%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT177^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 2.50s 1.57s
% Output : Refutation 2.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT177^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n005.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 06:09:14 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.41 ---- Original DTF file ---
% 0.17/0.41 thf(spec,logic,$$dhol).
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 % File : DAT177^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.41 % Domain : Data Structures
% 0.17/0.41 % Problem : Lazy lists II 375
% 0.17/0.41 % Version : [Bla16] axioms : Especial.
% 0.17/0.41 % English :
% 0.17/0.41
% 0.17/0.41 % Refs : [Fri04] Friedrich (2004), Lazy Lists II
% 0.17/0.41 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.17/0.41 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.17/0.41 % Source : [Bla16]
% 0.17/0.41 % Names : llist2__375.p [Bla16]
% 0.17/0.41
% 0.17/0.41 % Status : Theorem
% 0.17/0.41 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.17/0.41 % Syntax : Number of formulae : 326 ( 176 unt; 48 typ; 0 def)
% 0.17/0.41 % Number of atoms : 600 ( 301 equ; 0 cnn)
% 0.17/0.41 % Maximal formula atoms : 5 ( 2 avg)
% 0.17/0.41 % Number of connectives : 3790 ( 79 ~; 14 |; 54 &;3459 @)
% 0.17/0.41 % ( 0 <=>; 184 =>; 0 <=; 0 <~>)
% 0.17/0.41 % Maximal formula depth : 19 ( 6 avg)
% 0.17/0.41 % Number of types : 2 ( 1 usr)
% 0.17/0.41 % Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% 0.17/0.41 % Number of symbols : 48 ( 47 usr; 4 con; 0-5 aty)
% 0.17/0.41 % Number of variables : 892 ( 22 ^; 809 !; 20 ?; 892 :)
% 0.17/0.41 % ( 41 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.41 % SPC : TH1_THM_EQU_NAR
% 0.17/0.41
% 0.17/0.41 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.17/0.41 % 2016-07-13 14:46:04.744
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 %----Could-be-implicit typings (4)
% 0.17/0.41 thf(ty_t_Coinductive__List_Ollist,type,
% 0.17/0.41 coinductive_llist: $tType > $tType ).
% 0.17/0.41
% 0.17/0.41 thf(ty_t_Set_Oset,type,
% 0.17/0.41 set: $tType > $tType ).
% 0.17/0.41
% 0.17/0.41 thf(ty_t_itself,type,
% 0.17/0.41 itself: $tType > $tType ).
% 0.17/0.41
% 0.17/0.41 thf(ty_tf_a,type,
% 0.17/0.41 a: $tType ).
% 0.17/0.41
% 0.17/0.41 %----Explicit typings (44)
% 0.17/0.41 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.17/0.41 bounded_lattice:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_HOL_Otype,type,
% 0.17/0.41 type:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_Orderings_Obot,type,
% 0.17/0.41 bot:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_Orderings_Otop,type,
% 0.17/0.41 top:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.17/0.41 bounded_lattice_bot:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.17/0.41 bounded_lattice_top:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_Topological__Spaces_Operfect__space,type,
% 0.17/0.41 topolo890362671_space:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_Topological__Spaces_Ouniform__space,type,
% 0.17/0.41 topolo47006728_space:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_Lattices_Obounded__semilattice__inf__top,type,
% 0.17/0.41 bounde1561333602nf_top:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.17/0.41 bounde1808546759up_bot:
% 0.17/0.41 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.17/0.41 coindu328551480prefix:
% 0.17/0.41 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_Ogen__lset,type,
% 0.17/0.41 coinductive_gen_lset:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_OlSup,type,
% 0.17/0.41 coinductive_lSup:
% 0.17/0.41 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > ( coinductive_llist @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_Olappend,type,
% 0.17/0.41 coinductive_lappend:
% 0.17/0.41 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.17/0.41 coinductive_lfinite:
% 0.17/0.41 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_Ollast,type,
% 0.17/0.41 coinductive_llast:
% 0.17/0.41 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.17/0.41 coinductive_LCons:
% 0.17/0.41 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.17/0.41 coinductive_LNil:
% 0.17/0.41 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.17/0.41 coindu1478340336prefix:
% 0.17/0.41 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.17/0.41 minus_minus:
% 0.17/0.41 !>[A: $tType] : ( A > A > A ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 0.17/0.41 lList2435255213lllsts:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.17/0.41 lList2236698231inlsts:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.17/0.41 lList21916056377ts_rec:
% 0.17/0.41 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.17/0.41 lList22096119349pslsts:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 0.17/0.41 lList21612149805nflsts:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.17/0.41 lList21148268032oslsts:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.17/0.41 inf_inf:
% 0.17/0.41 !>[A: $tType] : ( A > A > A ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.17/0.41 sup_sup:
% 0.17/0.41 !>[A: $tType] : ( A > A > A ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.17/0.41 bot_bot:
% 0.17/0.41 !>[A: $tType] : A ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.17/0.41 top_top:
% 0.17/0.41 !>[A: $tType] : A ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Pure_Otype,type,
% 0.17/0.41 type2:
% 0.17/0.41 !>[A: $tType] : ( itself @ A ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Set_OCollect,type,
% 0.17/0.41 collect:
% 0.17/0.41 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Set_Oinsert,type,
% 0.17/0.41 insert:
% 0.17/0.41 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Set_Ois__empty,type,
% 0.17/0.41 is_empty:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Set_Ois__singleton,type,
% 0.17/0.41 is_singleton:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Set_Opairwise,type,
% 0.17/0.41 pairwise:
% 0.17/0.41 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Set_Oremove,type,
% 0.17/0.41 remove:
% 0.17/0.41 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Set_Othe__elem,type,
% 0.17/0.41 the_elem:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_Topological__Spaces_Ouniform__space__class_Ototally__bounded,type,
% 0.17/0.41 topolo406746546ounded:
% 0.17/0.41 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_c_member,type,
% 0.17/0.41 member:
% 0.17/0.41 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf(sy_v_A,type,
% 0.17/0.41 a2: set @ a ).
% 0.17/0.41
% 0.17/0.41 thf(sy_v_l______,type,
% 0.17/0.41 l: coinductive_llist @ a ).
% 0.17/0.41
% 0.17/0.41 thf(sy_v_r,type,
% 0.17/0.41 r: coinductive_llist @ a ).
% 0.17/0.41
% 0.17/0.41 thf(sy_v_sa____,type,
% 0.17/0.41 sa: coinductive_llist @ a ).
% 0.17/0.41
% 0.17/0.41 %----Relevant facts (256)
% 0.17/0.41 thf(fact_0_LNil__fin_Oprems,axiom,
% 0.17/0.41 member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ l @ sa ) @ ( lList21612149805nflsts @ a @ a2 ) ).
% 0.17/0.41
% 0.17/0.41 % LNil_fin.prems
% 0.17/0.41 thf(fact_1_assms,axiom,
% 0.17/0.41 member @ ( coinductive_llist @ a ) @ r @ ( lList2236698231inlsts @ a @ a2 ) ).
% 0.17/0.41
% 0.17/0.41 % assms
% 0.17/0.41 thf(fact_2_lapp__inf,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 => ( ( coinductive_lappend @ A @ S @ T )
% 0.17/0.41 = S ) ) ).
% 0.17/0.41
% 0.17/0.41 % lapp_inf
% 0.17/0.41 thf(fact_3_infsubsetall,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % infsubsetall
% 0.17/0.41 thf(fact_4_infT__simp,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % infT_simp
% 0.17/0.41 thf(fact_5_inflstsI2,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A,T: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % inflstsI2
% 0.17/0.41 thf(fact_6_inflsts__cases,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 => ~ ! [A4: A,L: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 => ( ( member @ A @ A4 @ A2 )
% 0.17/0.41 => ( S
% 0.17/0.41 != ( coinductive_LCons @ A @ A4 @ L ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % inflsts_cases
% 0.17/0.41 thf(fact_7_lapp__fin__infT,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lapp_fin_infT
% 0.17/0.41 thf(fact_8_LNil__is__lappend__conv,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.17/0.41 ( ( ( coinductive_LNil @ A )
% 0.17/0.41 = ( coinductive_lappend @ A @ S @ T ) )
% 0.17/0.41 = ( ( S
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 & ( T
% 0.17/0.41 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % LNil_is_lappend_conv
% 0.17/0.41 thf(fact_9_lappend__is__LNil__conv,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.17/0.41 ( ( ( coinductive_lappend @ A @ S @ T )
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 = ( ( S
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 & ( T
% 0.17/0.41 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lappend_is_LNil_conv
% 0.17/0.41 thf(fact_10_inflsts__empty,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( lList21612149805nflsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % inflsts_empty
% 0.17/0.41 thf(fact_11_notfin__inf,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A] :
% 0.17/0.41 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.17/0.41 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % notfin_inf
% 0.17/0.41 thf(fact_12_notinf__fin,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A] :
% 0.17/0.41 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.17/0.41 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % notinf_fin
% 0.17/0.41 thf(fact_13_LNil__fin_Ohyps,axiom,
% 0.17/0.41 ( l
% 0.17/0.41 = ( coinductive_LNil @ a ) ) ).
% 0.17/0.41
% 0.17/0.41 % LNil_fin.hyps
% 0.17/0.41 thf(fact_14_alllsts__UNIV,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % alllsts_UNIV
% 0.17/0.41 thf(fact_15_same__lappend__eq,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( ( coinductive_lappend @ A @ R @ S )
% 0.17/0.41 = ( coinductive_lappend @ A @ R @ T ) )
% 0.17/0.41 = ( S = T ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % same_lappend_eq
% 0.17/0.41 thf(fact_16_lapp__fin__fin__iff,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lapp_fin_fin_iff
% 0.17/0.41 thf(fact_17_LConsE,axiom,
% 0.17/0.41 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 = ( ( member @ A @ X @ A2 )
% 0.17/0.41 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % LConsE
% 0.17/0.41 thf(fact_18_inflstsI,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % inflstsI
% 0.17/0.41 thf(fact_19_lappT,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lappT
% 0.17/0.41 thf(fact_20_llistE,axiom,
% 0.17/0.41 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.17/0.41 ( ( Y
% 0.17/0.41 != ( coinductive_LNil @ A ) )
% 0.17/0.41 => ~ ! [X21: A,X22: coinductive_llist @ A] :
% 0.17/0.41 ( Y
% 0.17/0.41 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % llistE
% 0.17/0.41 thf(fact_21_finT__simp,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finT_simp
% 0.17/0.41 thf(fact_22_fin__finite,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % fin_finite
% 0.17/0.41 thf(fact_23_finite__lemma,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finite_lemma
% 0.17/0.41 thf(fact_24_finsubsetall,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finsubsetall
% 0.17/0.41 thf(fact_25_lappfin__finT,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lappfin_finT
% 0.17/0.41 thf(fact_26_alllsts_Ocases,axiom,
% 0.17/0.41 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ( ( A3
% 0.17/0.41 != ( coinductive_LNil @ A ) )
% 0.17/0.41 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 0.17/0.41 ( ( A3
% 0.17/0.41 = ( coinductive_LCons @ A @ A4 @ L ) )
% 0.17/0.41 => ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ~ ( member @ A @ A4 @ A2 ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % alllsts.cases
% 0.17/0.41 thf(fact_27_alllsts_Osimps,axiom,
% 0.17/0.41 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 = ( ( A3
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 | ? [L2: coinductive_llist @ A,A5: A] :
% 0.17/0.41 ( ( A3
% 0.17/0.41 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.17/0.41 & ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % alllsts.simps
% 0.17/0.41 thf(fact_28_finlsts_Ocases,axiom,
% 0.17/0.41 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( A3
% 0.17/0.41 != ( coinductive_LNil @ A ) )
% 0.17/0.41 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 0.17/0.41 ( ( A3
% 0.17/0.41 = ( coinductive_LCons @ A @ A4 @ L ) )
% 0.17/0.41 => ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ~ ( member @ A @ A4 @ A2 ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts.cases
% 0.17/0.41 thf(fact_29_finlsts_Osimps,axiom,
% 0.17/0.41 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 = ( ( A3
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 | ? [L2: coinductive_llist @ A,A5: A] :
% 0.17/0.41 ( ( A3
% 0.17/0.41 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.17/0.41 & ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts.simps
% 0.17/0.41 thf(fact_30_lapp__all__invT,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lapp_all_invT
% 0.17/0.41 thf(fact_31_finlsts__induct,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ! [L: coinductive_llist @ A] :
% 0.17/0.41 ( ( L
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 => ( P @ L ) )
% 0.17/0.41 => ( ! [A4: A,L: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( P @ L )
% 0.17/0.41 => ( ( member @ A @ A4 @ A2 )
% 0.17/0.41 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 0.17/0.41 => ( P @ X ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts_induct
% 0.17/0.41 thf(fact_32_finlsts_Oinducts,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.41 => ( ! [L: coinductive_llist @ A,A4: A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( P @ L )
% 0.17/0.41 => ( ( member @ A @ A4 @ A2 )
% 0.17/0.41 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 0.17/0.41 => ( P @ X ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts.inducts
% 0.17/0.41 thf(fact_33_alllsts_OLNil__all,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % alllsts.LNil_all
% 0.17/0.41 thf(fact_34_alllsts_Ocoinduct,axiom,
% 0.17/0.41 ! [A: $tType,X2: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( X2 @ X )
% 0.17/0.41 => ( ! [X3: coinductive_llist @ A] :
% 0.17/0.41 ( ( X2 @ X3 )
% 0.17/0.41 => ( ( X3
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 | ? [L3: coinductive_llist @ A,A6: A] :
% 0.17/0.41 ( ( X3
% 0.17/0.41 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 0.17/0.41 & ( ( X2 @ L3 )
% 0.17/0.41 | ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.17/0.41 & ( member @ A @ A6 @ A2 ) ) ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % alllsts.coinduct
% 0.17/0.41 thf(fact_35_finlsts_OLNil__fin,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts.LNil_fin
% 0.17/0.41 thf(fact_36_alllsts_OLCons__all,axiom,
% 0.17/0.41 ! [A: $tType,L4: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ( ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L4 ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % alllsts.LCons_all
% 0.17/0.41 thf(fact_37_finlsts_OLCons__fin,axiom,
% 0.17/0.41 ! [A: $tType,L4: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L4 ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts.LCons_fin
% 0.17/0.41 thf(fact_38_lapp__fin__fin__lemma,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lapp_fin_fin_lemma
% 0.17/0.41 thf(fact_39_inflstsE,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % inflstsE
% 0.17/0.41 thf(fact_40_fin__inf__cases,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A] :
% 0.17/0.41 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % fin_inf_cases
% 0.17/0.41 thf(fact_41_alllstsE,axiom,
% 0.17/0.41 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % alllstsE
% 0.17/0.41 thf(fact_42_lappend__code_I1_J,axiom,
% 0.17/0.41 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.17/0.41 = Ys ) ).
% 0.17/0.41
% 0.17/0.41 % lappend_code(1)
% 0.17/0.41 thf(fact_43_lappend__LNil2,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.17/0.41 = Xs ) ).
% 0.17/0.41
% 0.17/0.41 % lappend_LNil2
% 0.17/0.41 thf(fact_44_LNil__eq__lappend__iff,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.41 ( ( ( coinductive_LNil @ A )
% 0.17/0.41 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.41 = ( ( Xs
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 & ( Ys
% 0.17/0.41 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % LNil_eq_lappend_iff
% 0.17/0.41 thf(fact_45_mem__Collect__eq,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,P: A > $o] :
% 0.17/0.41 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.17/0.41 = ( P @ A3 ) ) ).
% 0.17/0.41
% 0.17/0.41 % mem_Collect_eq
% 0.17/0.41 thf(fact_46_Collect__mem__eq,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( collect @ A
% 0.17/0.41 @ ^ [X4: A] : ( member @ A @ X4 @ A2 ) )
% 0.17/0.41 = A2 ) ).
% 0.17/0.41
% 0.17/0.41 % Collect_mem_eq
% 0.17/0.41 thf(fact_47_Collect__cong,axiom,
% 0.17/0.41 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.17/0.41 ( ! [X3: A] :
% 0.17/0.41 ( ( P @ X3 )
% 0.17/0.41 = ( Q @ X3 ) )
% 0.17/0.41 => ( ( collect @ A @ P )
% 0.17/0.41 = ( collect @ A @ Q ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Collect_cong
% 0.17/0.41 thf(fact_48_ext,axiom,
% 0.17/0.41 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.17/0.41 ( ! [X3: A] :
% 0.17/0.41 ( ( F @ X3 )
% 0.17/0.41 = ( G @ X3 ) )
% 0.17/0.41 => ( F = G ) ) ).
