66_sup__top__left,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( top_top @ A ) @ X )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_67_sup__top__right,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( top_top @ A ) )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_68_Un__empty,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( ( A2
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 & ( B2
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_69_Diff__cancel,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ A2 @ A2 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_70_empty__Diff,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_71_Un__Diff__cancel2,axiom,
% 0.34/1.75 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) @ A2 )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_72_Un__Diff__cancel,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_73_inflsts__empty,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lList21612149805nflsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_74_compl__bot__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( uminus_uminus @ A @ ( bot_bot @ A ) )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_75_compl__top__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( uminus_uminus @ A @ ( top_top @ A ) )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_76_compl__sup__top,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ X )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_77_sup__compl__top,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( uminus_uminus @ A @ X ) )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_78_sup__compl__top__left1,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ ( sup_sup @ A @ X @ Y ) )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_79_sup__compl__top__left2,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ Y ) )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_80_Compl__Diff__eq,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( uminus_uminus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_81_UnE,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 => ( ~ ( member @ A @ C2 @ A2 )
% 0.34/1.75 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_82_UnI1,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ A2 )
% 0.34/1.75 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_83_UnI2,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ B2 )
% 0.34/1.75 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_84_ComplD,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.34/1.75 => ~ ( member @ A @ C2 @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_85_bex__Un,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.34/1.75 ( ( ? [X2: A] :
% 0.34/1.75 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 & ( P @ X2 ) ) )
% 0.34/1.75 = ( ? [X2: A] :
% 0.34/1.75 ( ( member @ A @ X2 @ A2 )
% 0.34/1.75 & ( P @ X2 ) )
% 0.34/1.75 | ? [X2: A] :
% 0.34/1.75 ( ( member @ A @ X2 @ B2 )
% 0.34/1.75 & ( P @ X2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_86_emptyE,axiom,
% 0.34/1.75 ! [A: $tType,A4: A] :
% 0.34/1.75 ~ ( member @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_87_ball__Un,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.34/1.75 ( ( ! [X2: A] :
% 0.34/1.75 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 => ( P @ X2 ) ) )
% 0.34/1.75 = ( ! [X2: A] :
% 0.34/1.75 ( ( member @ A @ X2 @ A2 )
% 0.34/1.75 => ( P @ X2 ) )
% 0.34/1.75 & ! [X2: A] :
% 0.34/1.75 ( ( member @ A @ X2 @ B2 )
% 0.34/1.75 => ( P @ X2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_88_Un__assoc,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_89_equals0D,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,A4: A] :
% 0.34/1.75 ( ( A2
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 => ~ ( member @ A @ A4 @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_90_equals0I,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ! [Y2: A] :
% 0.34/1.75 ~ ( member @ A @ Y2 @ A2 )
% 0.34/1.75 => ( A2
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_91_Un__absorb,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.34/1.75 = A2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_92_Un__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) )
% 0.34/1.75 = ( ^ [A3: set @ A,B3: set @ A] : ( sup_sup @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_93_ex__in__conv,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( ? [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.34/1.75 = ( A2
% 0.34/1.75 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_94_Un__empty__left,axiom,
% 0.34/1.75 ! [A: $tType,B2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.34/1.75 = B2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_95_Un__empty__right,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = A2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_96_Un__left__absorb,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_97_Compl__partition,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.34/1.75 = ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_98_Un__left__commute,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_99_Compl__partition2,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ A2 )
% 0.34/1.75 = ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_100_bot__fun__def,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( bot @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( bot_bot @ ( A > B ) )
% 0.34/1.75 = ( ^ [X2: A] : ( bot_bot @ B ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_101_double__complement,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.34/1.75 = A2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_102_sup__cancel__left1,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,A4: A,B4: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ A4 ) @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ B4 ) )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_103_sup__cancel__left2,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,A4: A,B4: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ A4 ) @ ( sup_sup @ A @ X @ B4 ) )
% 0.34/1.75 = ( top_top @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_104_sup__bot__right,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_105_sup__left__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.34/1.75 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_106_sup_Oleft__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [B4: A,A4: A,C2: A] :
% 0.34/1.75 ( ( sup_sup @ A @ B4 @ ( sup_sup @ A @ A4 @ C2 ) )
% 0.34/1.75 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_107_sup__bot__left,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_108_sup__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( sup_sup @ A )
% 0.34/1.75 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_109_sup_Ocommute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( sup_sup @ A )
% 0.34/1.75 = ( ^ [A5: A,B5: A] : ( sup_sup @ A @ B5 @ A5 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_110_minus__equation__iff,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( ( uminus_uminus @ A @ A4 )
% 0.34/1.75 = B4 )
% 0.34/1.75 = ( ( uminus_uminus @ A @ B4 )
% 0.34/1.75 = A4 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_111_equation__minus__iff,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( A4
% 0.34/1.75 = ( uminus_uminus @ A @ B4 ) )
% 0.34/1.75 = ( B4
% 0.34/1.75 = ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_112_sup__assoc,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.34/1.75 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_113_sup_Oassoc,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A,C2: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B4 ) @ C2 )
% 0.34/1.75 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_114_fun__Compl__def,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( uminus @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( uminus_uminus @ ( A > B ) )
% 0.34/1.75 = ( ^ [A3: A > B,X2: A] : ( uminus_uminus @ B @ ( A3 @ X2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_115_sup__fun__def,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( sup_sup @ ( A > B ) )
% 0.34/1.75 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_116_inf__sup__aci_I5_J,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( sup_sup @ A )