% 0.17/0.41
% 0.17/0.41 % ext
% 0.17/0.41 thf(fact_49_lappend__eq__LNil__iff,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.41 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 = ( ( Xs
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 & ( Ys
% 0.17/0.41 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lappend_eq_LNil_iff
% 0.17/0.41 thf(fact_50_lappend__code_I2_J,axiom,
% 0.17/0.41 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 0.17/0.41 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lappend_code(2)
% 0.17/0.41 thf(fact_51_lappend__snocL1__conv__LCons2,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.17/0.41 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lappend_snocL1_conv_LCons2
% 0.17/0.41 thf(fact_52_llist_Oinject,axiom,
% 0.17/0.41 ! [A: $tType,X212: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.17/0.41 ( ( ( coinductive_LCons @ A @ X212 @ X222 )
% 0.17/0.41 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.17/0.41 = ( ( X212 = Y21 )
% 0.17/0.41 & ( X222 = Y22 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % llist.inject
% 0.17/0.41 thf(fact_53_UNIV__I,axiom,
% 0.17/0.41 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % UNIV_I
% 0.17/0.41 thf(fact_54_iso__tuple__UNIV__I,axiom,
% 0.17/0.41 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % iso_tuple_UNIV_I
% 0.17/0.41 thf(fact_55_empty__iff,axiom,
% 0.17/0.41 ! [A: $tType,C: A] :
% 0.17/0.41 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % empty_iff
% 0.17/0.41 thf(fact_56_all__not__in__conv,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( ! [X4: A] :
% 0.17/0.41 ~ ( member @ A @ X4 @ A2 ) )
% 0.17/0.41 = ( A2
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % all_not_in_conv
% 0.17/0.41 thf(fact_57_empty__Collect__eq,axiom,
% 0.17/0.41 ! [A: $tType,P: A > $o] :
% 0.17/0.41 ( ( ( bot_bot @ ( set @ A ) )
% 0.17/0.41 = ( collect @ A @ P ) )
% 0.17/0.41 = ( ! [X4: A] :
% 0.17/0.41 ~ ( P @ X4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % empty_Collect_eq
% 0.17/0.41 thf(fact_58_Collect__empty__eq,axiom,
% 0.17/0.41 ! [A: $tType,P: A > $o] :
% 0.17/0.41 ( ( ( collect @ A @ P )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( ! [X4: A] :
% 0.17/0.41 ~ ( P @ X4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Collect_empty_eq
% 0.17/0.41 thf(fact_59_ex__in__conv,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( ? [X4: A] : ( member @ A @ X4 @ A2 ) )
% 0.17/0.41 = ( A2
% 0.17/0.41 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % ex_in_conv
% 0.17/0.41 thf(fact_60_equals0I,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ! [Y2: A] :
% 0.17/0.41 ~ ( member @ A @ Y2 @ A2 )
% 0.17/0.41 => ( A2
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % equals0I
% 0.17/0.41 thf(fact_61_equals0D,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,A3: A] :
% 0.17/0.41 ( ( A2
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % equals0D
% 0.17/0.41 thf(fact_62_emptyE,axiom,
% 0.17/0.41 ! [A: $tType,A3: A] :
% 0.17/0.41 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % emptyE
% 0.17/0.41 thf(fact_63_UNIV__witness,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % UNIV_witness
% 0.17/0.41 thf(fact_64_UNIV__eq__I,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.17/0.41 => ( ( top_top @ ( set @ A ) )
% 0.17/0.41 = A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % UNIV_eq_I
% 0.17/0.41 thf(fact_65_lappend__assoc,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.17/0.41 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lappend_assoc
% 0.17/0.41 thf(fact_66_empty__not__UNIV,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( bot_bot @ ( set @ A ) )
% 0.17/0.41 != ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % empty_not_UNIV
% 0.17/0.41 thf(fact_67_neq__LNil__conv,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.41 ( ( Xs
% 0.17/0.41 != ( coinductive_LNil @ A ) )
% 0.17/0.41 = ( ? [X4: A,Xs2: coinductive_llist @ A] :
% 0.17/0.41 ( Xs
% 0.17/0.41 = ( coinductive_LCons @ A @ X4 @ Xs2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % neq_LNil_conv
% 0.17/0.41 thf(fact_68_llist_Odistinct_I1_J,axiom,
% 0.17/0.41 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_LNil @ A )
% 0.17/0.41 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 0.17/0.41
% 0.17/0.41 % llist.distinct(1)
% 0.17/0.41 thf(fact_69_lappend__LNil__LNil,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.17/0.41 = ( coinductive_LNil @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 % lappend_LNil_LNil
% 0.17/0.41 thf(fact_70_top__apply,axiom,
% 0.17/0.41 ! [C2: $tType,D: $tType] :
% 0.17/0.41 ( ( top @ C2 @ ( type2 @ C2 ) )
% 0.17/0.41 => ( ( top_top @ ( D > C2 ) )
% 0.17/0.41 = ( ^ [X4: D] : ( top_top @ C2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % top_apply
% 0.17/0.41 thf(fact_71_bot__apply,axiom,
% 0.17/0.41 ! [C2: $tType,D: $tType] :
% 0.17/0.41 ( ( bot @ C2 @ ( type2 @ C2 ) )
% 0.17/0.41 => ( ( bot_bot @ ( D > C2 ) )
% 0.17/0.41 = ( ^ [X4: D] : ( bot_bot @ C2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % bot_apply
% 0.17/0.41 thf(fact_72_poslsts__empty,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( lList21148268032oslsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % poslsts_empty
% 0.17/0.41 thf(fact_73_fpslsts__empty,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( lList22096119349pslsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % fpslsts_empty
% 0.17/0.41 thf(fact_74_poslsts__iff,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.17/0.41 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.17/0.41 & ( S
% 0.17/0.41 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % poslsts_iff
% 0.17/0.41 thf(fact_75_fpslsts__iff,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.17/0.41 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 & ( S
% 0.17/0.41 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % fpslsts_iff
% 0.17/0.41 thf(fact_76_poslsts__UNIV,axiom,
% 0.17/0.41 ! [A: $tType,S: coinductive_llist @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.17/0.41 = ( S
% 0.17/0.41 != ( coinductive_LNil @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % poslsts_UNIV
% 0.17/0.41 thf(fact_77_bot__set__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( bot_bot @ ( set @ A ) )
% 0.17/0.41 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % bot_set_def
% 0.17/0.41 thf(fact_78_top__set__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( top_top @ ( set @ A ) )
% 0.17/0.41 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % top_set_def
% 0.17/0.41 thf(fact_79_bot__fun__def,axiom,
% 0.17/0.41 ! [B: $tType,A: $tType] :
% 0.17/0.41 ( ( bot @ B @ ( type2 @ B ) )
% 0.17/0.41 => ( ( bot_bot @ ( A > B ) )
% 0.17/0.41 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % bot_fun_def
% 0.17/0.41 thf(fact_80_fpslsts__cases,axiom,
% 0.17/0.41 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.17/0.41 => ~ ! [A4: A,Rs: coinductive_llist @ A] :
% 0.17/0.41 ( ( R
% 0.17/0.41 = ( coinductive_LCons @ A @ A4 @ Rs ) )
% 0.17/0.41 => ( ( member @ A @ A4 @ A2 )
% 0.17/0.41 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % fpslsts_cases
% 0.17/0.41 thf(fact_81_alllsts__empty,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( lList2435255213lllsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % alllsts_empty
% 0.17/0.41 thf(fact_82_finlsts__empty,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( lList2236698231inlsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts_empty
% 0.17/0.41 thf(fact_83_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.17/0.41 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.17/0.41 = ( ( Xs
% 0.17/0.41 = ( coinductive_LNil @ A ) )
% 0.17/0.41 | ? [Xs2: coinductive_llist @ A] :
% 0.17/0.41 ( ( Xs
% 0.17/0.41 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 0.17/0.41 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.17/0.41 thf(fact_84_finlsts__rec__LCons,axiom,
% 0.17/0.41 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C: B,D2: A > ( coinductive_llist @ A ) > B > B,A3: A] :
% 0.17/0.41 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( lList21916056377ts_rec @ B @ A @ C @ D2 @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.17/0.41 = ( D2 @ A3 @ R @ ( lList21916056377ts_rec @ B @ A @ C @ D2 @ R ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts_rec_LCons
% 0.17/0.41 thf(fact_85_finlsts__rec__LCons__def,axiom,
% 0.17/0.41 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.17/0.41 ( ( F
% 0.17/0.41 = ( lList21916056377ts_rec @ B @ A @ C @ D2 ) )
% 0.17/0.41 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.17/0.41 => ( ( F @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.17/0.41 = ( D2 @ A3 @ R @ ( F @ R ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts_rec_LCons_def
% 0.17/0.41 thf(fact_86_Set_Ois__empty__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( is_empty @ A )
% 0.17/0.41 = ( ^ [A7: set @ A] :
% 0.17/0.41 ( A7
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Set.is_empty_def
% 0.17/0.41 thf(fact_87_insertCI,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,B2: set @ A,B3: A] :
% 0.17/0.41 ( ( ~ ( member @ A @ A3 @ B2 )
% 0.17/0.41 => ( A3 = B3 ) )
% 0.17/0.41 => ( member @ A @ A3 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insertCI
% 0.17/0.41 thf(fact_88_insert__iff,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,B3: A,A2: set @ A] :
% 0.17/0.41 ( ( member @ A @ A3 @ ( insert @ A @ B3 @ A2 ) )
% 0.17/0.41 = ( ( A3 = B3 )
% 0.17/0.41 | ( member @ A @ A3 @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_iff
% 0.17/0.41 thf(fact_89_insert__absorb2,axiom,
% 0.17/0.41 ! [A: $tType,X: A,A2: set @ A] :
% 0.17/0.41 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 0.17/0.41 = ( insert @ A @ X @ A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_absorb2
% 0.17/0.41 thf(fact_90_top1I,axiom,
% 0.17/0.41 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.17/0.41
% 0.17/0.41 % top1I
% 0.17/0.41 thf(fact_91_singletonI,axiom,
% 0.17/0.41 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % singletonI
% 0.17/0.41 thf(fact_92_insertE,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,B3: A,A2: set @ A] :
% 0.17/0.41 ( ( member @ A @ A3 @ ( insert @ A @ B3 @ A2 ) )
% 0.17/0.41 => ( ( A3 != B3 )
% 0.17/0.41 => ( member @ A @ A3 @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insertE
% 0.17/0.41 thf(fact_93_insertI1,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,B2: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % insertI1
% 0.17/0.41 thf(fact_94_insertI2,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,B2: set @ A,B3: A] :
% 0.17/0.41 ( ( member @ A @ A3 @ B2 )
% 0.17/0.41 => ( member @ A @ A3 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insertI2
% 0.17/0.41 thf(fact_95_Set_Oset__insert,axiom,
% 0.17/0.41 ! [A: $tType,X: A,A2: set @ A] :
% 0.17/0.41 ( ( member @ A @ X @ A2 )
% 0.17/0.41 => ~ ! [B4: set @ A] :
% 0.17/0.41 ( ( A2
% 0.17/0.41 = ( insert @ A @ X @ B4 ) )
% 0.17/0.41 => ( member @ A @ X @ B4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Set.set_insert
% 0.17/0.41 thf(fact_96_insert__ident,axiom,
% 0.17/0.41 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ~ ( member @ A @ X @ A2 )
% 0.17/0.41 => ( ~ ( member @ A @ X @ B2 )
% 0.17/0.41 => ( ( ( insert @ A @ X @ A2 )
% 0.17/0.41 = ( insert @ A @ X @ B2 ) )
% 0.17/0.41 = ( A2 = B2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_ident
% 0.17/0.41 thf(fact_97_insert__absorb,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.41 ( ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ( ( insert @ A @ A3 @ A2 )
% 0.17/0.41 = A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_absorb
% 0.17/0.41 thf(fact_98_insert__eq__iff,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A,B3: A,B2: set @ A] :
% 0.17/0.41 ( ~ ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ( ~ ( member @ A @ B3 @ B2 )
% 0.17/0.41 => ( ( ( insert @ A @ A3 @ A2 )
% 0.17/0.41 = ( insert @ A @ B3 @ B2 ) )
% 0.17/0.41 = ( ( ( A3 = B3 )
% 0.17/0.41 => ( A2 = B2 ) )
% 0.17/0.41 & ( ( A3 != B3 )
% 0.17/0.41 => ? [C3: set @ A] :
% 0.17/0.41 ( ( A2
% 0.17/0.41 = ( insert @ A @ B3 @ C3 ) )
% 0.17/0.41 & ~ ( member @ A @ B3 @ C3 )
% 0.17/0.41 & ( B2
% 0.17/0.41 = ( insert @ A @ A3 @ C3 ) )
% 0.17/0.41 & ~ ( member @ A @ A3 @ C3 ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_eq_iff
% 0.17/0.41 thf(fact_99_insert__commute,axiom,
% 0.17/0.41 ! [A: $tType,X: A,Y: A,A2: set @ A] :
% 0.17/0.41 ( ( insert @ A @ X @ ( insert @ A @ Y @ A2 ) )
% 0.17/0.41 = ( insert @ A @ Y @ ( insert @ A @ X @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_commute
% 0.17/0.41 thf(fact_100_mk__disjoint__insert,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.41 ( ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ? [B4: set @ A] :
% 0.17/0.41 ( ( A2
% 0.17/0.41 = ( insert @ A @ A3 @ B4 ) )
% 0.17/0.41 & ~ ( member @ A @ A3 @ B4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % mk_disjoint_insert
% 0.17/0.41 thf(fact_101_singleton__inject,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,B3: A] :
% 0.17/0.41 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.41 => ( A3 = B3 ) ) ).
% 0.17/0.41
% 0.17/0.41 % singleton_inject
% 0.17/0.41 thf(fact_102_insert__not__empty,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.41 ( ( insert @ A @ A3 @ A2 )
% 0.17/0.41 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_not_empty
% 0.17/0.41 thf(fact_103_doubleton__eq__iff,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,B3: A,C: A,D2: A] :
% 0.17/0.41 ( ( ( insert @ A @ A3 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.41 = ( insert @ A @ C @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.41 = ( ( ( A3 = C )
% 0.17/0.41 & ( B3 = D2 ) )
% 0.17/0.41 | ( ( A3 = D2 )
% 0.17/0.41 & ( B3 = C ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % doubleton_eq_iff
% 0.17/0.41 thf(fact_104_singleton__iff,axiom,
% 0.17/0.41 ! [A: $tType,B3: A,A3: A] :
% 0.17/0.41 ( ( member @ A @ B3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.41 = ( B3 = A3 ) ) ).
% 0.17/0.41
% 0.17/0.41 % singleton_iff
% 0.17/0.41 thf(fact_105_singletonD,axiom,
% 0.17/0.41 ! [A: $tType,B3: A,A3: A] :
% 0.17/0.41 ( ( member @ A @ B3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.41 => ( B3 = A3 ) ) ).
% 0.17/0.41
% 0.17/0.41 % singletonD
% 0.17/0.41 thf(fact_106_insert__UNIV,axiom,
% 0.17/0.41 ! [A: $tType,X: A] :
% 0.17/0.41 ( ( insert @ A @ X @ ( top_top @ ( set @ A ) ) )
% 0.17/0.41 = ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_UNIV
% 0.17/0.41 thf(fact_107_finlsts__rec__LNil__def,axiom,
% 0.17/0.41 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 0.17/0.41 ( ( F
% 0.17/0.41 = ( lList21916056377ts_rec @ B @ A @ C @ D2 ) )
% 0.17/0.41 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.17/0.41 = C ) ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts_rec_LNil_def
% 0.17/0.41 thf(fact_108_finlsts__rec__LNil,axiom,
% 0.17/0.41 ! [B: $tType,A: $tType,C: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 0.17/0.41 ( ( lList21916056377ts_rec @ A @ B @ C @ D2 @ ( coinductive_LNil @ B ) )
% 0.17/0.41 = C ) ).
% 0.17/0.41
% 0.17/0.41 % finlsts_rec_LNil
% 0.17/0.41 thf(fact_109_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.41 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.17/0.41 = ( Xs
% 0.17/0.41 = ( coinductive_LNil @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.17/0.41 thf(fact_110_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.17/0.41
% 0.17/0.41 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.17/0.41 thf(fact_111_Topological__Spaces_OUNIV__not__singleton,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( topolo890362671_space @ A @ ( type2 @ A ) )
% 0.17/0.41 => ! [X: A] :
% 0.17/0.41 ( ( top_top @ ( set @ A ) )
% 0.17/0.41 != ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Topological_Spaces.UNIV_not_singleton
% 0.17/0.41 thf(fact_112_the__elem__eq,axiom,
% 0.17/0.41 ! [A: $tType,X: A] :
% 0.17/0.41 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.41 = X ) ).
% 0.17/0.41
% 0.17/0.41 % the_elem_eq
% 0.17/0.41 thf(fact_113_top__empty__eq,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( top_top @ ( A > $o ) )
% 0.17/0.41 = ( ^ [X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % top_empty_eq
% 0.17/0.41 thf(fact_114_bot__empty__eq,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( bot_bot @ ( A > $o ) )
% 0.17/0.41 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % bot_empty_eq
% 0.17/0.41 thf(fact_115_Collect__empty__eq__bot,axiom,
% 0.17/0.41 ! [A: $tType,P: A > $o] :
% 0.17/0.41 ( ( ( collect @ A @ P )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( P
% 0.17/0.41 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Collect_empty_eq_bot
% 0.17/0.41 thf(fact_116_is__singletonI,axiom,
% 0.17/0.41 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % is_singletonI
% 0.17/0.41 thf(fact_117_is__singleton__the__elem,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( is_singleton @ A )
% 0.17/0.41 = ( ^ [A7: set @ A] :
% 0.17/0.41 ( A7
% 0.17/0.41 = ( insert @ A @ ( the_elem @ A @ A7 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % is_singleton_the_elem
% 0.17/0.41 thf(fact_118_is__singletonI_H,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( A2
% 0.17/0.41 != ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 => ( ! [X3: A,Y2: A] :
% 0.17/0.41 ( ( member @ A @ X3 @ A2 )
% 0.17/0.41 => ( ( member @ A @ Y2 @ A2 )
% 0.17/0.41 => ( X3 = Y2 ) ) )
% 0.17/0.41 => ( is_singleton @ A @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % is_singletonI'
% 0.17/0.41 thf(fact_119_is__singleton__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( is_singleton @ A )
% 0.17/0.41 = ( ^ [A7: set @ A] :
% 0.17/0.41 ? [X4: A] :
% 0.17/0.41 ( A7
% 0.17/0.41 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % is_singleton_def
% 0.17/0.41 thf(fact_120_is__singletonE,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( is_singleton @ A @ A2 )
% 0.17/0.41 => ~ ! [X3: A] :
% 0.17/0.41 ( A2
% 0.17/0.41 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % is_singletonE
% 0.17/0.41 thf(fact_121_poslsts__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( lList21148268032oslsts @ A )
% 0.17/0.41 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A7 ) @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % poslsts_def
% 0.17/0.41 thf(fact_122_fpslsts__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( lList22096119349pslsts @ A )
% 0.17/0.41 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A7 ) @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % fpslsts_def
% 0.17/0.41 thf(fact_123_gen__lset__code_I2_J,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,X: A,Xs: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_gen_lset @ A @ A2 @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.17/0.41 = ( coinductive_gen_lset @ A @ ( insert @ A @ X @ A2 ) @ Xs ) ) ).
% 0.17/0.41
% 0.17/0.41 % gen_lset_code(2)
% 0.17/0.41 thf(fact_124_top__conj_I2_J,axiom,
% 0.17/0.41 ! [A: $tType,P: $o,X: A] :
% 0.17/0.41 ( ( P
% 0.17/0.41 & ( top_top @ ( A > $o ) @ X ) )
% 0.17/0.41 = P ) ).
% 0.17/0.41
% 0.17/0.41 % top_conj(2)
% 0.17/0.41 thf(fact_125_DiffI,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ C @ A2 )
% 0.17/0.41 => ( ~ ( member @ A @ C @ B2 )
% 0.17/0.41 => ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % DiffI
% 0.17/0.41 thf(fact_126_Diff__iff,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 = ( ( member @ A @ C @ A2 )
% 0.17/0.41 & ~ ( member @ A @ C @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_iff
% 0.17/0.41 thf(fact_127_Diff__idemp,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 0.17/0.41 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_idemp
% 0.17/0.41 thf(fact_128_Diff__cancel,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( minus_minus @ ( set @ A ) @ A2 @ A2 )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_cancel
% 0.17/0.41 thf(fact_129_empty__Diff,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % empty_Diff
% 0.17/0.41 thf(fact_130_Diff__empty,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( minus_minus @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = A2 ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_empty
% 0.17/0.41 thf(fact_131_Diff__insert0,axiom,
% 0.17/0.41 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ~ ( member @ A @ X @ A2 )
% 0.17/0.41 => ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X @ B2 ) )
% 0.17/0.41 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_insert0
% 0.17/0.41 thf(fact_132_insert__Diff1,axiom,
% 0.17/0.41 ! [A: $tType,X: A,B2: set @ A,A2: set @ A] :
% 0.17/0.41 ( ( member @ A @ X @ B2 )
% 0.17/0.41 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B2 )
% 0.17/0.41 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_Diff1
% 0.17/0.41 thf(fact_133_Diff__UNIV,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( minus_minus @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_UNIV
% 0.17/0.41 thf(fact_134_insert__Diff__single,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.41 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.41 = ( insert @ A @ A3 @ A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_Diff_single
% 0.17/0.41 thf(fact_135_insert__Diff__if,axiom,
% 0.17/0.41 ! [A: $tType,X: A,B2: set @ A,A2: set @ A] :
% 0.17/0.41 ( ( ( member @ A @ X @ B2 )
% 0.17/0.41 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B2 )
% 0.17/0.41 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) )
% 0.17/0.41 & ( ~ ( member @ A @ X @ B2 )
% 0.17/0.41 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B2 )
% 0.17/0.41 = ( insert @ A @ X @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_Diff_if
% 0.17/0.41 thf(fact_136_DiffE,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 => ~ ( ( member @ A @ C @ A2 )
% 0.17/0.41 => ( member @ A @ C @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % DiffE
% 0.17/0.41 thf(fact_137_DiffD1,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 => ( member @ A @ C @ A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % DiffD1
% 0.17/0.41 thf(fact_138_DiffD2,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 => ~ ( member @ A @ C @ B2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % DiffD2
% 0.17/0.41 thf(fact_139_Diff__insert,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,A3: A,B2: set @ A] :
% 0.17/0.41 ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 0.17/0.41 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_insert
% 0.17/0.41 thf(fact_140_insert__Diff,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A] :
% 0.17/0.41 ( ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.41 = A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_Diff
% 0.17/0.41 thf(fact_141_Diff__insert2,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,A3: A,B2: set @ A] :
% 0.17/0.41 ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 0.17/0.41 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_insert2
% 0.17/0.41 thf(fact_142_Diff__insert__absorb,axiom,
% 0.17/0.41 ! [A: $tType,X: A,A2: set @ A] :
% 0.17/0.41 ( ~ ( member @ A @ X @ A2 )
% 0.17/0.41 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.41 = A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_insert_absorb
% 0.17/0.41 thf(fact_143_gen__lset__code_I1_J,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( coinductive_gen_lset @ A @ A2 @ ( coinductive_LNil @ A ) )
% 0.17/0.41 = A2 ) ).
% 0.17/0.41
% 0.17/0.41 % gen_lset_code(1)
% 0.17/0.41 thf(fact_144_inflsts__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( lList21612149805nflsts @ A )
% 0.17/0.41 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A7 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % inflsts_def
% 0.17/0.41 thf(fact_145_top__conj_I1_J,axiom,
% 0.17/0.41 ! [A: $tType,X: A,P: $o] :
% 0.17/0.41 ( ( ( top_top @ ( A > $o ) @ X )
% 0.17/0.41 & P )
% 0.17/0.41 = P ) ).
% 0.17/0.41
% 0.17/0.41 % top_conj(1)
% 0.17/0.41 thf(fact_146_remove__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( remove @ A )
% 0.17/0.41 = ( ^ [X4: A,A7: set @ A] : ( minus_minus @ ( set @ A ) @ A7 @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % remove_def
% 0.17/0.41 thf(fact_147_lSup__minus__LNil,axiom,
% 0.17/0.41 ! [A: $tType,Y3: set @ ( coinductive_llist @ A )] :
% 0.17/0.41 ( ( coinductive_lSup @ A @ ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ Y3 @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) )
% 0.17/0.41 = ( coinductive_lSup @ A @ Y3 ) ) ).
% 0.17/0.41
% 0.17/0.41 % lSup_minus_LNil
% 0.17/0.41 thf(fact_148_lstrict__prefix__code_I2_J,axiom,
% 0.17/0.41 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.17/0.41
% 0.17/0.41 % lstrict_prefix_code(2)
% 0.17/0.41 thf(fact_149_lstrict__prefix__code_I3_J,axiom,
% 0.17/0.41 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.17/0.41 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.17/0.41
% 0.17/0.41 % lstrict_prefix_code(3)
% 0.17/0.41 thf(fact_150_member__remove,axiom,
% 0.17/0.41 ! [A: $tType,X: A,Y: A,A2: set @ A] :
% 0.17/0.41 ( ( member @ A @ X @ ( remove @ A @ Y @ A2 ) )
% 0.17/0.41 = ( ( member @ A @ X @ A2 )
% 0.17/0.41 & ( X != Y ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % member_remove
% 0.17/0.41 thf(fact_151_lstrict__prefix__code_I4_J,axiom,
% 0.17/0.41 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.17/0.41 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.17/0.41 = ( ( X = Y )
% 0.17/0.41 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lstrict_prefix_code(4)
% 0.17/0.41 thf(fact_152_lstrict__prefix__code_I1_J,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 % lstrict_prefix_code(1)
% 0.17/0.41 thf(fact_153_lSup__empty,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( coinductive_lSup @ A @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) )
% 0.17/0.41 = ( coinductive_LNil @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 % lSup_empty
% 0.17/0.41 thf(fact_154_lSup__singleton,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lSup @ A @ ( insert @ ( coinductive_llist @ A ) @ Xs @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) )
% 0.17/0.41 = Xs ) ).
% 0.17/0.41
% 0.17/0.41 % lSup_singleton
% 0.17/0.41 thf(fact_155_llist__less__induct,axiom,
% 0.17/0.41 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.17/0.41 ( ! [Xs3: coinductive_llist @ A] :
% 0.17/0.41 ( ! [Ys2: coinductive_llist @ A] :
% 0.17/0.41 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.17/0.41 => ( P @ Ys2 ) )
% 0.17/0.41 => ( P @ Xs3 ) )
% 0.17/0.41 => ( P @ Xs ) ) ).
% 0.17/0.41
% 0.17/0.41 % llist_less_induct
% 0.17/0.41 thf(fact_156_lSup__insert__LNil,axiom,
% 0.17/0.41 ! [A: $tType,Y3: set @ ( coinductive_llist @ A )] :
% 0.17/0.41 ( ( coinductive_lSup @ A @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ Y3 ) )
% 0.17/0.41 = ( coinductive_lSup @ A @ Y3 ) ) ).
% 0.17/0.41
% 0.17/0.41 % lSup_insert_LNil
% 0.17/0.41 thf(fact_157_llast__singleton,axiom,
% 0.17/0.41 ! [A: $tType,X: A] :
% 0.17/0.41 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 0.17/0.41 = X ) ).
% 0.17/0.41
% 0.17/0.41 % llast_singleton
% 0.17/0.41 thf(fact_158_totally__bounded__empty,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( topolo47006728_space @ A @ ( type2 @ A ) )
% 0.17/0.41 => ( topolo406746546ounded @ A @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % totally_bounded_empty
% 0.17/0.41 thf(fact_159_pairwise__singleton,axiom,
% 0.17/0.41 ! [A: $tType,P: A > A > $o,A2: A] : ( pairwise @ A @ P @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % pairwise_singleton
% 0.17/0.41 thf(fact_160_llast__LCons2,axiom,
% 0.17/0.41 ! [A: $tType,X: A,Y: A,Xs: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 0.17/0.41 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % llast_LCons2
% 0.17/0.41 thf(fact_161_pairwise__def,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( pairwise @ A )
% 0.17/0.41 = ( ^ [R2: A > A > $o,S2: set @ A] :
% 0.17/0.41 ! [X4: A] :
% 0.17/0.41 ( ( member @ A @ X4 @ S2 )
% 0.17/0.41 => ! [Y4: A] :
% 0.17/0.41 ( ( member @ A @ Y4 @ S2 )
% 0.17/0.41 => ( ( X4 != Y4 )
% 0.17/0.41 => ( R2 @ X4 @ Y4 ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % pairwise_def
% 0.17/0.41 thf(fact_162_pairwise__empty,axiom,
% 0.17/0.41 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % pairwise_empty
% 0.17/0.41 thf(fact_163_pairwise__insert,axiom,
% 0.17/0.41 ! [A: $tType,R: A > A > $o,X: A,S: set @ A] :
% 0.17/0.41 ( ( pairwise @ A @ R @ ( insert @ A @ X @ S ) )
% 0.17/0.41 = ( ! [Y4: A] :
% 0.17/0.41 ( ( ( member @ A @ Y4 @ S )
% 0.17/0.41 & ( Y4 != X ) )
% 0.17/0.41 => ( ( R @ X @ Y4 )
% 0.17/0.41 & ( R @ Y4 @ X ) ) )
% 0.17/0.41 & ( pairwise @ A @ R @ S ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % pairwise_insert
% 0.17/0.41 thf(fact_164_llast__lappend__LCons,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.41 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 0.17/0.41 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % llast_lappend_LCons
% 0.17/0.41 thf(fact_165_fin__Int__inf,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % fin_Int_inf
% 0.17/0.41 thf(fact_166_fin__Un__inf,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.17/0.41 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % fin_Un_inf
% 0.17/0.41 thf(fact_167_Int__iff,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 = ( ( member @ A @ C @ A2 )
% 0.17/0.41 & ( member @ A @ C @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_iff
% 0.17/0.41 thf(fact_168_IntI,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ C @ A2 )
% 0.17/0.41 => ( ( member @ A @ C @ B2 )
% 0.17/0.41 => ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % IntI
% 0.17/0.41 thf(fact_169_Un__iff,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 = ( ( member @ A @ C @ A2 )
% 0.17/0.41 | ( member @ A @ C @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_iff
% 0.17/0.41 thf(fact_170_UnCI,axiom,
% 0.17/0.41 ! [A: $tType,C: A,B2: set @ A,A2: set @ A] :
% 0.17/0.41 ( ( ~ ( member @ A @ C @ B2 )
% 0.17/0.41 => ( member @ A @ C @ A2 ) )
% 0.17/0.41 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % UnCI
% 0.17/0.41 thf(fact_171_Int__UNIV,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.17/0.41 = ( top_top @ ( set @ A ) ) )
% 0.17/0.41 = ( ( A2
% 0.17/0.41 = ( top_top @ ( set @ A ) ) )
% 0.17/0.41 & ( B2
% 0.17/0.41 = ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_UNIV
% 0.17/0.41 thf(fact_172_Un__empty,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( ( A2
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 & ( B2
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_empty
% 0.17/0.41 thf(fact_173_Int__insert__left__if0,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,C4: set @ A,B2: set @ A] :
% 0.17/0.41 ( ~ ( member @ A @ A3 @ C4 )
% 0.17/0.41 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_insert_left_if0
% 0.17/0.41 thf(fact_174_Int__insert__left__if1,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,C4: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ A3 @ C4 )
% 0.17/0.41 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 0.17/0.41 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_insert_left_if1
% 0.17/0.41 thf(fact_175_insert__inter__insert,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A2 ) @ ( insert @ A @ A3 @ B2 ) )
% 0.17/0.41 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_inter_insert
% 0.17/0.41 thf(fact_176_Int__insert__right__if0,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ~ ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_insert_right_if0
% 0.17/0.41 thf(fact_177_Int__insert__right__if1,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( member @ A @ A3 @ A2 )
% 0.17/0.41 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 0.17/0.41 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_insert_right_if1
% 0.17/0.41 thf(fact_178_Un__insert__left,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,B2: set @ A,C4: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 0.17/0.41 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_insert_left
% 0.17/0.41 thf(fact_179_Un__insert__right,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,A3: A,B2: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 0.17/0.41 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_insert_right
% 0.17/0.41 thf(fact_180_Un__Diff__cancel,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 0.17/0.41 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_Diff_cancel
% 0.17/0.41 thf(fact_181_Un__Diff__cancel2,axiom,
% 0.17/0.41 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) @ A2 )
% 0.17/0.41 = ( sup_sup @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_Diff_cancel2
% 0.17/0.41 thf(fact_182_lfinite__LCons,axiom,
% 0.17/0.41 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.17/0.41 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.17/0.41
% 0.17/0.41 % lfinite_LCons
% 0.17/0.41 thf(fact_183_lfinite__code_I2_J,axiom,
% 0.17/0.41 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.17/0.41 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 0.17/0.41 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.17/0.41
% 0.17/0.41 % lfinite_code(2)
% 0.17/0.41 thf(fact_184_lfinite__code_I1_J,axiom,
% 0.17/0.41 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.41
% 0.17/0.41 % lfinite_code(1)
% 0.17/0.41 thf(fact_185_lfinite__lappend,axiom,
% 0.17/0.41 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.41 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.17/0.41 = ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.41 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % lfinite_lappend
% 0.17/0.41 thf(fact_186_insert__disjoint_I1_J,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A2 ) @ B2 )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( ~ ( member @ A @ A3 @ B2 )
% 0.17/0.41 & ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_disjoint(1)
% 0.17/0.41 thf(fact_187_insert__disjoint_I2_J,axiom,
% 0.17/0.41 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( ( bot_bot @ ( set @ A ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A2 ) @ B2 ) )
% 0.17/0.41 = ( ~ ( member @ A @ A3 @ B2 )
% 0.17/0.41 & ( ( bot_bot @ ( set @ A ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % insert_disjoint(2)
% 0.17/0.41 thf(fact_188_disjoint__insert_I1_J,axiom,
% 0.17/0.41 ! [A: $tType,B2: set @ A,A3: A,A2: set @ A] :
% 0.17/0.41 ( ( ( inf_inf @ ( set @ A ) @ B2 @ ( insert @ A @ A3 @ A2 ) )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.41 = ( ~ ( member @ A @ A3 @ B2 )
% 0.17/0.41 & ( ( inf_inf @ ( set @ A ) @ B2 @ A2 )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % disjoint_insert(1)
% 0.17/0.41 thf(fact_189_disjoint__insert_I2_J,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B3: A,B2: set @ A] :
% 0.17/0.41 ( ( ( bot_bot @ ( set @ A ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ B2 ) ) )
% 0.17/0.41 = ( ~ ( member @ A @ B3 @ A2 )
% 0.17/0.41 & ( ( bot_bot @ ( set @ A ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % disjoint_insert(2)
% 0.17/0.41 thf(fact_190_Diff__disjoint,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 0.17/0.41 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Diff_disjoint
% 0.17/0.41 thf(fact_191_Int__left__commute,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ B2 @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_left_commute
% 0.17/0.41 thf(fact_192_Un__left__commute,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 0.17/0.41 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_left_commute
% 0.17/0.41 thf(fact_193_Un__Int__distrib2,axiom,
% 0.17/0.41 ! [A: $tType,B2: set @ A,C4: set @ A,A2: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) @ A2 )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ B2 @ A2 ) @ ( sup_sup @ ( set @ A ) @ C4 @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_Int_distrib2
% 0.17/0.41 thf(fact_194_Int__left__absorb,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_left_absorb
% 0.17/0.41 thf(fact_195_Int__Un__distrib2,axiom,
% 0.17/0.41 ! [A: $tType,B2: set @ A,C4: set @ A,A2: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) @ A2 )
% 0.17/0.41 = ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B2 @ A2 ) @ ( inf_inf @ ( set @ A ) @ C4 @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_Un_distrib2
% 0.17/0.41 thf(fact_196_Un__left__absorb,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_left_absorb
% 0.17/0.41 thf(fact_197_Un__Int__distrib,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_Int_distrib
% 0.17/0.41 thf(fact_198_Int__Un__distrib,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 0.17/0.41 = ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_Un_distrib
% 0.17/0.41 thf(fact_199_Un__Int__crazy,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) @ ( inf_inf @ ( set @ A ) @ C4 @ A2 ) )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) @ ( sup_sup @ ( set @ A ) @ C4 @ A2 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_Int_crazy
% 0.17/0.41 thf(fact_200_Int__commute,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) )
% 0.17/0.41 = ( ^ [A7: set @ A,B5: set @ A] : ( inf_inf @ ( set @ A ) @ B5 @ A7 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_commute
% 0.17/0.41 thf(fact_201_Un__commute,axiom,
% 0.17/0.41 ! [A: $tType] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) )
% 0.17/0.41 = ( ^ [A7: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A7 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_commute
% 0.17/0.41 thf(fact_202_Int__absorb,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) @ A2 @ A2 )
% 0.17/0.41 = A2 ) ).
% 0.17/0.41
% 0.17/0.41 % Int_absorb
% 0.17/0.41 thf(fact_203_Un__absorb,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.17/0.41 = A2 ) ).
% 0.17/0.41
% 0.17/0.41 % Un_absorb
% 0.17/0.41 thf(fact_204_Int__assoc,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.41 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 0.17/0.41 = ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Int_assoc
% 0.17/0.41 thf(fact_205_Un__assoc,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.41 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 0.17/0.41 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % Un_assoc
% 0.17/0.41 thf(fact_206_ball__Un,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.17/0.41 ( ( ! [X4: A] :
% 0.17/0.41 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 => ( P @ X4 ) ) )
% 0.17/0.41 = ( ! [X4: A] :
% 0.17/0.41 ( ( member @ A @ X4 @ A2 )
% 0.17/0.41 => ( P @ X4 ) )
% 0.17/0.41 & ! [X4: A] :
% 0.17/0.41 ( ( member @ A @ X4 @ B2 )
% 0.17/0.41 => ( P @ X4 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % ball_Un
% 0.17/0.41 thf(fact_207_bex__Un,axiom,
% 0.17/0.41 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.17/0.41 ( ( ? [X4: A] :
% 0.17/0.41 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.41 & ( P @ X4 ) ) )
% 0.17/0.41 = ( ? [X4: A] :
% 0.17/0.41 ( ( member @ A @ X4 @ A2 )
% 0.17/0.41 & ( P @ X4 ) )
% 0.17/0.41 | ? [X4: A] :
% 0.17/0.41 ( ( member @ A @ X4 @ B2 )
% 0.17/0.41 & ( P @ X4 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 % bex_Un
% 0.17/0.41 thf(fact_208_IntD2,axiom,
% 0.17/0.41 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.42 => ( member @ A @ C @ B2 ) ) ).