% 0.34/1.75 = ( ^ [X2: A,Y3: A] : ( sup_sup @ A @ Y3 @ X2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_117_inf__sup__aci_I6_J,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.34/1.75 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_118_inf__sup__aci_I7_J,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.34/1.75 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_119_inf__sup__aci_I8_J,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.34/1.75 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_120_Compl__empty__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( uminus_uminus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_121_Compl__UNIV__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( uminus_uminus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_122_Un__UNIV__left,axiom,
% 0.34/1.75 ! [A: $tType,B2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.34/1.75 = ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_123_Un__UNIV__right,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.34/1.75 = ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_124_Un__Diff,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_125_empty__not__UNIV,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bot_bot @ ( set @ A ) )
% 0.34/1.75 != ( top_top @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_126_finlsts_OLCons__fin,axiom,
% 0.34/1.75 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ( member @ A @ A4 @ A2 )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_127_alllsts_OLCons__all,axiom,
% 0.34/1.75 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 => ( ( member @ A @ A4 @ A2 )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_128_inflstsI2,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,A2: set @ A,T: coinductive_llist @ A] :
% 0.34/1.75 ( ( member @ A @ A4 @ A2 )
% 0.34/1.75 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_129_inflsts__cases,axiom,
% 0.34/1.75 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.34/1.75 => ~ ! [A6: A,L2: coinductive_llist @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.34/1.75 => ( ( member @ A @ A6 @ A2 )
% 0.34/1.75 => ( S
% 0.34/1.75 != ( coinductive_LCons @ A @ A6 @ L2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_130_llist_Oinject,axiom,
% 0.34/1.75 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.34/1.75 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.34/1.75 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.34/1.75 = ( ( X21 = Y21 )
% 0.34/1.75 & ( X22 = Y22 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_131_minus__diff__minus,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( minus_minus @ A @ ( uminus_uminus @ A @ A4 ) @ ( uminus_uminus @ A @ B4 ) )
% 0.34/1.75 = ( uminus_uminus @ A @ ( minus_minus @ A @ A4 @ B4 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_132_fpslsts__cases,axiom,
% 0.34/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.34/1.75 => ~ ! [A6: A,Rs: coinductive_llist @ A] :
% 0.34/1.75 ( ( R
% 0.34/1.75 = ( coinductive_LCons @ A @ A6 @ Rs ) )
% 0.34/1.75 => ( ( member @ A @ A6 @ A2 )
% 0.34/1.75 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_133_finlsts__rec__LCons,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,A4: A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.34/1.75 = ( D2 @ A4 @ R @ ( lList21916056377ts_rec @ B @ A @ C2 @ D2 @ R ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_134_finlsts__rec__LCons__def,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.34/1.75 ( ( F
% 0.34/1.75 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.34/1.75 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ( F @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.34/1.75 = ( D2 @ A4 @ R @ ( F @ R ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_135_top__conj_I2_J,axiom,
% 0.34/1.75 ! [A: $tType,P: $o,X: A] :
% 0.34/1.75 ( ( P
% 0.34/1.75 & ( top_top @ ( A > $o ) @ X ) )
% 0.34/1.75 = P ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_136_top__conj_I1_J,axiom,
% 0.34/1.75 ! [A: $tType,X: A,P: $o] :
% 0.34/1.75 ( ( ( top_top @ ( A > $o ) @ X )
% 0.34/1.75 & P )
% 0.34/1.75 = P ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_137_Set_Ois__empty__def,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( is_empty @ A )
% 0.34/1.75 = ( ^ [A3: set @ A] :
% 0.34/1.75 ( A3
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_138_poslsts__empty,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lList21148268032oslsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_139_fpslsts__empty,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lList22096119349pslsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_140_bot__empty__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bot_bot @ ( A > $o ) )
% 0.34/1.75 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_141_bot__set__def,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bot_bot @ ( set @ A ) )
% 0.34/1.75 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_142_compl__unique,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( ( inf_inf @ A @ X @ Y )
% 0.34/1.75 = ( bot_bot @ A ) )
% 0.34/1.75 => ( ( ( sup_sup @ A @ X @ Y )
% 0.34/1.75 = ( top_top @ A ) )
% 0.34/1.75 => ( ( uminus_uminus @ A @ X )
% 0.34/1.75 = Y ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_143_fin__Int__inf,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.34/1.75 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_144_poslsts__iff,axiom,
% 0.34/1.75 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.34/1.75 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 & ( S
% 0.34/1.75 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_145_fpslsts__iff,axiom,
% 0.34/1.75 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.34/1.75 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 & ( S
% 0.34/1.75 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_146_inf__apply,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( inf_inf @ ( A > B ) )
% 0.34/1.75 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( inf_inf @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_147_inf_Oidem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A] :
% 0.34/1.75 ( ( inf_inf @ A @ A4 @ A4 )
% 0.34/1.75 = A4 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_148_inf__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ X )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_149_inf_Oleft__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( inf_inf @ A @ A4 @ ( inf_inf @ A @ A4 @ B4 ) )
% 0.34/1.75 = ( inf_inf @ A @ A4 @ B4 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_150_inf__left__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.34/1.75 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_151_inf_Oright__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( inf_inf @ A @ A4 @ B4 ) @ B4 )
% 0.34/1.75 = ( inf_inf @ A @ A4 @ B4 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_152_inf__right__idem,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 0.34/1.75 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_153_IntI,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ A2 )
% 0.34/1.75 => ( ( member @ A @ C2 @ B2 )
% 0.34/1.75 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_154_Int__iff,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( ( member @ A @ C2 @ A2 )
% 0.34/1.75 & ( member @ A @ C2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_155_inf__bot__left,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_156_inf__bot__right,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_157_inf__top_Oright__neutral,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounde1561333602nf_top @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A] :
% 0.34/1.75 ( ( inf_inf @ A @ A4 @ ( top_top @ A ) )
% 0.34/1.75 = A4 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_158_inf__top_Oleft__neutral,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounde1561333602nf_top @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( top_top @ A ) @ A4 )
% 0.34/1.75 = A4 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_159_inf__eq__top__iff,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( ( inf_inf @ A @ X @ Y )
% 0.34/1.75 = ( top_top @ A ) )
% 0.34/1.75 = ( ( X
% 0.34/1.75 = ( top_top @ A ) )
% 0.34/1.75 & ( Y