% 0.17/0.42
% 0.17/0.42 % IntD2
% 0.17/0.42 thf(fact_209_IntD1,axiom,
% 0.17/0.42 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.42 => ( member @ A @ C @ A2 ) ) ).
% 0.17/0.42
% 0.17/0.42 % IntD1
% 0.17/0.42 thf(fact_210_UnI2,axiom,
% 0.17/0.42 ! [A: $tType,C: A,B2: set @ A,A2: set @ A] :
% 0.17/0.42 ( ( member @ A @ C @ B2 )
% 0.17/0.42 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % UnI2
% 0.17/0.42 thf(fact_211_UnI1,axiom,
% 0.17/0.42 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( member @ A @ C @ A2 )
% 0.17/0.42 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % UnI1
% 0.17/0.42 thf(fact_212_IntE,axiom,
% 0.17/0.42 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.42 => ~ ( ( member @ A @ C @ A2 )
% 0.17/0.42 => ~ ( member @ A @ C @ B2 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % IntE
% 0.17/0.42 thf(fact_213_UnE,axiom,
% 0.17/0.42 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.42 => ( ~ ( member @ A @ C @ A2 )
% 0.17/0.42 => ( member @ A @ C @ B2 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % UnE
% 0.17/0.42 thf(fact_214_Int__insert__left,axiom,
% 0.17/0.42 ! [A: $tType,A3: A,C4: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( ( member @ A @ A3 @ C4 )
% 0.17/0.42 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 0.17/0.42 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) )
% 0.17/0.42 & ( ~ ( member @ A @ A3 @ C4 )
% 0.17/0.42 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 0.17/0.42 = ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Int_insert_left
% 0.17/0.42 thf(fact_215_Int__insert__right,axiom,
% 0.17/0.42 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( ( member @ A @ A3 @ A2 )
% 0.17/0.42 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 0.17/0.42 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) )
% 0.17/0.42 & ( ~ ( member @ A @ A3 @ A2 )
% 0.17/0.42 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 0.17/0.42 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Int_insert_right
% 0.17/0.42 thf(fact_216_Int__UNIV__right,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A] :
% 0.17/0.42 ( ( inf_inf @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.17/0.42 = A2 ) ).
% 0.17/0.42
% 0.17/0.42 % Int_UNIV_right
% 0.17/0.42 thf(fact_217_Int__UNIV__left,axiom,
% 0.17/0.42 ! [A: $tType,B2: set @ A] :
% 0.17/0.42 ( ( inf_inf @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.17/0.42 = B2 ) ).
% 0.17/0.42
% 0.17/0.42 % Int_UNIV_left
% 0.17/0.42 thf(fact_218_disjoint__iff__not__equal,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.42 = ( ! [X4: A] :
% 0.17/0.42 ( ( member @ A @ X4 @ A2 )
% 0.17/0.42 => ! [Y4: A] :
% 0.17/0.42 ( ( member @ A @ Y4 @ B2 )
% 0.17/0.42 => ( X4 != Y4 ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % disjoint_iff_not_equal
% 0.17/0.42 thf(fact_219_Int__empty__right,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A] :
% 0.17/0.42 ( ( inf_inf @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Int_empty_right
% 0.17/0.42 thf(fact_220_Int__empty__left,axiom,
% 0.17/0.42 ! [A: $tType,B2: set @ A] :
% 0.17/0.42 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Int_empty_left
% 0.17/0.42 thf(fact_221_Int__emptyI,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ! [X3: A] :
% 0.17/0.42 ( ( member @ A @ X3 @ A2 )
% 0.17/0.42 => ~ ( member @ A @ X3 @ B2 ) )
% 0.17/0.42 => ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Int_emptyI
% 0.17/0.42 thf(fact_222_Un__UNIV__right,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A] :
% 0.17/0.42 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.17/0.42 = ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Un_UNIV_right
% 0.17/0.42 thf(fact_223_Un__UNIV__left,axiom,
% 0.17/0.42 ! [A: $tType,B2: set @ A] :
% 0.17/0.42 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 0.17/0.42 = ( top_top @ ( set @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Un_UNIV_left
% 0.17/0.42 thf(fact_224_Un__empty__right,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A] :
% 0.17/0.42 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.42 = A2 ) ).
% 0.17/0.42
% 0.17/0.42 % Un_empty_right
% 0.17/0.42 thf(fact_225_Un__empty__left,axiom,
% 0.17/0.42 ! [A: $tType,B2: set @ A] :
% 0.17/0.42 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.17/0.42 = B2 ) ).
% 0.17/0.42
% 0.17/0.42 % Un_empty_left
% 0.17/0.42 thf(fact_226_lappend__inf,axiom,
% 0.17/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.42 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.17/0.42 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.17/0.42 = Xs ) ) ).
% 0.17/0.42
% 0.17/0.42 % lappend_inf
% 0.17/0.42 thf(fact_227_lfinite__LNil,axiom,
% 0.17/0.42 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.17/0.42
% 0.17/0.42 % lfinite_LNil
% 0.17/0.42 thf(fact_228_lfinite__LConsI,axiom,
% 0.17/0.42 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.17/0.42 ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.42 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % lfinite_LConsI
% 0.17/0.42 thf(fact_229_lfinite__lSupD,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ ( coinductive_llist @ A )] :
% 0.17/0.42 ( ( coinductive_lfinite @ A @ ( coinductive_lSup @ A @ A2 ) )
% 0.17/0.42 => ! [X5: coinductive_llist @ A] :
% 0.17/0.42 ( ( member @ ( coinductive_llist @ A ) @ X5 @ A2 )
% 0.17/0.42 => ( coinductive_lfinite @ A @ X5 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % lfinite_lSupD
% 0.17/0.42 thf(fact_230_lstrict__prefix__lfinite1,axiom,
% 0.17/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.17/0.42 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 0.17/0.42 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.17/0.42
% 0.17/0.42 % lstrict_prefix_lfinite1
% 0.17/0.42 thf(fact_231_Diff__Int__distrib2,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.42 ( ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 0.17/0.42 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Diff_Int_distrib2
% 0.17/0.42 thf(fact_232_Diff__Int__distrib,axiom,
% 0.17/0.42 ! [A: $tType,C4: set @ A,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( inf_inf @ ( set @ A ) @ C4 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.42 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ C4 @ A2 ) @ ( inf_inf @ ( set @ A ) @ C4 @ B2 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Diff_Int_distrib
% 0.17/0.42 thf(fact_233_Diff__Diff__Int,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( minus_minus @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.42 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.17/0.42
% 0.17/0.42 % Diff_Diff_Int
% 0.17/0.42 thf(fact_234_Un__Diff__Int,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.42 = A2 ) ).
% 0.17/0.42
% 0.17/0.42 % Un_Diff_Int
% 0.17/0.42 thf(fact_235_Diff__Int2,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,C4: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) )
% 0.17/0.42 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) @ B2 ) ) ).
% 0.17/0.42
% 0.17/0.42 % Diff_Int2
% 0.17/0.42 thf(fact_236_Int__Diff,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.42 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 0.17/0.42 = ( inf_inf @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Int_Diff
% 0.17/0.42 thf(fact_237_Diff__Int,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.42 ( ( minus_minus @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) )
% 0.17/0.42 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( minus_minus @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Diff_Int
% 0.17/0.42 thf(fact_238_Un__Diff,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.42 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 0.17/0.42 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ C4 ) @ ( minus_minus @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Un_Diff
% 0.17/0.42 thf(fact_239_Diff__Un,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.17/0.42 ( ( minus_minus @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 0.17/0.42 = ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( minus_minus @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Diff_Un
% 0.17/0.42 thf(fact_240_lfinite_Ocases,axiom,
% 0.17/0.42 ! [A: $tType,A3: coinductive_llist @ A] :
% 0.17/0.42 ( ( coinductive_lfinite @ A @ A3 )
% 0.17/0.42 => ( ( A3
% 0.17/0.42 != ( coinductive_LNil @ A ) )
% 0.17/0.42 => ~ ! [Xs3: coinductive_llist @ A] :
% 0.17/0.42 ( ? [X3: A] :
% 0.17/0.42 ( A3
% 0.17/0.42 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 0.17/0.42 => ~ ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % lfinite.cases
% 0.17/0.42 thf(fact_241_lfinite_Osimps,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( coinductive_lfinite @ A )
% 0.17/0.42 = ( ^ [A5: coinductive_llist @ A] :
% 0.17/0.42 ( ( A5
% 0.17/0.42 = ( coinductive_LNil @ A ) )
% 0.17/0.42 | ? [Xs4: coinductive_llist @ A,X4: A] :
% 0.17/0.42 ( ( A5
% 0.17/0.42 = ( coinductive_LCons @ A @ X4 @ Xs4 ) )
% 0.17/0.42 & ( coinductive_lfinite @ A @ Xs4 ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % lfinite.simps
% 0.17/0.42 thf(fact_242_lfinite_Oinducts,axiom,
% 0.17/0.42 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.42 ( ( coinductive_lfinite @ A @ X )
% 0.17/0.42 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.42 => ( ! [Xs3: coinductive_llist @ A,X3: A] :
% 0.17/0.42 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.17/0.42 => ( ( P @ Xs3 )
% 0.17/0.42 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) )
% 0.17/0.42 => ( P @ X ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % lfinite.inducts
% 0.17/0.42 thf(fact_243_singleton__Un__iff,axiom,
% 0.17/0.42 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.42 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.17/0.42 = ( ( ( A2
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.42 & ( B2
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.42 | ( ( A2
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.42 & ( B2
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.42 | ( ( A2
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.42 & ( B2
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % singleton_Un_iff
% 0.17/0.42 thf(fact_244_Un__singleton__iff,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A,X: A] :
% 0.17/0.42 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.42 = ( ( ( A2
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.42 & ( B2
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.42 | ( ( A2
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.42 & ( B2
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.42 | ( ( A2
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.42 & ( B2
% 0.17/0.42 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % Un_singleton_iff
% 0.17/0.42 thf(fact_245_insert__is__Un,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( insert @ A )
% 0.17/0.42 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % insert_is_Un
% 0.17/0.42 thf(fact_246_Diff__triv,axiom,
% 0.17/0.42 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.17/0.42 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 0.17/0.42 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.42 => ( ( minus_minus @ ( set @ A ) @ A2 @ B2 )
% 0.17/0.42 = A2 ) ) ).
% 0.17/0.42
% 0.17/0.42 % Diff_triv
% 0.17/0.42 thf(fact_247_lfinite__rev__induct,axiom,
% 0.17/0.42 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.17/0.42 ( ( coinductive_lfinite @ A @ Xs )
% 0.17/0.42 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.42 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.17/0.42 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.17/0.42 => ( ( P @ Xs3 )
% 0.17/0.42 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 0.17/0.42 => ( P @ Xs ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % lfinite_rev_induct
% 0.17/0.42 thf(fact_248_llimit__induct,axiom,
% 0.17/0.42 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.17/0.42 ( ( P @ ( coinductive_LNil @ A ) )
% 0.17/0.42 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.17/0.42 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.17/0.42 => ( ( P @ Xs3 )
% 0.17/0.42 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) )
% 0.17/0.42 => ( ( ! [Ys2: coinductive_llist @ A] :
% 0.17/0.42 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs )
% 0.17/0.42 => ( P @ Ys2 ) )
% 0.17/0.42 => ( P @ Xs ) )
% 0.17/0.42 => ( P @ Xs ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % llimit_induct
% 0.17/0.42 thf(fact_249_sup__top__right,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.17/0.42 => ! [X: A] :
% 0.17/0.42 ( ( sup_sup @ A @ X @ ( top_top @ A ) )
% 0.17/0.42 = ( top_top @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % sup_top_right
% 0.17/0.42 thf(fact_250_sup__top__left,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.17/0.42 => ! [X: A] :
% 0.17/0.42 ( ( sup_sup @ A @ ( top_top @ A ) @ X )
% 0.17/0.42 = ( top_top @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % sup_top_left
% 0.17/0.42 thf(fact_251_sup__bot_Oright__neutral,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.17/0.42 => ! [A3: A] :
% 0.17/0.42 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 0.17/0.42 = A3 ) ) ).
% 0.17/0.42
% 0.17/0.42 % sup_bot.right_neutral
% 0.17/0.42 thf(fact_252_inf__bot__left,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.17/0.42 => ! [X: A] :
% 0.17/0.42 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 0.17/0.42 = ( bot_bot @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % inf_bot_left
% 0.17/0.42 thf(fact_253_inf__bot__right,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.17/0.42 => ! [X: A] :
% 0.17/0.42 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 0.17/0.42 = ( bot_bot @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % inf_bot_right
% 0.17/0.42 thf(fact_254_inf__eq__top__iff,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.17/0.42 => ! [X: A,Y: A] :
% 0.17/0.42 ( ( ( inf_inf @ A @ X @ Y )
% 0.17/0.42 = ( top_top @ A ) )
% 0.17/0.42 = ( ( X
% 0.17/0.42 = ( top_top @ A ) )
% 0.17/0.42 & ( Y
% 0.17/0.42 = ( top_top @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 % inf_eq_top_iff
% 0.17/0.42 thf(fact_255_inf__top_Oleft__neutral,axiom,
% 0.17/0.42 ! [A: $tType] :
% 0.17/0.42 ( ( bounde1561333602nf_top @ A @ ( type2 @ A ) )
% 0.17/0.42 => ! [A3: A] :
% 0.17/0.42 ( ( inf_inf @ A @ ( top_top @ A ) @ A3 )
% 0.17/0.42 = A3 ) ) ).
% 0.17/0.42
% 0.17/0.42 % inf_top.left_neutral
% 0.17/0.42
% 0.17/0.42 %----Type constructors (21)
% 0.17/0.42 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.17/0.42 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.17/0.42 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.17/0.42 ! [A8: $tType,A9: $tType] :
% 0.17/0.42 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.17/0.42 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.17/0.42 ! [A8: $tType,A9: $tType] :
% 0.17/0.42 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.17/0.42 => ( bounde1808546759up_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_fun___Lattices_Obounded__semilattice__inf__top,axiom,
% 0.17/0.42 ! [A8: $tType,A9: $tType] :
% 0.17/0.42 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.17/0.42 => ( bounde1561333602nf_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.17/0.42 ! [A8: $tType,A9: $tType] :
% 0.17/0.42 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.17/0.42 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.17/0.42 ! [A8: $tType,A9: $tType] :
% 0.17/0.42 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.17/0.42 => ( bounded_lattice_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_fun___Orderings_Otop,axiom,
% 0.17/0.42 ! [A8: $tType,A9: $tType] :
% 0.17/0.42 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.17/0.42 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_fun___Orderings_Obot,axiom,
% 0.17/0.42 ! [A8: $tType,A9: $tType] :
% 0.17/0.42 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 0.17/0.42 => ( bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 0.17/0.42 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_4,axiom,
% 0.17/0.42 ! [A8: $tType] : ( bounde1561333602nf_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5,axiom,
% 0.17/0.42 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6,axiom,
% 0.17/0.42 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_Set_Oset___Orderings_Otop_7,axiom,
% 0.17/0.42 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_Set_Oset___Orderings_Obot_8,axiom,
% 0.17/0.42 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_9,axiom,
% 0.17/0.42 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_10,axiom,
% 0.17/0.42 bounde1561333602nf_top @ $o @ ( type2 @ $o ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_11,axiom,
% 0.17/0.42 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12,axiom,
% 0.17/0.42 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_HOL_Obool___Orderings_Otop_13,axiom,
% 0.17/0.42 top @ $o @ ( type2 @ $o ) ).
% 0.17/0.42
% 0.17/0.42 thf(tcon_HOL_Obool___Orderings_Obot_14,axiom,
% 0.17/0.42 bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.42
% 0.17/0.42 %----Conjectures (1)
% 0.17/0.42 thf(conj_0,conjecture,
% 0.17/0.42 member @ ( coinductive_llist @ a ) @ sa @ ( lList21612149805nflsts @ a @ a2 ) ).
% 0.17/0.42
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 ------------------------
% 2.26/1.37 ---- Embedded in THF ---
% 2.26/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.26/1.37 %%% Generated on Tue Feb 24 06:09:15 EST 2026
% 2.26/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 2.26/1.37 %%% Logic specification used:
% 2.26/1.37 %%% thf(spec, logic, $$dhol).
% 2.26/1.37
% 2.26/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vlkqeUQ3AI/DTF2DTF11852.p
% 2.26/1.37 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.26/1.37 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.26/1.37 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.26/1.37 thf(ty_tf_a, type, a: $tType).
% 2.26/1.37 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_Topological__Spaces_Operfect__space, type, topolo890362671_space: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_Topological__Spaces_Ouniform__space, type, topolo47006728_space: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_Lattices_Obounded__semilattice__inf__top, type, bounde1561333602nf_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.26/1.37 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.26/1.37 thf(sy_c_Coinductive__List_Ogen__lset, type, coinductive_gen_lset: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ A)))))).
% 2.26/1.37 thf(sy_c_Coinductive__List_OlSup, type, coinductive_lSup: (!> [A:$tType]: (((set @ (coinductive_llist @ A)) > (coinductive_llist @ A))))).
% 2.26/1.37 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.26/1.37 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.26/1.37 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.26/1.37 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.26/1.37 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.26/1.37 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.26/1.37 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.26/1.37 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts, type, lList2435255213lllsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.26/1.37 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts, type, lList2236698231inlsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.26/1.37 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)))))).
% 2.26/1.37 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts, type, lList22096119349pslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.26/1.37 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts, type, lList21612149805nflsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.26/1.37 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts, type, lList21148268032oslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.26/1.37 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.26/1.37 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.26/1.37 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.26/1.37 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.26/1.37 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.26/1.37 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.26/1.37 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.26/1.37 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.26/1.37 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.26/1.37 thf(sy_c_Set_Opairwise, type, pairwise: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.26/1.37 thf(sy_c_Set_Oremove, type, remove: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.26/1.37 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.26/1.37 thf(sy_c_Topological__Spaces_Ouniform__space__class_Ototally__bounded, type, topolo406746546ounded: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.26/1.37 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.26/1.37 thf(sy_v_A, type, a2: (set @ a)).
% 2.26/1.37 thf(sy_v_l______, type, l: (coinductive_llist @ a)).