% 0.34/1.75 = ( top_top @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_160_inf__sup__absorb,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_161_sup__inf__absorb,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_162_Int__UNIV,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.34/1.75 = ( top_top @ ( set @ A ) ) )
% 0.34/1.75 = ( ( A2
% 0.34/1.75 = ( top_top @ ( set @ A ) ) )
% 0.34/1.75 & ( B2
% 0.34/1.75 = ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_163_inf__compl__bot__right,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ ( uminus_uminus @ A @ X ) ) )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_164_inf__compl__bot__left2,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ Y ) )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_165_inf__compl__bot__left1,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ ( inf_inf @ A @ X @ Y ) )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_166_inf__compl__bot,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( uminus_uminus @ A @ X ) )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_167_compl__inf__bot,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ X )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_168_compl__sup,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( uminus_uminus @ A @ ( sup_sup @ A @ X @ Y ) )
% 0.34/1.75 = ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_169_compl__inf,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( uminus_uminus @ A @ ( inf_inf @ A @ X @ Y ) )
% 0.34/1.75 = ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_170_Diff__disjoint,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_171_Compl__disjoint,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_172_Compl__disjoint2,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ A2 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_173_Diff__Compl,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_174_poslsts__UNIV,axiom,
% 0.34/1.75 ! [A: $tType,S: coinductive_llist @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.34/1.75 = ( S
% 0.34/1.75 != ( coinductive_LNil @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_175_neq__LNil__conv,axiom,
% 0.34/1.75 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.34/1.75 ( ( Xs
% 0.34/1.75 != ( coinductive_LNil @ A ) )
% 0.34/1.75 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.34/1.75 ( Xs
% 0.34/1.75 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_176_llist_Odistinct_I1_J,axiom,
% 0.34/1.75 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.34/1.75 ( ( coinductive_LNil @ A )
% 0.34/1.75 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_177_inf__top__right,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( top_top @ A ) )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_178_inf__top__left,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( top_top @ A ) @ X )
% 0.34/1.75 = X ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_179_distrib__imp1,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ! [X3: A,Y2: A,Z2: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X3 @ ( sup_sup @ A @ Y2 @ Z2 ) )
% 0.34/1.75 = ( sup_sup @ A @ ( inf_inf @ A @ X3 @ Y2 ) @ ( inf_inf @ A @ X3 @ Z2 ) ) )
% 0.34/1.75 => ( ( sup_sup @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.34/1.75 = ( inf_inf @ A @ ( sup_sup @ A @ X @ Y ) @ ( sup_sup @ A @ X @ Z ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_180_distrib__imp2,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ! [X3: A,Y2: A,Z2: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X3 @ ( inf_inf @ A @ Y2 @ Z2 ) )
% 0.34/1.75 = ( inf_inf @ A @ ( sup_sup @ A @ X3 @ Y2 ) @ ( sup_sup @ A @ X3 @ Z2 ) ) )
% 0.34/1.75 => ( ( inf_inf @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.34/1.75 = ( sup_sup @ A @ ( inf_inf @ A @ X @ Y ) @ ( inf_inf @ A @ X @ Z ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_181_inf__sup__distrib1,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( distrib_lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.34/1.75 = ( sup_sup @ A @ ( inf_inf @ A @ X @ Y ) @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_182_inf__sup__distrib2,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( distrib_lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [Y: A,Z: A,X: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( sup_sup @ A @ Y @ Z ) @ X )
% 0.34/1.75 = ( sup_sup @ A @ ( inf_inf @ A @ Y @ X ) @ ( inf_inf @ A @ Z @ X ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_183_sup__inf__distrib1,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( distrib_lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( sup_sup @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.34/1.75 = ( inf_inf @ A @ ( sup_sup @ A @ X @ Y ) @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_184_sup__inf__distrib2,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( distrib_lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [Y: A,Z: A,X: A] :
% 0.34/1.75 ( ( sup_sup @ A @ ( inf_inf @ A @ Y @ Z ) @ X )
% 0.34/1.75 = ( inf_inf @ A @ ( sup_sup @ A @ Y @ X ) @ ( sup_sup @ A @ Z @ X ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_185_disjoint__iff__not__equal,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( ! [X2: A] :
% 0.34/1.75 ( ( member @ A @ X2 @ A2 )
% 0.34/1.75 => ! [Y3: A] :
% 0.34/1.75 ( ( member @ A @ Y3 @ B2 )
% 0.34/1.75 => ( X2 != Y3 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_186_Int__empty__right,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_187_Int__empty__left,axiom,
% 0.34/1.75 ! [A: $tType,B2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_188_Int__emptyI,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ! [X3: A] :
% 0.34/1.75 ( ( member @ A @ X3 @ A2 )
% 0.34/1.75 => ~ ( member @ A @ X3 @ B2 ) )
% 0.34/1.75 => ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_189_Int__UNIV__right,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.34/1.75 = A2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_190_Int__UNIV__left,axiom,
% 0.34/1.75 ! [A: $tType,B2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.34/1.75 = B2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_191_Un__Int__distrib2,axiom,
% 0.34/1.75 ! [A: $tType,B2: set @ A,C3: set @ A,A2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) @ A2 )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ B2 @ A2 ) @ ( sup_sup @ ( set @ A ) @ C3 @ A2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_192_Int__Un__distrib2,axiom,
% 0.34/1.75 ! [A: $tType,B2: set @ A,C3: set @ A,A2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) @ A2 )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B2 @ A2 ) @ ( inf_inf @ ( set @ A ) @ C3 @ A2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_193_Un__Int__distrib,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_194_Int__Un__distrib,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_195_Un__Int__crazy,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) @ ( inf_inf @ ( set @ A ) @ C3 @ A2 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) @ ( sup_sup @ ( set @ A ) @ C3 @ A2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_196_Int__Diff,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_197_Diff__Int2,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,C3: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.34/1.75 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_198_Diff__Diff__Int,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_199_Diff__Int__distrib,axiom,
% 0.34/1.75 ! [A: $tType,C3: set @ A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ C3 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ C3 @ A2 ) @ ( inf_inf @ ( set @ A ) @ C3 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_200_Diff__Int__distrib2,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.34/1.75 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_201_llistE,axiom,
% 0.34/1.75 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.34/1.75 ( ( Y
% 0.34/1.75 != ( coinductive_LNil @ A ) )
% 0.34/1.75 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.34/1.75 ( Y
% 0.34/1.75 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_202_finlsts_OLNil__fin,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_203_alllsts_OLNil__all,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_204_IntE,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 => ~ ( ( member @ A @ C2 @ A2 )
% 0.34/1.75 => ~ ( member @ A @ C2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_205_IntD1,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 => ( member @ A @ C2 @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_206_IntD2,axiom,
% 0.34/1.75 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 => ( member @ A @ C2 @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_207_Int__assoc,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_208_Int__absorb,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A2 @ A2 )
% 0.34/1.75 = A2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_209_Int__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) )
% 0.34/1.75 = ( ^ [A3: set @ A,B3: set @ A] : ( inf_inf @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_210_Int__left__absorb,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_211_Int__left__commute,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ B2 @ ( inf_inf @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_212_inf__sup__aci_I4_J,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.34/1.75 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_213_inf__sup__aci_I3_J,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.34/1.75 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_214_inf__sup__aci_I2_J,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Z )
% 0.34/1.75 = ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_215_inf__sup__aci_I1_J,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lattice @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( inf_inf @ A )
% 0.34/1.75 = ( ^ [X2: A,Y3: A] : ( inf_inf @ A @ Y3 @ X2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_216_inf__fun__def,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.34/1.75 => ( ( inf_inf @ ( A > B ) )
% 0.34/1.75 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( inf_inf @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_217_inf_Oassoc,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [A4: A,B4: A,C2: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( inf_inf @ A @ A4 @ B4 ) @ C2 )
% 0.34/1.75 = ( inf_inf @ A @ A4 @ ( inf_inf @ A @ B4 @ C2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_218_inf__assoc,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Z )
% 0.34/1.75 = ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_219_inf_Ocommute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( inf_inf @ A )
% 0.34/1.75 = ( ^ [A5: A,B5: A] : ( inf_inf @ A @ B5 @ A5 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_220_inf__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( inf_inf @ A )
% 0.34/1.75 = ( ^ [X2: A,Y3: A] : ( inf_inf @ A @ Y3 @ X2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_221_inf_Oleft__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [B4: A,A4: A,C2: A] :
% 0.34/1.75 ( ( inf_inf @ A @ B4 @ ( inf_inf @ A @ A4 @ C2 ) )
% 0.34/1.75 = ( inf_inf @ A @ A4 @ ( inf_inf @ A @ B4 @ C2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_222_inf__left__commute,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,Y: A,Z: A] :
% 0.34/1.75 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.34/1.75 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_223_finlsts__rec__LNil__def,axiom,
% 0.34/1.75 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C2: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 0.34/1.75 ( ( F
% 0.34/1.75 = ( lList21916056377ts_rec @ B @ A @ C2 @ D2 ) )
% 0.34/1.75 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.34/1.75 = C2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_224_finlsts__rec__LNil,axiom,
% 0.34/1.75 ! [B: $tType,A: $tType,C2: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 0.34/1.75 ( ( lList21916056377ts_rec @ A @ B @ C2 @ D2 @ ( coinductive_LNil @ B ) )
% 0.34/1.75 = C2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_225_diff__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ( ( minus_minus @ A )
% 0.34/1.75 = ( ^ [X2: A,Y3: A] : ( inf_inf @ A @ X2 @ ( uminus_uminus @ A @ Y3 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_226_inf__cancel__left2,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,A4: A,B4: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ A4 ) @ ( inf_inf @ A @ X @ B4 ) )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_227_inf__cancel__left1,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.34/1.75 => ! [X: A,A4: A,B4: A] :
% 0.34/1.75 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ A4 ) @ ( inf_inf @ A @ ( uminus_uminus @ A @ X ) @ B4 ) )
% 0.34/1.75 = ( bot_bot @ A ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_228_Diff__triv,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 => ( ( minus_minus @ ( set @ A ) @ A2 @ B2 )
% 0.34/1.75 = A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_229_Un__Diff__Int,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = A2 ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_230_Diff__Int,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_231_Diff__Un,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( minus_minus @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_232_Compl__Un,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( uminus_uminus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_233_Compl__Int,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( uminus_uminus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.34/1.75 = ( sup_sup @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_234_Diff__eq,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( minus_minus @ ( set @ A ) )
% 0.34/1.75 = ( ^ [A3: set @ A,B3: set @ A] : ( inf_inf @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ B3 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_235_finlsts_Ocases,axiom,
% 0.34/1.75 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ( A4
% 0.34/1.75 != ( coinductive_LNil @ A ) )
% 0.34/1.75 => ~ ! [L2: coinductive_llist @ A,A6: A] :
% 0.34/1.75 ( ( A4
% 0.34/1.75 = ( coinductive_LCons @ A @ A6 @ L2 ) )
% 0.34/1.75 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ~ ( member @ A @ A6 @ A2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_236_finlsts_Osimps,axiom,
% 0.34/1.75 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 = ( ( A4
% 0.34/1.75 = ( coinductive_LNil @ A ) )
% 0.34/1.75 | ? [L3: coinductive_llist @ A,A5: A] :
% 0.34/1.75 ( ( A4
% 0.34/1.75 = ( coinductive_LCons @ A @ A5 @ L3 ) )
% 0.34/1.75 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_237_finlsts__induct,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ! [L2: coinductive_llist @ A] :
% 0.34/1.75 ( ( L2
% 0.34/1.75 = ( coinductive_LNil @ A ) )
% 0.34/1.75 => ( P @ L2 ) )
% 0.34/1.75 => ( ! [A6: A,L2: coinductive_llist @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ( P @ L2 )
% 0.34/1.75 => ( ( member @ A @ A6 @ A2 )
% 0.34/1.75 => ( P @ ( coinductive_LCons @ A @ A6 @ L2 ) ) ) ) )
% 0.34/1.75 => ( P @ X ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_238_finlsts_Oinducts,axiom,
% 0.34/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.34/1.75 => ( ! [L2: coinductive_llist @ A,A6: A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.34/1.75 => ( ( P @ L2 )
% 0.34/1.75 => ( ( member @ A @ A6 @ A2 )
% 0.34/1.75 => ( P @ ( coinductive_LCons @ A @ A6 @ L2 ) ) ) ) )
% 0.34/1.75 => ( P @ X ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_239_alllsts_Ocoinduct,axiom,
% 0.34/1.75 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( X4 @ X )
% 0.34/1.75 => ( ! [X3: coinductive_llist @ A] :
% 0.34/1.75 ( ( X4 @ X3 )
% 0.34/1.75 => ( ( X3
% 0.34/1.75 = ( coinductive_LNil @ A ) )
% 0.34/1.75 | ? [L4: coinductive_llist @ A,A7: A] :
% 0.34/1.75 ( ( X3
% 0.34/1.75 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 0.34/1.75 & ( ( X4 @ L4 )
% 0.34/1.75 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.34/1.75 & ( member @ A @ A7 @ A2 ) ) ) )
% 0.34/1.75 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_240_alllsts_Osimps,axiom,
% 0.34/1.75 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 = ( ( A4
% 0.34/1.75 = ( coinductive_LNil @ A ) )
% 0.34/1.75 | ? [L3: coinductive_llist @ A,A5: A] :
% 0.34/1.75 ( ( A4
% 0.34/1.75 = ( coinductive_LCons @ A @ A5 @ L3 ) )
% 0.34/1.75 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_241_alllsts_Ocases,axiom,
% 0.34/1.75 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.34/1.75 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 => ( ( A4
% 0.34/1.75 != ( coinductive_LNil @ A ) )
% 0.34/1.75 => ~ ! [L2: coinductive_llist @ A,A6: A] :