% 2.26/1.37 thf(sy_v_r, type, r: (coinductive_llist @ a)).
% 2.26/1.37 thf(sy_v_sa____, type, sa: (coinductive_llist @ a)).
% 2.26/1.37 thf(fact_0_LNil__fin_Oprems, axiom, (((member @ (coinductive_llist @ a)) @ (((coinductive_lappend @ a) @ l) @ sa)) @ ((lList21612149805nflsts @ a) @ a2))).
% 2.26/1.37 thf(fact_1_assms, axiom, (((member @ (coinductive_llist @ a)) @ r) @ ((lList2236698231inlsts @ a) @ a2))).
% 2.26/1.37 thf(fact_2_lapp__inf, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => ((((coinductive_lappend @ A) @ S) @ T) = S))))).
% 2.26/1.37 thf(fact_3_infsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.26/1.37 thf(fact_4_infT__simp, axiom, (! [A:$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)))))))).
% 2.26/1.37 thf(fact_5_inflstsI2, axiom, (! [A:$tType,A3:A,A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ A) @ A3) @ A2) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_6_inflsts__cases, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => (~ ((! [A4:A,L:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ A) @ A4) @ A2) => (S != (((coinductive_LCons @ A) @ A4) @ L)))))))))))).
% 2.26/1.37 thf(fact_7_lapp__fin__infT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_8_LNil__is__lappend__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ S) @ T)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.26/1.37 thf(fact_9_lappend__is__LNil__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ S) @ T) = (coinductive_LNil @ A)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.26/1.37 thf(fact_10_inflsts__empty, axiom, (! [A:$tType]: ((((lList21612149805nflsts @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ (coinductive_llist @ A))))))).
% 2.26/1.37 thf(fact_11_notfin__inf, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.26/1.37 thf(fact_12_notinf__fin, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.26/1.37 thf(fact_13_LNil__fin_Ohyps, axiom, (l = (coinductive_LNil @ a))).
% 2.26/1.37 thf(fact_14_alllsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ (top_top @ (set @ A))))))).
% 2.26/1.37 thf(fact_15_same__lappend__eq, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((((coinductive_lappend @ A) @ R) @ S) = (((coinductive_lappend @ A) @ R) @ T)) = (S = T)))))).
% 2.26/1.37 thf(fact_16_lapp__fin__fin__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_17_LConsE, axiom, (! [A:$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))))))).
% 2.26/1.37 thf(fact_18_inflstsI, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_19_lappT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_20_llistE, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X21:A,X22:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X21) @ X22)))))))))).
% 2.26/1.37 thf(fact_21_finT__simp, axiom, (! [A:$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)))))))).
% 2.26/1.37 thf(fact_22_fin__finite, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.26/1.37 thf(fact_23_finite__lemma, axiom, (! [A:$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))))))).
% 2.26/1.37 thf(fact_24_finsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.26/1.37 thf(fact_25_lappfin__finT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_26_alllsts_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2435255213lllsts @ A) @ A2)) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [L:(coinductive_llist @ A),A4:A]: (((A3 = (((coinductive_LCons @ A) @ A4) @ L)) => ((((member @ (coinductive_llist @ A)) @ L) @ ((lList2435255213lllsts @ A) @ A2)) => (~ ((((member @ A) @ A4) @ A2)))))))))))))).
% 2.26/1.37 thf(fact_27_alllsts_Osimps, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2435255213lllsts @ A) @ A2)) = ((A3 = (coinductive_LNil @ A)) | (? [L2:(coinductive_llist @ A),A5:A]: (((A3 = (((coinductive_LCons @ A) @ A5) @ L2)) & ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ A) @ A5) @ A2)))))))))).
% 2.26/1.37 thf(fact_28_finlsts_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2236698231inlsts @ A) @ A2)) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [L:(coinductive_llist @ A),A4:A]: (((A3 = (((coinductive_LCons @ A) @ A4) @ L)) => ((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => (~ ((((member @ A) @ A4) @ A2)))))))))))))).
% 2.26/1.37 thf(fact_29_finlsts_Osimps, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2236698231inlsts @ A) @ A2)) = ((A3 = (coinductive_LNil @ A)) | (? [L2:(coinductive_llist @ A),A5:A]: (((A3 = (((coinductive_LCons @ A) @ A5) @ L2)) & ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ A) @ A5) @ A2)))))))))).
% 2.26/1.37 thf(fact_30_lapp__all__invT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.26/1.37 thf(fact_31_finlsts__induct, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((! [L:(coinductive_llist @ A)]: (((L = (coinductive_LNil @ A)) => (P @ L)))) => ((! [A4:A,L:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L) => ((((member @ A) @ A4) @ A2) => (P @ (((coinductive_LCons @ A) @ A4) @ L))))))) => (P @ X))))))).
% 2.26/1.37 thf(fact_32_finlsts_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [L:(coinductive_llist @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L) => ((((member @ A) @ A4) @ A2) => (P @ (((coinductive_LCons @ A) @ A4) @ L))))))) => (P @ X))))))).
% 2.26/1.37 thf(fact_33_alllsts_OLNil__all, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2435255213lllsts @ A) @ A2))))).
% 2.26/1.37 thf(fact_34_alllsts_Ocoinduct, axiom, (! [A:$tType,X2:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A),A2:(set @ A)]: (((X2 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X2 @ X3) => ((X3 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A6:A]: (((X3 = (((coinductive_LCons @ A) @ A6) @ L3)) & (((X2 @ L3) | (((member @ (coinductive_llist @ A)) @ L3) @ ((lList2435255213lllsts @ A) @ A2))) & (((member @ A) @ A6) @ A2))))))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_35_finlsts_OLNil__fin, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2236698231inlsts @ A) @ A2))))).
% 2.26/1.37 thf(fact_36_alllsts_OLCons__all, axiom, (! [A:$tType,L4:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ L4) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ A) @ A3) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ L4)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_37_finlsts_OLCons__fin, axiom, (! [A:$tType,L4:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ L4) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A3) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ L4)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.26/1.37 thf(fact_38_lapp__fin__fin__lemma, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.26/1.37 thf(fact_39_inflstsE, axiom, (! [A:$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))))))))))).
% 2.26/1.37 thf(fact_40_fin__inf__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.26/1.37 thf(fact_41_alllstsE, axiom, (! [A:$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))))))).
% 2.26/1.37 thf(fact_42_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.26/1.37 thf(fact_43_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 2.26/1.37 thf(fact_44_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.26/1.37 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.26/1.37 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A2)))) = A2)))).
% 2.26/1.37 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.26/1.37 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.26/1.37 thf(fact_49_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.26/1.37 thf(fact_50_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_LCons @ A) @ Xa) @ X)) @ Ys) = (((coinductive_LCons @ A) @ Xa) @ (((coinductive_lappend @ A) @ X) @ Ys)))))).
% 2.26/1.37 thf(fact_51_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 2.26/1.37 thf(fact_52_llist_Oinject, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X212) @ X222) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X212 = Y21) & (X222 = Y22)))))).
% 2.26/1.37 thf(fact_53_UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.26/1.37 thf(fact_54_iso__tuple__UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.26/1.37 thf(fact_55_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 2.26/1.37 thf(fact_56_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.26/1.37 thf(fact_57_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.26/1.37 thf(fact_58_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.26/1.37 thf(fact_59_ex__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((? [X4:A]: ((((member @ A) @ X4) @ A2))) = (A2 != (bot_bot @ (set @ A))))))).
% 2.26/1.37 thf(fact_60_equals0I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [Y2:A]: ((~ ((((member @ A) @ Y2) @ A2))))) => (A2 = (bot_bot @ (set @ A))))))).
% 2.26/1.37 thf(fact_61_equals0D, axiom, (! [A:$tType,A2:(set @ A),A3:A]: (((A2 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A2))))))).
% 2.26/1.37 thf(fact_62_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.26/1.37 thf(fact_63_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 2.26/1.37 thf(fact_64_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.26/1.37 thf(fact_65_lappend__assoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ Zs) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_lappend @ A) @ Ys) @ Zs)))))).
% 2.26/1.37 thf(fact_66_empty__not__UNIV, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) != (top_top @ (set @ A)))))).
% 2.26/1.37 thf(fact_67_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X4:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X4) @ Xs2)))))))).
% 2.26/1.37 thf(fact_68_llist_Odistinct_I1_J, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X212) @ X222))))).
% 2.26/1.37 thf(fact_69_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.26/1.37 thf(fact_70_top__apply, axiom, (! [C2:$tType,D:$tType]: ((((top @ C2) @ (type2 @ C2)) => ((top_top @ (D > C2)) = (^ [X4:D]: ((top_top @ C2)))))))).
% 2.26/1.37 thf(fact_71_bot__apply, axiom, (! [C2:$tType,D:$tType]: ((((bot @ C2) @ (type2 @ C2)) => ((bot_bot @ (D > C2)) = (^ [X4:D]: ((bot_bot @ C2)))))))).
% 2.26/1.37 thf(fact_72_poslsts__empty, axiom, (! [A:$tType]: ((((lList21148268032oslsts @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ (coinductive_llist @ A))))))).
% 2.26/1.37 thf(fact_73_fpslsts__empty, axiom, (! [A:$tType]: ((((lList22096119349pslsts @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ (coinductive_llist @ A))))))).
% 2.26/1.37 thf(fact_74_poslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2)) & (S != (coinductive_LNil @ A))))))).
% 2.26/1.37 thf(fact_75_fpslsts__iff, axiom, (! [A:$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))))))).
% 2.26/1.37 thf(fact_76_poslsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ (top_top @ (set @ A)))) = (S != (coinductive_LNil @ A)))))).
% 2.26/1.37 thf(fact_77_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.26/1.37 thf(fact_78_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.26/1.37 thf(fact_79_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X4:A]: ((bot_bot @ B)))))))).
% 2.26/1.37 thf(fact_80_fpslsts__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList22096119349pslsts @ A) @ A2)) => (~ ((! [A4:A,Rs:(coinductive_llist @ A)]: (((R = (((coinductive_LCons @ A) @ A4) @ Rs)) => ((((member @ A) @ A4) @ A2) => (~ ((((member @ (coinductive_llist @ A)) @ Rs) @ ((lList2236698231inlsts @ A) @ A2)))))))))))))).
% 2.26/1.37 thf(fact_81_alllsts__empty, axiom, (! [A:$tType]: ((((lList2435255213lllsts @ A) @ (bot_bot @ (set @ A))) = (((insert @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (bot_bot @ (set @ (coinductive_llist @ A)))))))).
% 2.26/1.37 thf(fact_82_finlsts__empty, axiom, (! [A:$tType]: ((((lList2236698231inlsts @ A) @ (bot_bot @ (set @ A))) = (((insert @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (bot_bot @ (set @ (coinductive_llist @ A)))))))).
% 2.26/1.37 thf(fact_83_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Xs2)) & (((coindu328551480prefix @ A) @ Xs2) @ Ys))))))))).
% 2.26/1.37 thf(fact_84_finlsts__rec__LCons, axiom, (! [B:$tType,A:$tType,R:(coinductive_llist @ A),A2:(set @ A),C:B,D2:(A > ((coinductive_llist @ A) > (B > B))),A3:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((((lList21916056377ts_rec @ B) @ A) @ C) @ D2) @ (((coinductive_LCons @ A) @ A3) @ R)) = (((D2 @ A3) @ R) @ (((((lList21916056377ts_rec @ B) @ A) @ C) @ D2) @ R))))))).
% 2.26/1.37 thf(fact_85_finlsts__rec__LCons__def, axiom, (! [B:$tType,A:$tType,F:((coinductive_llist @ A) > B),C:B,D2:(A > ((coinductive_llist @ A) > (B > B))),R:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C) @ D2)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((F @ (((coinductive_LCons @ A) @ A3) @ R)) = (((D2 @ A3) @ R) @ (F @ R)))))))).
% 2.26/1.37 thf(fact_86_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A7:(set @ A)]: ((A7 = (bot_bot @ (set @ A))))))))).
% 2.26/1.37 thf(fact_87_insertCI, axiom, (! [A:$tType,A3:A,B2:(set @ A),B3:A]: ((((~ ((((member @ A) @ A3) @ B2))) => (A3 = B3)) => (((member @ A) @ A3) @ (((insert @ A) @ B3) @ B2)))))).
% 2.26/1.37 thf(fact_88_insert__iff, axiom, (! [A:$tType,A3:A,B3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B3) @ A2)) = ((A3 = B3) | (((member @ A) @ A3) @ A2)))))).
% 2.26/1.37 thf(fact_89_insert__absorb2, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A2)) = (((insert @ A) @ X) @ A2))))).
% 2.26/1.37 thf(fact_90_top1I, axiom, (! [A:$tType,X:A]: (((top_top @ (A > $o)) @ X)))).
% 2.26/1.37 thf(fact_91_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.26/1.37 thf(fact_92_insertE, axiom, (! [A:$tType,A3:A,B3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B3) @ A2)) => ((A3 != B3) => (((member @ A) @ A3) @ A2)))))).
% 2.26/1.37 thf(fact_93_insertI1, axiom, (! [A:$tType,A3:A,B2:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B2))))).
% 2.26/1.37 thf(fact_94_insertI2, axiom, (! [A:$tType,A3:A,B2:(set @ A),B3:A]: (((((member @ A) @ A3) @ B2) => (((member @ A) @ A3) @ (((insert @ A) @ B3) @ B2)))))).
% 2.26/1.37 thf(fact_95_Set_Oset__insert, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((member @ A) @ X) @ A2) => (~ ((! [B4:(set @ A)]: (((A2 = (((insert @ A) @ X) @ B4)) => (((member @ A) @ X) @ B4)))))))))).
% 2.26/1.37 thf(fact_96_insert__ident, axiom, (! [A:$tType,X:A,A2:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ A2))) => ((~ ((((member @ A) @ X) @ B2))) => (((((insert @ A) @ X) @ A2) = (((insert @ A) @ X) @ B2)) = (A2 = B2))))))).
% 2.26/1.37 thf(fact_97_insert__absorb, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((insert @ A) @ A3) @ A2) = A2))))).
% 2.26/1.37 thf(fact_98_insert__eq__iff, axiom, (! [A:$tType,A3:A,A2:(set @ A),B3:A,B2:(set @ A)]: (((~ ((((member @ A) @ A3) @ A2))) => ((~ ((((member @ A) @ B3) @ B2))) => (((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B3) @ B2)) = (((A3 = B3) => (A2 = B2)) & ((A3 != B3) => (? [C3:(set @ A)]: (((A2 = (((insert @ A) @ B3) @ C3)) & ((~ ((((member @ A) @ B3) @ C3))) & ((B2 = (((insert @ A) @ A3) @ C3)) & (~ ((((member @ A) @ A3) @ C3)))))))))))))))).
% 2.26/1.37 thf(fact_99_insert__commute, axiom, (! [A:$tType,X:A,Y:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y) @ A2)) = (((insert @ A) @ Y) @ (((insert @ A) @ X) @ A2)))))).
% 2.26/1.37 thf(fact_100_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => (? [B4:(set @ A)]: (((A2 = (((insert @ A) @ A3) @ B4)) & (~ ((((member @ A) @ A3) @ B4)))))))))).
% 2.26/1.37 thf(fact_101_singleton__inject, axiom, (! [A:$tType,A3:A,B3:A]: ((((((insert @ A) @ A3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A3 = B3))))).
% 2.26/1.37 thf(fact_102_insert__not__empty, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((insert @ A) @ A3) @ A2) != (bot_bot @ (set @ A)))))).
% 2.26/1.37 thf(fact_103_doubleton__eq__iff, axiom, (! [A:$tType,A3:A,B3:A,C:A,D2:A]: ((((((insert @ A) @ A3) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A3 = C) & (B3 = D2)) | ((A3 = D2) & (B3 = C))))))).
% 2.26/1.37 thf(fact_104_singleton__iff, axiom, (! [A:$tType,B3:A,A3:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = (B3 = A3))))).
% 2.26/1.37 thf(fact_105_singletonD, axiom, (! [A:$tType,B3:A,A3:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) => (B3 = A3))))).
% 2.26/1.37 thf(fact_106_insert__UNIV, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.26/1.37 thf(fact_107_finlsts__rec__LNil__def, axiom, (! [A:$tType,B:$tType,F:((coinductive_llist @ A) > B),C:B,D2:(A > ((coinductive_llist @ A) > (B > B)))]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C) @ D2)) => ((F @ (coinductive_LNil @ A)) = C))))).
% 2.26/1.37 thf(fact_108_finlsts__rec__LNil, axiom, (! [B:$tType,A:$tType,C:A,D2:(B > ((coinductive_llist @ B) > (A > A)))]: (((((((lList21916056377ts_rec @ A) @ B) @ C) @ D2) @ (coinductive_LNil @ B)) = C)))).
% 2.26/1.37 thf(fact_109_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 2.26/1.37 thf(fact_110_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.26/1.37 thf(fact_111_Topological__Spaces_OUNIV__not__singleton, axiom, (! [A:$tType]: ((((topolo890362671_space @ A) @ (type2 @ A)) => (! [X:A]: (((top_top @ (set @ A)) != (((insert @ A) @ X) @ (bot_bot @ (set @ A)))))))))).
% 2.26/1.37 thf(fact_112_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 2.26/1.37 thf(fact_113_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X4:A]: ((((member @ A) @ X4) @ (top_top @ (set @ A))))))))).
% 2.26/1.37 thf(fact_114_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X4:A]: ((((member @ A) @ X4) @ (bot_bot @ (set @ A))))))))).
% 2.26/1.37 thf(fact_115_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.26/1.37 thf(fact_116_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 2.26/1.37 thf(fact_117_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A7:(set @ A)]: ((A7 = (((insert @ A) @ ((the_elem @ A) @ A7)) @ (bot_bot @ (set @ A)))))))))).
% 2.26/1.37 thf(fact_118_is__singletonI_H, axiom, (! [A:$tType,A2:(set @ A)]: (((A2 != (bot_bot @ (set @ A))) => ((! [X3:A,Y2:A]: (((((member @ A) @ X3) @ A2) => ((((member @ A) @ Y2) @ A2) => (X3 = Y2))))) => ((is_singleton @ A) @ A2)))))).
% 2.26/1.37 thf(fact_119_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A7:(set @ A)]: ((? [X4:A]: ((A7 = (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 2.26/1.37 thf(fact_120_is__singletonE, axiom, (! [A:$tType,A2:(set @ A)]: ((((is_singleton @ A) @ A2) => (~ ((! [X3:A]: ((A2 != (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))))))).
% 2.26/1.37 thf(fact_121_poslsts__def, axiom, (! [A:$tType]: (((lList21148268032oslsts @ A) = (^ [A7:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A7)) @ (((insert @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (bot_bot @ (set @ (coinductive_llist @ A))))))))))).
% 2.26/1.37 thf(fact_122_fpslsts__def, axiom, (! [A:$tType]: (((lList22096119349pslsts @ A) = (^ [A7:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A7)) @ (((insert @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (bot_bot @ (set @ (coinductive_llist @ A))))))))))).
% 2.26/1.37 thf(fact_123_gen__lset__code_I2_J, axiom, (! [A:$tType,A2:(set @ A),X:A,Xs:(coinductive_llist @ A)]: (((((coinductive_gen_lset @ A) @ A2) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((coinductive_gen_lset @ A) @ (((insert @ A) @ X) @ A2)) @ Xs))))).
% 2.26/1.37 thf(fact_124_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X:A]: (((P & ((top_top @ (A > $o)) @ X)) = P)))).
% 2.26/1.37 thf(fact_125_DiffI, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ A2) => ((~ ((((member @ A) @ C) @ B2))) => (((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2))))))).
% 2.26/1.37 thf(fact_126_Diff__iff, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C) @ A2) & (~ ((((member @ A) @ C) @ B2)))))))).
% 2.26/1.37 thf(fact_127_Diff__idemp, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ B2) = (((minus_minus @ (set @ A)) @ A2) @ B2))))).
% 2.26/1.37 thf(fact_128_Diff__cancel, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ A2) = (bot_bot @ (set @ A)))))).
% 2.26/1.37 thf(fact_129_empty__Diff, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2) = (bot_bot @ (set @ A)))))).
% 2.26/1.37 thf(fact_130_Diff__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 2.26/1.37 thf(fact_131_Diff__insert0, axiom, (! [A:$tType,X:A,A2:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ A2))) => ((((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ X) @ B2)) = (((minus_minus @ (set @ A)) @ A2) @ B2)))))).
% 2.26/1.37 thf(fact_132_insert__Diff1, axiom, (! [A:$tType,X:A,B2:(set @ A),A2:(set @ A)]: (((((member @ A) @ X) @ B2) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X) @ A2)) @ B2) = (((minus_minus @ (set @ A)) @ A2) @ B2)))))).
% 2.26/1.37 thf(fact_133_Diff__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.26/1.37 thf(fact_134_insert__Diff__single, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = (((insert @ A) @ A3) @ A2))))).
% 2.26/1.37 thf(fact_135_insert__Diff__if, axiom, (! [A:$tType,X:A,B2:(set @ A),A2:(set @ A)]: ((((((member @ A) @ X) @ B2) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X) @ A2)) @ B2) = (((minus_minus @ (set @ A)) @ A2) @ B2))) & ((~ ((((member @ A) @ X) @ B2))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X) @ A2)) @ B2) = (((insert @ A) @ X) @ (((minus_minus @ (set @ A)) @ A2) @ B2)))))))).
% 2.26/1.37 thf(fact_136_DiffE, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ (((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B2)))))))).
% 2.26/1.37 thf(fact_137_DiffD1, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C) @ A2))))).
% 2.26/1.37 thf(fact_138_DiffD2, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ ((((member @ A) @ C) @ B2))))))).
% 2.26/1.37 thf(fact_139_Diff__insert, axiom, (! [A:$tType,A2:(set @ A),A3:A,B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B2)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.26/1.37 thf(fact_140_insert__Diff, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = A2))))).
% 2.26/1.37 thf(fact_141_Diff__insert2, axiom, (! [A:$tType,A2:(set @ A),A3:A,B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B2)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) @ B2))))).
% 2.26/1.37 thf(fact_142_Diff__insert__absorb, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((~ ((((member @ A) @ X) @ A2))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X) @ A2)) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = A2))))).
% 2.26/1.37 thf(fact_143_gen__lset__code_I1_J, axiom, (! [A:$tType,A2:(set @ A)]: (((((coinductive_gen_lset @ A) @ A2) @ (coinductive_LNil @ A)) = A2)))).
% 2.26/1.37 thf(fact_144_inflsts__def, axiom, (! [A:$tType]: (((lList21612149805nflsts @ A) = (^ [A7:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A7)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))))).
% 2.26/1.37 thf(fact_145_top__conj_I1_J, axiom, (! [A:$tType,X:A,P:$o]: (((((top_top @ (A > $o)) @ X) & P) = P)))).
% 2.26/1.37 thf(fact_146_remove__def, axiom, (! [A:$tType]: (((remove @ A) = (^ [X4:A,A7:(set @ A)]: ((((minus_minus @ (set @ A)) @ A7) @ (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))).
% 2.26/1.37 thf(fact_147_lSup__minus__LNil, axiom, (! [A:$tType,Y3:(set @ (coinductive_llist @ A))]: ((((coinductive_lSup @ A) @ (((minus_minus @ (set @ (coinductive_llist @ A))) @ Y3) @ (((insert @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ (bot_bot @ (set @ (coinductive_llist @ A)))))) = ((coinductive_lSup @ A) @ Y3))))).
% 2.26/1.37 thf(fact_148_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y) @ Ys))))).
% 2.26/1.37 thf(fact_149_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (coinductive_LNil @ B))))))).
% 2.26/1.37 thf(fact_150_member__remove, axiom, (! [A:$tType,X:A,Y:A,A2:(set @ A)]: (((((member @ A) @ X) @ (((remove @ A) @ Y) @ A2)) = ((((member @ A) @ X) @ A2) & (X != Y)))))).
% 2.26/1.37 thf(fact_151_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B),Y:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (((coinductive_LCons @ B) @ Y) @ Ys)) = ((X = Y) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 2.26/1.37 thf(fact_152_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.26/1.37 thf(fact_153_lSup__empty, axiom, (! [A:$tType]: ((((coinductive_lSup @ A) @ (bot_bot @ (set @ (coinductive_llist @ A)))) = (coinductive_LNil @ A))))).
% 2.26/1.37 thf(fact_154_lSup__singleton, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lSup @ A) @ (((insert @ (coinductive_llist @ A)) @ Xs) @ (bot_bot @ (set @ (coinductive_llist @ A))))) = Xs)))).
% 2.26/1.37 thf(fact_155_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs3:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs3) => (P @ Ys2)))) => (P @ Xs3)))) => (P @ Xs))))).
% 2.26/1.37 thf(fact_156_lSup__insert__LNil, axiom, (! [A:$tType,Y3:(set @ (coinductive_llist @ A))]: ((((coinductive_lSup @ A) @ (((insert @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ Y3)) = ((coinductive_lSup @ A) @ Y3))))).
% 2.26/1.37 thf(fact_157_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) = X)))).
% 2.26/1.37 thf(fact_158_totally__bounded__empty, axiom, (! [A:$tType]: ((((topolo47006728_space @ A) @ (type2 @ A)) => ((topolo406746546ounded @ A) @ (bot_bot @ (set @ A))))))).
% 2.26/1.37 thf(fact_159_pairwise__singleton, axiom, (! [A:$tType,P:(A > (A > $o)),A2:A]: ((((pairwise @ A) @ P) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.26/1.37 thf(fact_160_llast__LCons2, axiom, (! [A:$tType,X:A,Y:A,Xs:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Xs)))))).
% 2.26/1.37 thf(fact_161_pairwise__def, axiom, (! [A:$tType]: (((pairwise @ A) = (^ [R2:(A > (A > $o)),S2:(set @ A)]: ((! [X4:A]: (((((member @ A) @ X4) @ S2) => (! [Y4:A]: (((((member @ A) @ Y4) @ S2) => ((X4 != Y4) => ((R2 @ X4) @ Y4)))))))))))))).
% 2.26/1.37 thf(fact_162_pairwise__empty, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((pairwise @ A) @ P) @ (bot_bot @ (set @ A)))))).
% 2.26/1.37 thf(fact_163_pairwise__insert, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,S:(set @ A)]: (((((pairwise @ A) @ R) @ (((insert @ A) @ X) @ S)) = ((! [Y4:A]: ((((((member @ A) @ Y4) @ S) & (Y4 != X)) => (((R @ X) @ Y4) & ((R @ Y4) @ X))))) & (((pairwise @ A) @ R) @ S)))))).
% 2.26/1.37 thf(fact_164_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Ys))))))).
% 2.26/1.37 thf(fact_165_fin__Int__inf, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A2)) @ ((lList21612149805nflsts @ A) @ A2)) = (bot_bot @ (set @ (coinductive_llist @ A))))))).
% 2.26/1.37 thf(fact_166_fin__Un__inf, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A2)) @ ((lList21612149805nflsts @ A) @ A2)) = ((lList2435255213lllsts @ A) @ A2))))).
% 2.26/1.37 thf(fact_167_Int__iff, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C) @ A2) & (((member @ A) @ C) @ B2)))))).
% 2.26/1.37 thf(fact_168_IntI, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ A2) => ((((member @ A) @ C) @ B2) => (((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A2) @ B2))))))).
% 2.26/1.37 thf(fact_169_Un__iff, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C) @ A2) | (((member @ A) @ C) @ B2)))))).
% 2.26/1.37 thf(fact_170_UnCI, axiom, (! [A:$tType,C:A,B2:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C) @ B2))) => (((member @ A) @ C) @ A2)) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.26/1.37 thf(fact_171_Int__UNIV, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A2) @ B2) = (top_top @ (set @ A))) = ((A2 = (top_top @ (set @ A))) & (B2 = (top_top @ (set @ A)))))))).
% 2.26/1.37 thf(fact_172_Un__empty, axiom, (! [A:$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)))))))).
% 2.26/1.37 thf(fact_173_Int__insert__left__if0, axiom, (! [A:$tType,A3:A,C4:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ A3) @ C4))) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ B2)) @ C4) = (((inf_inf @ (set @ A)) @ B2) @ C4)))))).
% 2.26/1.37 thf(fact_174_Int__insert__left__if1, axiom, (! [A:$tType,A3:A,C4:(set @ A),B2:(set @ A)]: (((((member @ A) @ A3) @ C4) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ B2)) @ C4) = (((insert @ A) @ A3) @ (((inf_inf @ (set @ A)) @ B2) @ C4))))))).
% 2.26/1.37 thf(fact_175_insert__inter__insert, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ A2)) @ (((insert @ A) @ A3) @ B2)) = (((insert @ A) @ A3) @ (((inf_inf @ (set @ A)) @ A2) @ B2)))))).
% 2.26/1.37 thf(fact_176_Int__insert__right__if0, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ A3) @ A2))) => ((((inf_inf @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B2)) = (((inf_inf @ (set @ A)) @ A2) @ B2)))))).
% 2.26/1.37 thf(fact_177_Int__insert__right__if1, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((inf_inf @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B2)) = (((insert @ A) @ A3) @ (((inf_inf @ (set @ A)) @ A2) @ B2))))))).
% 2.26/1.37 thf(fact_178_Un__insert__left, axiom, (! [A:$tType,A3:A,B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A3) @ B2)) @ C4) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ B2) @ C4)))))).
% 2.26/1.37 thf(fact_179_Un__insert__right, axiom, (! [A:$tType,A2:(set @ A),A3:A,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B2)) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.26/1.37 thf(fact_180_Un__Diff__cancel, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.26/1.37 thf(fact_181_Un__Diff__cancel2, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) @ A2) = (((sup_sup @ (set @ A)) @ B2) @ A2))))).
% 2.26/1.37 thf(fact_182_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 2.26/1.37 thf(fact_183_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((((coinductive_lfinite @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) = ((coinductive_lfinite @ B) @ Xs))))).
% 2.26/1.37 thf(fact_184_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.26/1.37 thf(fact_185_lfinite__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & ((coinductive_lfinite @ A) @ Ys)))))).
% 2.26/1.37 thf(fact_186_insert__disjoint_I1_J, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ A2)) @ B2) = (bot_bot @ (set @ A))) = ((~ ((((member @ A) @ A3) @ B2))) & ((((inf_inf @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A)))))))).
% 2.26/1.37 thf(fact_187_insert__disjoint_I2_J, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:(set @ A)]: ((((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ A2)) @ B2)) = ((~ ((((member @ A) @ A3) @ B2))) & ((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A2) @ B2))))))).
% 2.26/1.37 thf(fact_188_disjoint__insert_I1_J, axiom, (! [A:$tType,B2:(set @ A),A3:A,A2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ B2) @ (((insert @ A) @ A3) @ A2)) = (bot_bot @ (set @ A))) = ((~ ((((member @ A) @ A3) @ B2))) & ((((inf_inf @ (set @ A)) @ B2) @ A2) = (bot_bot @ (set @ A)))))))).
% 2.26/1.37 thf(fact_189_disjoint__insert_I2_J, axiom, (! [A:$tType,A2:(set @ A),B3:A,B2:(set @ A)]: ((((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A2) @ (((insert @ A) @ B3) @ B2))) = ((~ ((((member @ A) @ B3) @ A2))) & ((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A2) @ B2))))))).
% 2.26/1.37 thf(fact_190_Diff__disjoint, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B2) @ A2)) = (bot_bot @ (set @ A)))))).
% 2.26/1.37 thf(fact_191_Int__left__commute, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ B2) @ C4)) = (((inf_inf @ (set @ A)) @ B2) @ (((inf_inf @ (set @ A)) @ A2) @ C4)))))).
% 2.26/1.37 thf(fact_192_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C4)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A2) @ C4)))))).
% 2.26/1.37 thf(fact_193_Un__Int__distrib2, axiom, (! [A:$tType,B2:(set @ A),C4:(set @ A),A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((inf_inf @ (set @ A)) @ B2) @ C4)) @ A2) = (((inf_inf @ (set @ A)) @ (((sup_sup @ (set @ A)) @ B2) @ A2)) @ (((sup_sup @ (set @ A)) @ C4) @ A2)))))).
% 2.26/1.37 thf(fact_194_Int__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) = (((inf_inf @ (set @ A)) @ A2) @ B2))))).
% 2.26/1.37 thf(fact_195_Int__Un__distrib2, axiom, (! [A:$tType,B2:(set @ A),C4:(set @ A),A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((sup_sup @ (set @ A)) @ B2) @ C4)) @ A2) = (((sup_sup @ (set @ A)) @ (((inf_inf @ (set @ A)) @ B2) @ A2)) @ (((inf_inf @ (set @ A)) @ C4) @ A2)))))).
% 2.26/1.37 thf(fact_196_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.26/1.37 thf(fact_197_Un__Int__distrib, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ B2) @ C4)) = (((inf_inf @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ (((sup_sup @ (set @ A)) @ A2) @ C4)))))).
% 2.26/1.37 thf(fact_198_Int__Un__distrib, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C4)) = (((sup_sup @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ (((inf_inf @ (set @ A)) @ A2) @ C4)))))).
% 2.26/1.37 thf(fact_199_Un__Int__crazy, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ (((inf_inf @ (set @ A)) @ B2) @ C4))) @ (((inf_inf @ (set @ A)) @ C4) @ A2)) = (((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ (((sup_sup @ (set @ A)) @ B2) @ C4))) @ (((sup_sup @ (set @ A)) @ C4) @ A2)))))).
% 2.26/1.37 thf(fact_200_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A7:(set @ A),B5:(set @ A)]: ((((inf_inf @ (set @ A)) @ B5) @ A7))))))).
% 2.26/1.37 thf(fact_201_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A7:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A7))))))).
% 2.26/1.37 thf(fact_202_Int__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ A2) = A2)))).
% 2.26/1.37 thf(fact_203_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 2.26/1.37 thf(fact_204_Int__assoc, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ C4) = (((inf_inf @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ B2) @ C4)))))).
% 2.26/1.37 thf(fact_205_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C4) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C4)))))).
% 2.26/1.37 thf(fact_206_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => (P @ X4)))) = ((! [X4:A]: (((((member @ A) @ X4) @ A2) => (P @ X4)))) & (! [X4:A]: (((((member @ A) @ X4) @ B2) => (P @ X4))))))))).
% 2.26/1.37 thf(fact_207_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) & (P @ X4)))) = ((? [X4:A]: (((((member @ A) @ X4) @ A2) & (P @ X4)))) | (? [X4:A]: (((((member @ A) @ X4) @ B2) & (P @ X4))))))))).
% 2.26/1.37 thf(fact_208_IntD2, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C) @ B2))))).
% 2.26/1.37 thf(fact_209_IntD1, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C) @ A2))))).
% 2.26/1.37 thf(fact_210_UnI2, axiom, (! [A:$tType,C:A,B2:(set @ A),A2:(set @ A)]: (((((member @ A) @ C) @ B2) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.26/1.37 thf(fact_211_UnI1, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.26/1.37 thf(fact_212_IntE, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) => (~ (((((member @ A) @ C) @ A2) => (~ ((((member @ A) @ C) @ B2)))))))))).
% 2.26/1.37 thf(fact_213_UnE, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => ((~ ((((member @ A) @ C) @ A2))) => (((member @ A) @ C) @ B2)))))).
% 2.26/1.37 thf(fact_214_Int__insert__left, axiom, (! [A:$tType,A3:A,C4:(set @ A),B2:(set @ A)]: ((((((member @ A) @ A3) @ C4) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ B2)) @ C4) = (((insert @ A) @ A3) @ (((inf_inf @ (set @ A)) @ B2) @ C4)))) & ((~ ((((member @ A) @ A3) @ C4))) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A3) @ B2)) @ C4) = (((inf_inf @ (set @ A)) @ B2) @ C4))))))).
% 2.26/1.37 thf(fact_215_Int__insert__right, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:(set @ A)]: ((((((member @ A) @ A3) @ A2) => ((((inf_inf @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B2)) = (((insert @ A) @ A3) @ (((inf_inf @ (set @ A)) @ A2) @ B2)))) & ((~ ((((member @ A) @ A3) @ A2))) => ((((inf_inf @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B2)) = (((inf_inf @ (set @ A)) @ A2) @ B2))))))).
% 2.26/1.37 thf(fact_216_Int__UNIV__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = A2)))).
% 2.26/1.37 thf(fact_217_Int__UNIV__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (top_top @ (set @ A))) @ B2) = B2)))).
% 2.26/1.37 thf(fact_218_disjoint__iff__not__equal, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A))) = (! [X4:A]: (((((member @ A) @ X4) @ A2) => (! [Y4:A]: (((((member @ A) @ Y4) @ B2) => (X4 != Y4))))))))))).