% 0.34/1.75 ( ( A4
% 0.34/1.75 = ( coinductive_LCons @ A @ A6 @ L2 ) )
% 0.34/1.75 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.34/1.75 => ~ ( member @ A @ A6 @ A2 ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_242_disjnt__def,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( disjnt @ A )
% 0.34/1.75 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ A3 @ B3 )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_243_Collect__empty__eq__bot,axiom,
% 0.34/1.75 ! [A: $tType,P: A > $o] :
% 0.34/1.75 ( ( ( collect @ A @ P )
% 0.34/1.75 = ( bot_bot @ ( set @ A ) ) )
% 0.34/1.75 = ( P
% 0.34/1.75 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_244_poslsts__def,axiom,
% 0.34/1.75 ! [A: $tType] :
% 0.34/1.75 ( ( lList21148268032oslsts @ A )
% 0.34/1.75 = ( ^ [A3: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A3 ) @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_245_insert__absorb2,axiom,
% 0.34/1.75 ! [A: $tType,X: A,A2: set @ A] :
% 0.34/1.75 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 0.34/1.75 = ( insert @ A @ X @ A2 ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_246_insert__iff,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,B4: A,A2: set @ A] :
% 0.34/1.75 ( ( member @ A @ A4 @ ( insert @ A @ B4 @ A2 ) )
% 0.34/1.75 = ( ( A4 = B4 )
% 0.34/1.75 | ( member @ A @ A4 @ A2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_247_insertCI,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,B2: set @ A,B4: A] :
% 0.34/1.75 ( ( ~ ( member @ A @ A4 @ B2 )
% 0.34/1.75 => ( A4 = B4 ) )
% 0.34/1.75 => ( member @ A @ A4 @ ( insert @ A @ B4 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_248_singletonI,axiom,
% 0.34/1.75 ! [A: $tType,A4: A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_249_Int__insert__left__if0,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,C3: set @ A,B2: set @ A] :
% 0.34/1.75 ( ~ ( member @ A @ A4 @ C3 )
% 0.34/1.75 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A4 @ B2 ) @ C3 )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_250_Int__insert__left__if1,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,C3: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ A4 @ C3 )
% 0.34/1.75 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A4 @ B2 ) @ C3 )
% 0.34/1.75 = ( insert @ A @ A4 @ ( inf_inf @ ( set @ A ) @ B2 @ C3 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_251_insert__inter__insert,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A4 @ A2 ) @ ( insert @ A @ A4 @ B2 ) )
% 0.34/1.75 = ( insert @ A @ A4 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_252_Int__insert__right__if0,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ~ ( member @ A @ A4 @ A2 )
% 0.34/1.75 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A4 @ B2 ) )
% 0.34/1.75 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_253_Int__insert__right__if1,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,A2: set @ A,B2: set @ A] :
% 0.34/1.75 ( ( member @ A @ A4 @ A2 )
% 0.34/1.75 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A4 @ B2 ) )
% 0.34/1.75 = ( insert @ A @ A4 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_254_Un__insert__left,axiom,
% 0.34/1.75 ! [A: $tType,A4: A,B2: set @ A,C3: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A4 @ B2 ) @ C3 )
% 0.34/1.75 = ( insert @ A @ A4 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(fact_255_Un__insert__right,axiom,
% 0.34/1.75 ! [A: $tType,A2: set @ A,A4: A,B2: set @ A] :
% 0.34/1.75 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A4 @ B2 ) )
% 0.34/1.75 = ( insert @ A @ A4 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.34/1.75 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.34/1.75 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( bounde1808546759up_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Obounded__semilattice__inf__top,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( bounde1561333602nf_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( bounded_lattice_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( semilattice_inf @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( semilattice_inf @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Odistrib__lattice,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( distrib_lattice @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( distrib_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( boolean_algebra @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( boolean_algebra @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Orderings_Otop,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Orderings_Obot,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( uminus @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( uminus @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_fun___Groups_Ominus,axiom,
% 0.34/1.75 ! [A8: $tType,A9: $tType] :
% 0.34/1.75 ( ( minus @ A9 @ ( type2 @ A9 ) )
% 0.34/1.75 => ( minus @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 0.34/1.75 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_4,axiom,
% 0.34/1.75 ! [A8: $tType] : ( bounde1561333602nf_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5,axiom,
% 0.34/1.75 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6,axiom,
% 0.34/1.75 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_7,axiom,
% 0.34/1.75 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_8,axiom,
% 0.34/1.75 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Odistrib__lattice_9,axiom,
% 0.34/1.75 ! [A8: $tType] : ( distrib_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_10,axiom,
% 0.34/1.75 ! [A8: $tType] : ( boolean_algebra @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Lattices_Olattice_11,axiom,
% 0.34/1.75 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Orderings_Otop_12,axiom,
% 0.34/1.75 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Orderings_Obot_13,axiom,
% 0.34/1.75 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Groups_Ouminus_14,axiom,
% 0.34/1.75 ! [A8: $tType] : ( uminus @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_Set_Oset___Groups_Ominus_15,axiom,
% 0.34/1.75 ! [A8: $tType] : ( minus @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_16,axiom,
% 0.34/1.75 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_17,axiom,
% 0.34/1.75 bounde1561333602nf_top @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_18,axiom,
% 0.34/1.75 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_19,axiom,
% 0.34/1.75 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_20,axiom,
% 0.34/1.75 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_21,axiom,
% 0.34/1.75 semilattice_inf @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Odistrib__lattice_22,axiom,
% 0.34/1.75 distrib_lattice @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_23,axiom,
% 0.34/1.75 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Lattices_Olattice_24,axiom,
% 0.34/1.75 lattice @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Orderings_Otop_25,axiom,
% 0.34/1.75 top @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Orderings_Obot_26,axiom,
% 0.34/1.75 bot @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Groups_Ouminus_27,axiom,
% 0.34/1.75 uminus @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(tcon_HOL_Obool___Groups_Ominus_28,axiom,
% 0.34/1.75 minus @ $o @ ( type2 @ $o ) ).
% 0.34/1.75
% 0.34/1.75 thf(conj_0,conjecture,
% 0.34/1.75 ( ( ~ ( member @ ( coinductive_llist @ a ) @ x @ ( lList21612149805nflsts @ a @ ( top_top @ ( set @ a ) ) ) ) )
% 0.34/1.75 = ( member @ ( coinductive_llist @ a ) @ x @ ( lList2236698231inlsts @ a @ ( top_top @ ( set @ a ) ) ) ) ) ).
% 0.34/1.75 ------------------------
% 0.34/1.78 % (5245)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_5135 for (2999ds/27Mi)
% 0.34/1.78 % (5243)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5135 for (2999ds/183Mi)
% 0.34/1.78 % (5244)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_5135 for (2999ds/4Mi)
% 0.34/1.78 % (5246)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5135 for (2999ds/2Mi)
% 0.34/1.78 % (5247)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_5135 for (2999ds/2Mi)
% 0.34/1.78 % (5248)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_5135 for (2999ds/275Mi)
% 0.34/1.78 % (5249)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5135 for (2999ds/18Mi)
% 0.34/1.78 % (5246)Instruction limit reached!