% 2.26/1.37 thf(fact_219_Int__empty__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.26/1.37 thf(fact_220_Int__empty__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (bot_bot @ (set @ A))) @ B2) = (bot_bot @ (set @ A)))))).
% 2.26/1.37 thf(fact_221_Int__emptyI, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A2) => (~ ((((member @ A) @ X3) @ B2)))))) => ((((inf_inf @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A))))))).
% 2.26/1.37 thf(fact_222_Un__UNIV__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.26/1.37 thf(fact_223_Un__UNIV__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (top_top @ (set @ A))) @ B2) = (top_top @ (set @ A)))))).
% 2.26/1.37 thf(fact_224_Un__empty__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 2.26/1.37 thf(fact_225_Un__empty__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B2) = B2)))).
% 2.26/1.37 thf(fact_226_lappend__inf, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.26/1.37 thf(fact_227_lfinite__LNil, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.26/1.37 thf(fact_228_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 2.26/1.37 thf(fact_229_lfinite__lSupD, axiom, (! [A:$tType,A2:(set @ (coinductive_llist @ A))]: ((((coinductive_lfinite @ A) @ ((coinductive_lSup @ A) @ A2)) => (! [X5:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ X5) @ A2) => ((coinductive_lfinite @ A) @ X5)))))))).
% 2.26/1.37 thf(fact_230_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ Ys) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.26/1.37 thf(fact_231_Diff__Int__distrib2, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ C4) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ C4)) @ (((inf_inf @ (set @ A)) @ B2) @ C4)))))).
% 2.26/1.37 thf(fact_232_Diff__Int__distrib, axiom, (! [A:$tType,C4:(set @ A),A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (set @ A)) @ C4) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ C4) @ A2)) @ (((inf_inf @ (set @ A)) @ C4) @ B2)))))).
% 2.26/1.37 thf(fact_233_Diff__Diff__Int, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = (((inf_inf @ (set @ A)) @ A2) @ B2))))).
% 2.26/1.37 thf(fact_234_Un__Diff__Int, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) = A2)))).
% 2.26/1.37 thf(fact_235_Diff__Int2, axiom, (! [A:$tType,A2:(set @ A),C4:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ C4)) @ (((inf_inf @ (set @ A)) @ B2) @ C4)) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ C4)) @ B2))))).
% 2.26/1.37 thf(fact_236_Int__Diff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ C4) = (((inf_inf @ (set @ A)) @ A2) @ (((minus_minus @ (set @ A)) @ B2) @ C4)))))).
% 2.26/1.37 thf(fact_237_Diff__Int, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((inf_inf @ (set @ A)) @ B2) @ C4)) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ (((minus_minus @ (set @ A)) @ A2) @ C4)))))).
% 2.26/1.37 thf(fact_238_Un__Diff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C4) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ C4)) @ (((minus_minus @ (set @ A)) @ B2) @ C4)))))).
% 2.26/1.37 thf(fact_239_Diff__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C4)) = (((inf_inf @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ (((minus_minus @ (set @ A)) @ A2) @ C4)))))).
% 2.26/1.37 thf(fact_240_lfinite_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ A3) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [Xs3:(coinductive_llist @ A)]: (((? [X3:A]: ((A3 = (((coinductive_LCons @ A) @ X3) @ Xs3)))) => (~ (((coinductive_lfinite @ A) @ Xs3))))))))))))).
% 2.26/1.37 thf(fact_241_lfinite_Osimps, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) = (^ [A5:(coinductive_llist @ A)]: (((A5 = (coinductive_LNil @ A)) | (? [Xs4:(coinductive_llist @ A),X4:A]: (((A5 = (((coinductive_LCons @ A) @ X4) @ Xs4)) & ((coinductive_lfinite @ A) @ Xs4))))))))))).
% 2.26/1.37 thf(fact_242_lfinite_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ X) => ((P @ (coinductive_LNil @ A)) => ((! [Xs3:(coinductive_llist @ A),X3:A]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_LCons @ A) @ X3) @ Xs3)))))) => (P @ X))))))).
% 2.26/1.37 thf(fact_243_singleton__Un__iff, axiom, (! [A:$tType,X:A,A2:(set @ A),B2:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((A2 = (bot_bot @ (set @ A))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (bot_bot @ (set @ A)))) | ((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.26/1.37 thf(fact_244_Un__singleton__iff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A2) @ B2) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A2 = (bot_bot @ (set @ A))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (bot_bot @ (set @ A)))) | ((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.26/1.37 thf(fact_245_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A5:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))))))))).
% 2.26/1.37 thf(fact_246_Diff__triv, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A))) => ((((minus_minus @ (set @ A)) @ A2) @ B2) = A2))))).
% 2.26/1.37 thf(fact_247_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ Xs) => ((P @ (coinductive_LNil @ A)) => ((! [X3:A,Xs3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A)))))))) => (P @ Xs))))))).
% 2.26/1.37 thf(fact_248_llimit__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((P @ (coinductive_LNil @ A)) => ((! [X3:A,Xs3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ Xs3) => (P @ (((coinductive_LCons @ A) @ X3) @ Xs3)))))) => (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs) => (P @ Ys2)))) => (P @ Xs)) => (P @ Xs))))))).
% 2.26/1.37 thf(fact_249_sup__top__right, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (top_top @ A)) = (top_top @ A)))))))).
% 2.26/1.37 thf(fact_250_sup__top__left, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (top_top @ A)) @ X) = (top_top @ A)))))))).
% 2.26/1.37 thf(fact_251_sup__bot_Oright__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ (bot_bot @ A)) = A3))))))).
% 2.26/1.37 thf(fact_252_inf__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X) = (bot_bot @ A)))))))).
% 2.26/1.37 thf(fact_253_inf__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 2.26/1.37 thf(fact_254_inf__eq__top__iff, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((inf_inf @ A) @ X) @ Y) = (top_top @ A)) = ((X = (top_top @ A)) & (Y = (top_top @ A)))))))))).
% 2.26/1.37 thf(fact_255_inf__top_Oleft__neutral, axiom, (! [A:$tType]: ((((bounde1561333602nf_top @ A) @ (type2 @ A)) => (! [A3:A]: (((((inf_inf @ A) @ (top_top @ A)) @ A3) = A3))))))).
% 2.26/1.37 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.26/1.37 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: (((bounded_lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.26/1.37 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.26/1.37 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))))))).
% 2.26/1.37 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))))))).
% 2.26/1.37 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))))))).
% 2.26/1.37 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))))))).
% 2.26/1.37 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.26/1.37 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: ((((bot @ A9) @ (type2 @ A9)) => ((bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.26/1.37 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3, axiom, (! [A8:$tType]: (((bounde1808546759up_bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.26/1.37 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_4, axiom, (! [A8:$tType]: (((bounde1561333602nf_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.26/1.37 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5, axiom, (! [A8:$tType]: (((bounded_lattice_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.26/1.37 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6, axiom, (! [A8:$tType]: (((bounded_lattice_bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.26/1.37 thf(tcon_Set_Oset___Orderings_Otop_7, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.26/1.37 thf(tcon_Set_Oset___Orderings_Obot_8, axiom, (! [A8:$tType]: (((bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.26/1.37 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_9, axiom, ((bounde1808546759up_bot @ $o) @ (type2 @ $o))).
% 2.26/1.37 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_10, axiom, ((bounde1561333602nf_top @ $o) @ (type2 @ $o))).
% 2.26/1.37 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_11, axiom, ((bounded_lattice_top @ $o) @ (type2 @ $o))).
% 2.26/1.37 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12, axiom, ((bounded_lattice_bot @ $o) @ (type2 @ $o))).
% 2.26/1.37 thf(tcon_HOL_Obool___Orderings_Otop_13, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.26/1.37 thf(tcon_HOL_Obool___Orderings_Obot_14, axiom, ((bot @ $o) @ (type2 @ $o))).
% 2.26/1.37 thf(conj_0, conjecture, (((member @ (coinductive_llist @ a)) @ sa) @ ((lList21612149805nflsts @ a) @ a2))).
% 2.26/1.37 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vlkqeUQ3AI/DTF2DTF11852.p
% 2.26/1.37 ------------------------
% 2.26/1.39 ---- Cleaned THF ---
% 2.26/1.39 thf(ty_t_Coinductive__List_Ollist,type,
% 2.26/1.39 coinductive_llist: $tType > $tType ).
% 2.26/1.39
% 2.26/1.39 thf(ty_t_Set_Oset,type,
% 2.26/1.39 set: $tType > $tType ).
% 2.26/1.39
% 2.26/1.39 thf(ty_t_itself,type,
% 2.26/1.39 itself: $tType > $tType ).
% 2.26/1.39
% 2.26/1.39 thf(ty_tf_a,type,
% 2.26/1.39 a: $tType ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.26/1.39 bounded_lattice:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_HOL_Otype,type,
% 2.26/1.39 type:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Orderings_Obot,type,
% 2.26/1.39 bot:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Orderings_Otop,type,
% 2.26/1.39 top:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 2.26/1.39 bounded_lattice_bot:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 2.26/1.39 bounded_lattice_top:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Topological__Spaces_Operfect__space,type,
% 2.26/1.39 topolo890362671_space:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Topological__Spaces_Ouniform__space,type,
% 2.26/1.39 topolo47006728_space:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Lattices_Obounded__semilattice__inf__top,type,
% 2.26/1.39 bounde1561333602nf_top:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 2.26/1.39 bounde1808546759up_bot:
% 2.26/1.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.26/1.39 coindu328551480prefix:
% 2.26/1.39 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_Ogen__lset,type,
% 2.26/1.39 coinductive_gen_lset:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_OlSup,type,
% 2.26/1.39 coinductive_lSup:
% 2.26/1.39 !>[A: $tType] : ( ( set @ ( coinductive_llist @ A ) ) > ( coinductive_llist @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_Olappend,type,
% 2.26/1.39 coinductive_lappend:
% 2.26/1.39 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_Olfinite,type,
% 2.26/1.39 coinductive_lfinite:
% 2.26/1.39 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_Ollast,type,
% 2.26/1.39 coinductive_llast:
% 2.26/1.39 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.26/1.39 coinductive_LCons:
% 2.26/1.39 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.26/1.39 coinductive_LNil:
% 2.26/1.39 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.26/1.39 coindu1478340336prefix:
% 2.26/1.39 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.26/1.39 minus_minus:
% 2.26/1.39 !>[A: $tType] : ( A > A > A ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 2.26/1.39 lList2435255213lllsts:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 2.26/1.39 lList2236698231inlsts:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 2.26/1.39 lList21916056377ts_rec:
% 2.26/1.39 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 2.26/1.39 lList22096119349pslsts:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 2.26/1.39 lList21612149805nflsts:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 2.26/1.39 lList21148268032oslsts:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.26/1.39 inf_inf:
% 2.26/1.39 !>[A: $tType] : ( A > A > A ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.26/1.39 sup_sup:
% 2.26/1.39 !>[A: $tType] : ( A > A > A ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.26/1.39 bot_bot:
% 2.26/1.39 !>[A: $tType] : A ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.26/1.39 top_top:
% 2.26/1.39 !>[A: $tType] : A ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Pure_Otype,type,
% 2.26/1.39 type2:
% 2.26/1.39 !>[A: $tType] : ( itself @ A ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Set_OCollect,type,
% 2.26/1.39 collect:
% 2.26/1.39 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Set_Oinsert,type,
% 2.26/1.39 insert:
% 2.26/1.39 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Set_Ois__empty,type,
% 2.26/1.39 is_empty:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Set_Ois__singleton,type,
% 2.26/1.39 is_singleton:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Set_Opairwise,type,
% 2.26/1.39 pairwise:
% 2.26/1.39 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Set_Oremove,type,
% 2.26/1.39 remove:
% 2.26/1.39 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Set_Othe__elem,type,
% 2.26/1.39 the_elem:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_Topological__Spaces_Ouniform__space__class_Ototally__bounded,type,
% 2.26/1.39 topolo406746546ounded:
% 2.26/1.39 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_c_member,type,
% 2.26/1.39 member:
% 2.26/1.39 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(sy_v_A,type,
% 2.26/1.39 a2: set @ a ).
% 2.26/1.39
% 2.26/1.39 thf(sy_v_l______,type,
% 2.26/1.39 l: coinductive_llist @ a ).
% 2.26/1.39
% 2.26/1.39 thf(sy_v_r,type,
% 2.26/1.39 r: coinductive_llist @ a ).
% 2.26/1.39
% 2.26/1.39 thf(sy_v_sa____,type,
% 2.26/1.39 sa: coinductive_llist @ a ).
% 2.26/1.39
% 2.26/1.39 thf(fact_0_LNil__fin_Oprems,axiom,
% 2.26/1.39 member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ l @ sa ) @ ( lList21612149805nflsts @ a @ a2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_1_assms,axiom,
% 2.26/1.39 member @ ( coinductive_llist @ a ) @ r @ ( lList2236698231inlsts @ a @ a2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_2_lapp__inf,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 => ( ( coinductive_lappend @ A @ S @ T )
% 2.26/1.39 = S ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_3_infsubsetall,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_4_infT__simp,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_5_inflstsI2,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A,T: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_6_inflsts__cases,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 => ~ ! [A4: A,L: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 => ( ( member @ A @ A4 @ A2 )
% 2.26/1.39 => ( S
% 2.26/1.39 != ( coinductive_LCons @ A @ A4 @ L ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_7_lapp__fin__infT,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_8_LNil__is__lappend__conv,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.26/1.39 ( ( ( coinductive_LNil @ A )
% 2.26/1.39 = ( coinductive_lappend @ A @ S @ T ) )
% 2.26/1.39 = ( ( S
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 & ( T
% 2.26/1.39 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_9_lappend__is__LNil__conv,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.26/1.39 ( ( ( coinductive_lappend @ A @ S @ T )
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 = ( ( S
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 & ( T
% 2.26/1.39 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_10_inflsts__empty,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( lList21612149805nflsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_11_notfin__inf,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A] :
% 2.26/1.39 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.26/1.39 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_12_notinf__fin,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A] :
% 2.26/1.39 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.26/1.39 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_13_LNil__fin_Ohyps,axiom,
% 2.26/1.39 ( l
% 2.26/1.39 = ( coinductive_LNil @ a ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_14_alllsts__UNIV,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_15_same__lappend__eq,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( ( coinductive_lappend @ A @ R @ S )
% 2.26/1.39 = ( coinductive_lappend @ A @ R @ T ) )
% 2.26/1.39 = ( S = T ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_16_lapp__fin__fin__iff,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_17_LConsE,axiom,
% 2.26/1.39 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 = ( ( member @ A @ X @ A2 )
% 2.26/1.39 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_18_inflstsI,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_19_lappT,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_20_llistE,axiom,
% 2.26/1.39 ! [A: $tType,Y: coinductive_llist @ A] :
% 2.26/1.39 ( ( Y
% 2.26/1.39 != ( coinductive_LNil @ A ) )
% 2.26/1.39 => ~ ! [X21: A,X22: coinductive_llist @ A] :
% 2.26/1.39 ( Y
% 2.26/1.39 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_21_finT__simp,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_22_fin__finite,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_23_finite__lemma,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_24_finsubsetall,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_25_lappfin__finT,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_26_alllsts_Ocases,axiom,
% 2.26/1.39 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ( ( A3
% 2.26/1.39 != ( coinductive_LNil @ A ) )
% 2.26/1.39 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 2.26/1.39 ( ( A3
% 2.26/1.39 = ( coinductive_LCons @ A @ A4 @ L ) )
% 2.26/1.39 => ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ~ ( member @ A @ A4 @ A2 ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_27_alllsts_Osimps,axiom,
% 2.26/1.39 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 = ( ( A3
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 | ? [L2: coinductive_llist @ A,A5: A] :
% 2.26/1.39 ( ( A3
% 2.26/1.39 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.26/1.39 & ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_28_finlsts_Ocases,axiom,
% 2.26/1.39 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( A3
% 2.26/1.39 != ( coinductive_LNil @ A ) )
% 2.26/1.39 => ~ ! [L: coinductive_llist @ A,A4: A] :
% 2.26/1.39 ( ( A3
% 2.26/1.39 = ( coinductive_LCons @ A @ A4 @ L ) )
% 2.26/1.39 => ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ~ ( member @ A @ A4 @ A2 ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_29_finlsts_Osimps,axiom,
% 2.26/1.39 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 = ( ( A3
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 | ? [L2: coinductive_llist @ A,A5: A] :
% 2.26/1.39 ( ( A3
% 2.26/1.39 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.26/1.39 & ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 & ( member @ A @ A5 @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_30_lapp__all__invT,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_31_finlsts__induct,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ! [L: coinductive_llist @ A] :
% 2.26/1.39 ( ( L
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 => ( P @ L ) )
% 2.26/1.39 => ( ! [A4: A,L: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( P @ L )
% 2.26/1.39 => ( ( member @ A @ A4 @ A2 )
% 2.26/1.39 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 2.26/1.39 => ( P @ X ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_32_finlsts_Oinducts,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.26/1.39 => ( ! [L: coinductive_llist @ A,A4: A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( P @ L )
% 2.26/1.39 => ( ( member @ A @ A4 @ A2 )
% 2.26/1.39 => ( P @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) )
% 2.26/1.39 => ( P @ X ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_33_alllsts_OLNil__all,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_34_alllsts_Ocoinduct,axiom,
% 2.26/1.39 ! [A: $tType,X2: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( X2 @ X )
% 2.26/1.39 => ( ! [X3: coinductive_llist @ A] :
% 2.26/1.39 ( ( X2 @ X3 )
% 2.26/1.39 => ( ( X3
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 | ? [L3: coinductive_llist @ A,A6: A] :
% 2.26/1.39 ( ( X3
% 2.26/1.39 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 2.26/1.39 & ( ( X2 @ L3 )
% 2.26/1.39 | ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.26/1.39 & ( member @ A @ A6 @ A2 ) ) ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_35_finlsts_OLNil__fin,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_36_alllsts_OLCons__all,axiom,
% 2.26/1.39 ! [A: $tType,L4: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ( ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L4 ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_37_finlsts_OLCons__fin,axiom,
% 2.26/1.39 ! [A: $tType,L4: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L4 ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_38_lapp__fin__fin__lemma,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_39_inflstsE,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_40_fin__inf__cases,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A] :
% 2.26/1.39 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_41_alllstsE,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_42_lappend__code_I1_J,axiom,