% 0.34/1.78 % (5246)------------------------------
% 0.34/1.78 % (5246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.78 % (5246)Termination reason: Unknown
% 0.34/1.78 % (5246)Termination phase: shuffling
% 0.34/1.78 % (5247)Instruction limit reached!
% 0.34/1.78 % (5247)------------------------------
% 0.34/1.78 % (5247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.78 % (5247)Termination reason: Unknown
% 0.34/1.78 % (5247)Termination phase: shuffling
% 0.34/1.78
% 0.34/1.78 % (5247)Memory used [KB]: 1279
% 0.34/1.78 % (5247)Time elapsed: 0.003 s
% 0.34/1.78 % (5247)Instructions burned: 3 (million)
% 0.34/1.78 % (5247)------------------------------
% 0.34/1.78 % (5247)------------------------------
% 0.34/1.78
% 0.34/1.78 % (5246)Memory used [KB]: 1279
% 0.34/1.78 % (5246)Time elapsed: 0.003 s
% 0.34/1.78 % (5246)Instructions burned: 3 (million)
% 0.34/1.78 % (5246)------------------------------
% 0.34/1.78 % (5246)------------------------------
% 0.34/1.78 % (5244)Instruction limit reached!
% 0.34/1.78 % (5244)------------------------------
% 0.34/1.78 % (5244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.78 % (5244)Termination reason: Unknown
% 0.34/1.78 % (5244)Termination phase: shuffling
% 0.34/1.78
% 0.34/1.78 % (5244)Memory used [KB]: 1279
% 0.34/1.78 % (5244)Time elapsed: 0.004 s
% 0.34/1.78 % (5244)Instructions burned: 5 (million)
% 0.34/1.78 % (5244)------------------------------
% 0.34/1.78 % (5244)------------------------------
% 0.34/1.79 % (5249)Instruction limit reached!
% 0.34/1.79 % (5249)------------------------------
% 0.34/1.79 % (5249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.79 % (5249)Termination reason: Unknown
% 0.34/1.79 % (5249)Termination phase: Property scanning
% 0.34/1.79
% 0.34/1.79 % (5249)Memory used [KB]: 1535
% 0.34/1.79 % (5249)Time elapsed: 0.011 s
% 0.34/1.79 % (5249)Instructions burned: 19 (million)
% 0.34/1.79 % (5249)------------------------------
% 0.34/1.79 % (5249)------------------------------
% 0.34/1.79 % (5245)Instruction limit reached!
% 0.34/1.79 % (5245)------------------------------
% 0.34/1.79 % (5245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.79 % (5245)Termination reason: Unknown
% 0.34/1.79 % (5245)Termination phase: Property scanning
% 0.34/1.79
% 0.34/1.79 % (5245)Memory used [KB]: 1535
% 0.34/1.79 % (5245)Time elapsed: 0.015 s
% 0.34/1.79 % (5245)Instructions burned: 27 (million)
% 0.34/1.79 % (5245)------------------------------
% 0.34/1.79 % (5245)------------------------------
% 3.24/1.80 % (5250)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5135 for (2999ds/3Mi)
% 3.24/1.80 % (5251)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_5135 for (2999ds/37Mi)
% 3.24/1.80 % (5252)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_5135 for (2999ds/15Mi)
% 3.24/1.80 % (5250)Instruction limit reached!
% 3.24/1.80 % (5250)------------------------------
% 3.24/1.80 % (5250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.80 % (5250)Termination reason: Unknown
% 3.24/1.80 % (5250)Termination phase: shuffling
% 3.24/1.80
% 3.24/1.80 % (5250)Memory used [KB]: 1279
% 3.24/1.80 % (5250)Time elapsed: 0.003 s
% 3.24/1.80 % (5250)Instructions burned: 3 (million)
% 3.24/1.80 % (5250)------------------------------
% 3.24/1.80 % (5250)------------------------------
% 3.24/1.81 % (5253)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_5135 for (2999ds/3Mi)
% 3.24/1.81 % (5252)Instruction limit reached!
% 3.24/1.81 % (5252)------------------------------
% 3.24/1.81 % (5252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.81 % (5252)Termination reason: Unknown
% 3.24/1.81 % (5252)Termination phase: shuffling
% 3.24/1.81
% 3.24/1.81 % (5252)Memory used [KB]: 1535
% 3.24/1.81 % (5252)Time elapsed: 0.009 s
% 3.24/1.81 % (5252)Instructions burned: 15 (million)
% 3.24/1.81 % (5252)------------------------------
% 3.24/1.81 % (5252)------------------------------
% 3.24/1.81 % (5253)Instruction limit reached!
% 3.24/1.81 % (5253)------------------------------
% 3.24/1.81 % (5253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.81 % (5253)Termination reason: Unknown
% 3.24/1.81 % (5253)Termination phase: shuffling
% 3.24/1.81
% 3.24/1.81 % (5253)Memory used [KB]: 1279
% 3.24/1.81 % (5253)Time elapsed: 0.003 s
% 3.24/1.81 % (5253)Instructions burned: 3 (million)
% 3.24/1.81 % (5253)------------------------------
% 3.24/1.81 % (5253)------------------------------
% 3.24/1.81 % (5254)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_5135 for (2999ds/1041Mi)
% 3.24/1.82 % (5255)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5135 for (2999ds/7Mi)
% 3.24/1.82 % (5251)Instruction limit reached!
% 3.24/1.82 % (5251)------------------------------
% 3.24/1.82 % (5251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.82 % (5251)Termination reason: Unknown
% 3.24/1.82 % (5251)Termination phase: Property scanning
% 3.24/1.82
% 3.24/1.82 % (5251)Memory used [KB]: 2046
% 3.24/1.82 % (5251)Time elapsed: 0.019 s
% 3.24/1.82 % (5251)Instructions burned: 38 (million)
% 3.24/1.82 % (5251)------------------------------
% 3.24/1.82 % (5251)------------------------------
% 3.24/1.82 % (5248)First to succeed.
% 3.24/1.82 % (5248)Refutation found. Thanks to Tanya!
% 3.24/1.82 % SZS status Theorem for DTF2THF_5135
% 3.24/1.82 % SZS output start Proof for DTF2THF_5135
% 3.24/1.82 thf(type_def_5, type, itself: ($tType) > $tType).
% 3.24/1.82 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 3.24/1.82 thf(type_def_8, type, set: ($tType) > $tType).
% 3.24/1.82 thf(type_def_9, type, a: $tType).
% 3.24/1.82 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 3.24/1.82 thf(func_def_1, type, set: ($tType) > $tType).
% 3.24/1.82 thf(func_def_2, type, itself: ($tType) > $tType).
% 3.24/1.82 thf(func_def_3, type, a: $tType).
% 3.24/1.82 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_6, type, minus: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_7, type, uminus: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_8, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_9, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_10, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_11, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_12, type, ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_13, type, boolean_algebra: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_14, type, distrib_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_15, type, semilattice_inf: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_16, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_17, type, bounded_lattice_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_18, type, bounded_lattice_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_19, type, cancel146912293up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_20, type, bounde1561333602nf_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_21, type, bounde1808546759up_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.24/1.82 thf(func_def_22, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_23, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_24, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.24/1.82 thf(func_def_25, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 3.24/1.82 thf(func_def_26, type, lList2435255213lllsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_27, type, lList2236698231inlsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_28, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0)).
% 3.24/1.82 thf(func_def_29, type, lList22096119349pslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_30, type, lList21612149805nflsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_31, type, lList21148268032oslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_32, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.24/1.82 thf(func_def_33, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.24/1.82 thf(func_def_34, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.24/1.82 thf(func_def_35, type, top_top: !>[X0: $tType]:(X0)).
% 3.24/1.82 thf(func_def_36, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.24/1.82 thf(func_def_37, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.24/1.82 thf(func_def_38, type, disjnt: !>[X0: $tType]:(set @ X0 > set @ X0 > $o)).
% 3.24/1.82 thf(func_def_39, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 3.24/1.82 thf(func_def_40, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 3.24/1.82 thf(func_def_41, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.24/1.82 thf(func_def_42, type, x: coinductive_llist @ a).
% 3.24/1.82 thf(func_def_51, type, sK0: !>[X0: $tType]:(X0)).
% 3.24/1.82 thf(func_def_52, type, sK1: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_53, type, sK2: !>[X0: $tType]:(set @ X0 > X0)).
% 3.24/1.82 thf(func_def_54, type, sK3: !>[X0: $tType]:(set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_55, type, sK4: !>[X0: $tType]:(set @ X0 > X0)).
% 3.24/1.82 thf(func_def_56, type, sK5: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_57, type, sK6: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_58, type, sK7: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_59, type, sK8: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 3.24/1.82 thf(func_def_60, type, sK9: !>[X0: $tType]:((X0 > $o) > set @ X0 > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_61, type, sK10: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_62, type, sK11: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_63, type, sK12: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.24/1.82 thf(func_def_64, type, sK13: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_65, type, sK14: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 3.24/1.82 thf(func_def_66, type, sK15: !>[X0: $tType]:(set @ X0 > X0)).
% 3.24/1.82 thf(func_def_67, type, sK16: !>[X0: $tType]:(set @ X0 > X0)).
% 3.24/1.82 thf(func_def_68, type, sK17: !>[X0: $tType]:((X0 > $o) > set @ X0 > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_69, type, sK18: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_70, type, sK19: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 3.24/1.82 thf(func_def_71, type, sK20: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 3.24/1.82 thf(func_def_72, type, sK21: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 3.24/1.82 thf(func_def_74, type, ph23: !>[X0: $tType]:(X0)).
% 3.24/1.82 thf(f1178,plain,(
% 3.24/1.82 $false),
% 3.24/1.82 inference(subsumption_resolution,[status(thm)],[f1177,f1156])).
% 3.24/1.82 thf(f1156,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) != $true)),
% 3.24/1.82 inference(subsumption_resolution,[status(thm)],[f1153,f1155])).
% 3.24/1.82 thf(f1155,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) != $true)),
% 3.24/1.82 inference(subsumption_resolution,[status(thm)],[f1154,f1150])).
% 3.24/1.82 thf(f1150,plain,(
% 3.24/1.82 ( ! [X0 : $tType,X2 : set @ X0,X1 : coinductive_llist @ X0] : (((member @ coinductive_llist @ X0 @ X1 @ (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ X2) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) != $true) | ($true != (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))) )),
% 3.24/1.82 inference(beta_eta_normalization,[status(thm)],[f1113])).
% 3.24/1.82 thf(f1113,plain,(
% 3.24/1.82 ( ! [X0 : $tType,X2 : set @ X0,X1 : coinductive_llist @ X0] : (($true != (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) | ($true != (member @ coinductive_llist @ X0 @ X1 @ ((^[Y0 : set @ X0]: (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ Y0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) @ X2)))) )),
% 3.24/1.82 inference(definition_unfolding,[status(thm)],[f1096,f1092])).
% 3.24/1.82 thf(f1092,plain,(
% 3.24/1.82 ( ! [X0 : $tType] : ((lList21612149805nflsts @ X0 = (^[Y0 : set @ X0]: (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ Y0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))) )),
% 3.24/1.82 inference(cnf_transformation,[status(thm)],[f573])).
% 3.24/1.82 thf(f573,plain,(
% 3.24/1.82 ! [X0 : $tType] : (lList21612149805nflsts @ X0 = (^[Y0 : set @ X0]: (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ Y0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))),
% 3.24/1.82 inference(fool_elimination,[status(thm)],[f572])).
% 3.24/1.82 thf(f572,plain,(
% 3.24/1.82 ! [X0 : $tType] : (lList21612149805nflsts @ X0 = (^[X1 : set @ X0] : (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ X1) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))),
% 3.24/1.82 inference(rectify,[status(thm)],[f15])).
% 3.24/1.82 thf(f15,axiom,(
% 3.24/1.82 ! [X0 : $tType] : (lList21612149805nflsts @ X0 = (^[X10 : set @ X0] : (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ X10) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))),
% 3.24/1.82 file('/export/starexec/sandbox/tmp/tmp.dhScex8tFU/DTF2THF_5135.p',fact_14_inflsts__def)).
% 3.24/1.82 thf(f1096,plain,(
% 3.24/1.82 ( ! [X0 : $tType,X2 : set @ X0,X1 : coinductive_llist @ X0] : (($true != (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) | ($true != (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ X2)))) )),
% 3.24/1.82 inference(cnf_transformation,[status(thm)],[f860])).
% 3.24/1.82 thf(f860,plain,(
% 3.24/1.82 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : set @ X0] : ((($true != (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) & ($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ X2)))) | ($true != (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ X2))))),
% 3.24/1.82 inference(ennf_transformation,[status(thm)],[f713])).
% 3.24/1.82 thf(f713,plain,(
% 3.24/1.82 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : set @ X0] : (($true = (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ X2))) => ~(($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ X2))) => ($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))))),
% 3.24/1.82 inference(fool_elimination,[status(thm)],[f712])).
% 3.24/1.82 thf(f712,plain,(
% 3.24/1.82 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : set @ X0] : ((member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ X2)) => ~((member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ X2)) => (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))),
% 3.24/1.82 inference(rectify,[status(thm)],[f10])).
% 3.24/1.82 thf(f10,axiom,(
% 3.24/1.82 ! [X0 : $tType,X2 : coinductive_llist @ X0,X4 : set @ X0] : ((member @ coinductive_llist @ X0 @ X2 @ (lList21612149805nflsts @ X0 @ X4)) => ~((member @ coinductive_llist @ X0 @ X2 @ (lList2435255213lllsts @ X0 @ X4)) => (member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))),
% 3.24/1.82 file('/export/starexec/sandbox/tmp/tmp.dhScex8tFU/DTF2THF_5135.p',fact_9_inflstsE)).
% 3.24/1.82 thf(f1154,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) != $true) | ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true)),
% 3.24/1.82 inference(beta_eta_normalization,[status(thm)],[f1109])).
% 3.24/1.82 thf(f1109,plain,(
% 3.24/1.82 ($true != (member @ coinductive_llist @ a @ x @ ((^[Y0 : set @ a]: (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ Y0) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) @ top_top @ set @ a))) | ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true)),
% 3.24/1.82 inference(definition_unfolding,[status(thm)],[f1062,f1092])).
% 3.24/1.82 thf(f1062,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) != $true) | ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true)),
% 3.24/1.82 inference(cnf_transformation,[status(thm)],[f932])).
% 3.24/1.82 thf(f932,plain,(
% 3.24/1.82 (((member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) = $true) | ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) != $true)) & (((member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) != $true) | ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true))),
% 3.24/1.82 inference(nnf_transformation,[status(thm)],[f857])).
% 3.24/1.82 thf(f857,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true) <~> ((member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) != $true)),
% 3.24/1.82 inference(ennf_transformation,[status(thm)],[f760])).
% 3.24/1.82 thf(f760,plain,(
% 3.24/1.82 ~(((member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) != $true) <=> ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true))),
% 3.24/1.82 inference(flattening,[status(thm)],[f757])).
% 3.24/1.82 thf(f757,plain,(
% 3.24/1.82 ~(((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true) <=> ~((member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) = $true))),
% 3.24/1.82 inference(fool_elimination,[status(thm)],[f756])).
% 3.24/1.82 thf(f756,plain,(
% 3.24/1.82 ~((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = ~(member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)))),
% 3.24/1.82 inference(rectify,[status(thm)],[f300])).
% 3.24/1.82 thf(f300,negated_conjecture,(
% 3.24/1.82 ~((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = ~(member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)))),
% 3.24/1.82 inference(negated_conjecture,[status(cth)],[f299])).
% 3.24/1.82 thf(f299,conjecture,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = ~(member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)))),
% 3.24/1.82 file('/export/starexec/sandbox/tmp/tmp.dhScex8tFU/DTF2THF_5135.p',conj_0)).
% 3.24/1.82 thf(f1153,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $true) | ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) != $true)),
% 3.24/1.82 inference(beta_eta_normalization,[status(thm)],[f1108])).
% 3.24/1.82 thf(f1108,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) != $true) | ($true = (member @ coinductive_llist @ a @ x @ ((^[Y0 : set @ a]: (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ Y0) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) @ top_top @ set @ a)))),
% 3.24/1.82 inference(definition_unfolding,[status(thm)],[f1063,f1092])).
% 3.24/1.82 thf(f1063,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) = $true) | ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) != $true)),
% 3.24/1.82 inference(cnf_transformation,[status(thm)],[f932])).
% 3.24/1.82 thf(f1177,plain,(
% 3.24/1.82 ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true)),
% 3.24/1.82 inference(trivial_inequality_removal,[status(thm)],[f1166])).
% 3.24/1.82 thf(f1166,plain,(
% 3.24/1.82 ($true != $true) | ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a)) = $true)),
% 3.24/1.82 inference(superposition,[status(thm)],[f1155,f1141])).
% 3.24/1.82 thf(f1141,plain,(
% 3.24/1.82 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (member @ coinductive_llist @ X0 @ X1 @ (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))) | ($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))) )),
% 3.24/1.82 inference(beta_eta_normalization,[status(thm)],[f1104])).
% 3.24/1.82 thf(f1104,plain,(
% 3.24/1.82 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (member @ coinductive_llist @ X0 @ X1 @ ((^[Y0 : set @ X0]: (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ Y0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) @ top_top @ set @ X0))) | ($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))) )),
% 3.24/1.82 inference(definition_unfolding,[status(thm)],[f1031,f1092])).
% 3.24/1.82 thf(f1031,plain,(
% 3.24/1.82 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0))) | ($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))) )),
% 3.24/1.82 inference(cnf_transformation,[status(thm)],[f918])).
% 3.24/1.82 thf(f918,plain,(
% 3.24/1.82 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((($true = (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0))) | ($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))) & (($true != (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) | ($true != (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0)))))),
% 3.24/1.82 inference(nnf_transformation,[status(thm)],[f761])).
% 3.24/1.82 thf(f761,plain,(
% 3.24/1.82 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0))) <=> ($true != (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))),
% 3.24/1.82 inference(flattening,[status(thm)],[f723])).
% 3.24/1.82 thf(f723,plain,(
% 3.24/1.82 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0))) <=> ~($true = (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))),
% 3.24/1.82 inference(fool_elimination,[status(thm)],[f722])).
% 3.24/1.82 thf(f722,plain,(
% 3.24/1.82 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0)) = ~(member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))),
% 3.24/1.82 inference(rectify,[status(thm)],[f1])).
% 3.24/1.82 thf(f1,axiom,(
% 3.24/1.82 ! [X0 : $tType,X2 : coinductive_llist @ X0] : ((member @ coinductive_llist @ X0 @ X2 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0)) = ~(member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))),
% 3.24/1.82 file('/export/starexec/sandbox/tmp/tmp.dhScex8tFU/DTF2THF_5135.p',fact_0_notfin__inf)).
% 3.24/1.82 % SZS output end Proof for DTF2THF_5135
% 3.24/1.82 % (5248)------------------------------
% 3.24/1.82 % (5248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.82 % (5248)Termination reason: Refutation
% 3.24/1.82
% 3.24/1.82 % (5248)Memory used [KB]: 6524
% 3.24/1.82 % (5248)Time elapsed: 0.038 s
% 3.24/1.82 % (5248)Instructions burned: 71 (million)
% 3.24/1.82 % (5248)------------------------------
% 3.24/1.82 % (5248)------------------------------
% 3.24/1.82 % (5242)Success in time 0.063 s
%------------------------------------------------------------------------------