% 2.26/1.39 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.26/1.39 = Ys ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_43_lappend__LNil2,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.26/1.39 = Xs ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_44_LNil__eq__lappend__iff,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( ( coinductive_LNil @ A )
% 2.26/1.39 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.26/1.39 = ( ( Xs
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 & ( Ys
% 2.26/1.39 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_45_mem__Collect__eq,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,P: A > $o] :
% 2.26/1.39 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.26/1.39 = ( P @ A3 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_46_Collect__mem__eq,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( collect @ A
% 2.26/1.39 @ ^ [X4: A] : ( member @ A @ X4 @ A2 ) )
% 2.26/1.39 = A2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_47_Collect__cong,axiom,
% 2.26/1.39 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.26/1.39 ( ! [X3: A] :
% 2.26/1.39 ( ( P @ X3 )
% 2.26/1.39 = ( Q @ X3 ) )
% 2.26/1.39 => ( ( collect @ A @ P )
% 2.26/1.39 = ( collect @ A @ Q ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_48_ext,axiom,
% 2.26/1.39 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.26/1.39 ( ! [X3: A] :
% 2.26/1.39 ( ( F @ X3 )
% 2.26/1.39 = ( G @ X3 ) )
% 2.26/1.39 => ( F = G ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_49_lappend__eq__LNil__iff,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 = ( ( Xs
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 & ( Ys
% 2.26/1.39 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_50_lappend__code_I2_J,axiom,
% 2.26/1.39 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 2.26/1.39 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_51_lappend__snocL1__conv__LCons2,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.26/1.39 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_52_llist_Oinject,axiom,
% 2.26/1.39 ! [A: $tType,X212: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.26/1.39 ( ( ( coinductive_LCons @ A @ X212 @ X222 )
% 2.26/1.39 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.26/1.39 = ( ( X212 = Y21 )
% 2.26/1.39 & ( X222 = Y22 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_53_UNIV__I,axiom,
% 2.26/1.39 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_54_iso__tuple__UNIV__I,axiom,
% 2.26/1.39 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_55_empty__iff,axiom,
% 2.26/1.39 ! [A: $tType,C: A] :
% 2.26/1.39 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_56_all__not__in__conv,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( ! [X4: A] :
% 2.26/1.39 ~ ( member @ A @ X4 @ A2 ) )
% 2.26/1.39 = ( A2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_57_empty__Collect__eq,axiom,
% 2.26/1.39 ! [A: $tType,P: A > $o] :
% 2.26/1.39 ( ( ( bot_bot @ ( set @ A ) )
% 2.26/1.39 = ( collect @ A @ P ) )
% 2.26/1.39 = ( ! [X4: A] :
% 2.26/1.39 ~ ( P @ X4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_58_Collect__empty__eq,axiom,
% 2.26/1.39 ! [A: $tType,P: A > $o] :
% 2.26/1.39 ( ( ( collect @ A @ P )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( ! [X4: A] :
% 2.26/1.39 ~ ( P @ X4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_59_ex__in__conv,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( ? [X4: A] : ( member @ A @ X4 @ A2 ) )
% 2.26/1.39 = ( A2
% 2.26/1.39 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_60_equals0I,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ! [Y2: A] :
% 2.26/1.39 ~ ( member @ A @ Y2 @ A2 )
% 2.26/1.39 => ( A2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_61_equals0D,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,A3: A] :
% 2.26/1.39 ( ( A2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_62_emptyE,axiom,
% 2.26/1.39 ! [A: $tType,A3: A] :
% 2.26/1.39 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_63_UNIV__witness,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_64_UNIV__eq__I,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 2.26/1.39 => ( ( top_top @ ( set @ A ) )
% 2.26/1.39 = A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_65_lappend__assoc,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 2.26/1.39 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_66_empty__not__UNIV,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bot_bot @ ( set @ A ) )
% 2.26/1.39 != ( top_top @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_67_neq__LNil__conv,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ( Xs
% 2.26/1.39 != ( coinductive_LNil @ A ) )
% 2.26/1.39 = ( ? [X4: A,Xs2: coinductive_llist @ A] :
% 2.26/1.39 ( Xs
% 2.26/1.39 = ( coinductive_LCons @ A @ X4 @ Xs2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_68_llist_Odistinct_I1_J,axiom,
% 2.26/1.39 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_LNil @ A )
% 2.26/1.39 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_69_lappend__LNil__LNil,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.26/1.39 = ( coinductive_LNil @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_70_top__apply,axiom,
% 2.26/1.39 ! [C2: $tType,D: $tType] :
% 2.26/1.39 ( ( top @ C2 @ ( type2 @ C2 ) )
% 2.26/1.39 => ( ( top_top @ ( D > C2 ) )
% 2.26/1.39 = ( ^ [X4: D] : ( top_top @ C2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_71_bot__apply,axiom,
% 2.26/1.39 ! [C2: $tType,D: $tType] :
% 2.26/1.39 ( ( bot @ C2 @ ( type2 @ C2 ) )
% 2.26/1.39 => ( ( bot_bot @ ( D > C2 ) )
% 2.26/1.39 = ( ^ [X4: D] : ( bot_bot @ C2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_72_poslsts__empty,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( lList21148268032oslsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_73_fpslsts__empty,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( lList22096119349pslsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_74_poslsts__iff,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.26/1.39 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.26/1.39 & ( S
% 2.26/1.39 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_75_fpslsts__iff,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.26/1.39 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 & ( S
% 2.26/1.39 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_76_poslsts__UNIV,axiom,
% 2.26/1.39 ! [A: $tType,S: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.26/1.39 = ( S
% 2.26/1.39 != ( coinductive_LNil @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_77_bot__set__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bot_bot @ ( set @ A ) )
% 2.26/1.39 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_78_top__set__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( top_top @ ( set @ A ) )
% 2.26/1.39 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_79_bot__fun__def,axiom,
% 2.26/1.39 ! [B: $tType,A: $tType] :
% 2.26/1.39 ( ( bot @ B @ ( type2 @ B ) )
% 2.26/1.39 => ( ( bot_bot @ ( A > B ) )
% 2.26/1.39 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_80_fpslsts__cases,axiom,
% 2.26/1.39 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.26/1.39 => ~ ! [A4: A,Rs: coinductive_llist @ A] :
% 2.26/1.39 ( ( R
% 2.26/1.39 = ( coinductive_LCons @ A @ A4 @ Rs ) )
% 2.26/1.39 => ( ( member @ A @ A4 @ A2 )
% 2.26/1.39 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_81_alllsts__empty,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( lList2435255213lllsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_82_finlsts__empty,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( lList2236698231inlsts @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_83_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.26/1.39 = ( ( Xs
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 | ? [Xs2: coinductive_llist @ A] :
% 2.26/1.39 ( ( Xs
% 2.26/1.39 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 2.26/1.39 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_84_finlsts__rec__LCons,axiom,
% 2.26/1.39 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C: B,D2: A > ( coinductive_llist @ A ) > B > B,A3: A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( lList21916056377ts_rec @ B @ A @ C @ D2 @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.26/1.39 = ( D2 @ A3 @ R @ ( lList21916056377ts_rec @ B @ A @ C @ D2 @ R ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_85_finlsts__rec__LCons__def,axiom,
% 2.26/1.39 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.26/1.39 ( ( F
% 2.26/1.39 = ( lList21916056377ts_rec @ B @ A @ C @ D2 ) )
% 2.26/1.39 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.26/1.39 => ( ( F @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.26/1.39 = ( D2 @ A3 @ R @ ( F @ R ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_86_Set_Ois__empty__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( is_empty @ A )
% 2.26/1.39 = ( ^ [A7: set @ A] :
% 2.26/1.39 ( A7
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_87_insertCI,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,B2: set @ A,B3: A] :
% 2.26/1.39 ( ( ~ ( member @ A @ A3 @ B2 )
% 2.26/1.39 => ( A3 = B3 ) )
% 2.26/1.39 => ( member @ A @ A3 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_88_insert__iff,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,B3: A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ A3 @ ( insert @ A @ B3 @ A2 ) )
% 2.26/1.39 = ( ( A3 = B3 )
% 2.26/1.39 | ( member @ A @ A3 @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_89_insert__absorb2,axiom,
% 2.26/1.39 ! [A: $tType,X: A,A2: set @ A] :
% 2.26/1.39 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 2.26/1.39 = ( insert @ A @ X @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_90_top1I,axiom,
% 2.26/1.39 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_91_singletonI,axiom,
% 2.26/1.39 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_92_insertE,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,B3: A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ A3 @ ( insert @ A @ B3 @ A2 ) )
% 2.26/1.39 => ( ( A3 != B3 )
% 2.26/1.39 => ( member @ A @ A3 @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_93_insertI1,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,B2: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_94_insertI2,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,B2: set @ A,B3: A] :
% 2.26/1.39 ( ( member @ A @ A3 @ B2 )
% 2.26/1.39 => ( member @ A @ A3 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_95_Set_Oset__insert,axiom,
% 2.26/1.39 ! [A: $tType,X: A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ X @ A2 )
% 2.26/1.39 => ~ ! [B4: set @ A] :
% 2.26/1.39 ( ( A2
% 2.26/1.39 = ( insert @ A @ X @ B4 ) )
% 2.26/1.39 => ( member @ A @ X @ B4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_96_insert__ident,axiom,
% 2.26/1.39 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ~ ( member @ A @ X @ A2 )
% 2.26/1.39 => ( ~ ( member @ A @ X @ B2 )
% 2.26/1.39 => ( ( ( insert @ A @ X @ A2 )
% 2.26/1.39 = ( insert @ A @ X @ B2 ) )
% 2.26/1.39 = ( A2 = B2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_97_insert__absorb,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( ( insert @ A @ A3 @ A2 )
% 2.26/1.39 = A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_98_insert__eq__iff,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A,B3: A,B2: set @ A] :
% 2.26/1.39 ( ~ ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( ~ ( member @ A @ B3 @ B2 )
% 2.26/1.39 => ( ( ( insert @ A @ A3 @ A2 )
% 2.26/1.39 = ( insert @ A @ B3 @ B2 ) )
% 2.26/1.39 = ( ( ( A3 = B3 )
% 2.26/1.39 => ( A2 = B2 ) )
% 2.26/1.39 & ( ( A3 != B3 )
% 2.26/1.39 => ? [C3: set @ A] :
% 2.26/1.39 ( ( A2
% 2.26/1.39 = ( insert @ A @ B3 @ C3 ) )
% 2.26/1.39 & ~ ( member @ A @ B3 @ C3 )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( insert @ A @ A3 @ C3 ) )
% 2.26/1.39 & ~ ( member @ A @ A3 @ C3 ) ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_99_insert__commute,axiom,
% 2.26/1.39 ! [A: $tType,X: A,Y: A,A2: set @ A] :
% 2.26/1.39 ( ( insert @ A @ X @ ( insert @ A @ Y @ A2 ) )
% 2.26/1.39 = ( insert @ A @ Y @ ( insert @ A @ X @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_100_mk__disjoint__insert,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ? [B4: set @ A] :
% 2.26/1.39 ( ( A2
% 2.26/1.39 = ( insert @ A @ A3 @ B4 ) )
% 2.26/1.39 & ~ ( member @ A @ A3 @ B4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_101_singleton__inject,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,B3: A] :
% 2.26/1.39 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 => ( A3 = B3 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_102_insert__not__empty,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A] :
% 2.26/1.39 ( ( insert @ A @ A3 @ A2 )
% 2.26/1.39 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_103_doubleton__eq__iff,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,B3: A,C: A,D2: A] :
% 2.26/1.39 ( ( ( insert @ A @ A3 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 = ( insert @ A @ C @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.26/1.39 = ( ( ( A3 = C )
% 2.26/1.39 & ( B3 = D2 ) )
% 2.26/1.39 | ( ( A3 = D2 )
% 2.26/1.39 & ( B3 = C ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_104_singleton__iff,axiom,
% 2.26/1.39 ! [A: $tType,B3: A,A3: A] :
% 2.26/1.39 ( ( member @ A @ B3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 = ( B3 = A3 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_105_singletonD,axiom,
% 2.26/1.39 ! [A: $tType,B3: A,A3: A] :
% 2.26/1.39 ( ( member @ A @ B3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 => ( B3 = A3 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_106_insert__UNIV,axiom,
% 2.26/1.39 ! [A: $tType,X: A] :
% 2.26/1.39 ( ( insert @ A @ X @ ( top_top @ ( set @ A ) ) )
% 2.26/1.39 = ( top_top @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_107_finlsts__rec__LNil__def,axiom,
% 2.26/1.39 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 2.26/1.39 ( ( F
% 2.26/1.39 = ( lList21916056377ts_rec @ B @ A @ C @ D2 ) )
% 2.26/1.39 => ( ( F @ ( coinductive_LNil @ A ) )
% 2.26/1.39 = C ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_108_finlsts__rec__LNil,axiom,
% 2.26/1.39 ! [B: $tType,A: $tType,C: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 2.26/1.39 ( ( lList21916056377ts_rec @ A @ B @ C @ D2 @ ( coinductive_LNil @ B ) )
% 2.26/1.39 = C ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_109_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.26/1.39 = ( Xs
% 2.26/1.39 = ( coinductive_LNil @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_110_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_111_Topological__Spaces_OUNIV__not__singleton,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( topolo890362671_space @ A @ ( type2 @ A ) )
% 2.26/1.39 => ! [X: A] :
% 2.26/1.39 ( ( top_top @ ( set @ A ) )
% 2.26/1.39 != ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_112_the__elem__eq,axiom,
% 2.26/1.39 ! [A: $tType,X: A] :
% 2.26/1.39 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 = X ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_113_top__empty__eq,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( top_top @ ( A > $o ) )
% 2.26/1.39 = ( ^ [X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_114_bot__empty__eq,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bot_bot @ ( A > $o ) )
% 2.26/1.39 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_115_Collect__empty__eq__bot,axiom,
% 2.26/1.39 ! [A: $tType,P: A > $o] :
% 2.26/1.39 ( ( ( collect @ A @ P )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( P
% 2.26/1.39 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_116_is__singletonI,axiom,
% 2.26/1.39 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_117_is__singleton__the__elem,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( is_singleton @ A )
% 2.26/1.39 = ( ^ [A7: set @ A] :
% 2.26/1.39 ( A7
% 2.26/1.39 = ( insert @ A @ ( the_elem @ A @ A7 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_118_is__singletonI_H,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( A2
% 2.26/1.39 != ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 => ( ! [X3: A,Y2: A] :
% 2.26/1.39 ( ( member @ A @ X3 @ A2 )
% 2.26/1.39 => ( ( member @ A @ Y2 @ A2 )
% 2.26/1.39 => ( X3 = Y2 ) ) )
% 2.26/1.39 => ( is_singleton @ A @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_119_is__singleton__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( is_singleton @ A )
% 2.26/1.39 = ( ^ [A7: set @ A] :
% 2.26/1.39 ? [X4: A] :
% 2.26/1.39 ( A7
% 2.26/1.39 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_120_is__singletonE,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( is_singleton @ A @ A2 )
% 2.26/1.39 => ~ ! [X3: A] :
% 2.26/1.39 ( A2
% 2.26/1.39 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_121_poslsts__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( lList21148268032oslsts @ A )
% 2.26/1.39 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A7 ) @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_122_fpslsts__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( lList22096119349pslsts @ A )
% 2.26/1.39 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A7 ) @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_123_gen__lset__code_I2_J,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,X: A,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_gen_lset @ A @ A2 @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.26/1.39 = ( coinductive_gen_lset @ A @ ( insert @ A @ X @ A2 ) @ Xs ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_124_top__conj_I2_J,axiom,
% 2.26/1.39 ! [A: $tType,P: $o,X: A] :
% 2.26/1.39 ( ( P
% 2.26/1.39 & ( top_top @ ( A > $o ) @ X ) )
% 2.26/1.39 = P ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_125_DiffI,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ A2 )
% 2.26/1.39 => ( ~ ( member @ A @ C @ B2 )
% 2.26/1.39 => ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_126_Diff__iff,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = ( ( member @ A @ C @ A2 )
% 2.26/1.39 & ~ ( member @ A @ C @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_127_Diff__idemp,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_128_Diff__cancel,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ A2 @ A2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_129_empty__Diff,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_130_Diff__empty,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = A2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_131_Diff__insert0,axiom,
% 2.26/1.39 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ~ ( member @ A @ X @ A2 )
% 2.26/1.39 => ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X @ B2 ) )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_132_insert__Diff1,axiom,
% 2.26/1.39 ! [A: $tType,X: A,B2: set @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ X @ B2 )
% 2.26/1.39 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B2 )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_133_Diff__UNIV,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_134_insert__Diff__single,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A] :
% 2.26/1.39 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.26/1.39 = ( insert @ A @ A3 @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_135_insert__Diff__if,axiom,
% 2.26/1.39 ! [A: $tType,X: A,B2: set @ A,A2: set @ A] :
% 2.26/1.39 ( ( ( member @ A @ X @ B2 )
% 2.26/1.39 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B2 )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) )
% 2.26/1.39 & ( ~ ( member @ A @ X @ B2 )
% 2.26/1.39 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B2 )
% 2.26/1.39 = ( insert @ A @ X @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_136_DiffE,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 => ~ ( ( member @ A @ C @ A2 )
% 2.26/1.39 => ( member @ A @ C @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_137_DiffD1,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 => ( member @ A @ C @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_138_DiffD2,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 => ~ ( member @ A @ C @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_139_Diff__insert,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,A3: A,B2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_140_insert__Diff,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.26/1.39 = A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_141_Diff__insert2,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,A3: A,B2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_142_Diff__insert__absorb,axiom,
% 2.26/1.39 ! [A: $tType,X: A,A2: set @ A] :
% 2.26/1.39 ( ~ ( member @ A @ X @ A2 )
% 2.26/1.39 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 = A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_143_gen__lset__code_I1_J,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( coinductive_gen_lset @ A @ A2 @ ( coinductive_LNil @ A ) )
% 2.26/1.39 = A2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_144_inflsts__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( lList21612149805nflsts @ A )
% 2.26/1.39 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A7 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_145_top__conj_I1_J,axiom,
% 2.26/1.39 ! [A: $tType,X: A,P: $o] :
% 2.26/1.39 ( ( ( top_top @ ( A > $o ) @ X )
% 2.26/1.39 & P )
% 2.26/1.39 = P ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_146_remove__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( remove @ A )
% 2.26/1.39 = ( ^ [X4: A,A7: set @ A] : ( minus_minus @ ( set @ A ) @ A7 @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_147_lSup__minus__LNil,axiom,
% 2.26/1.39 ! [A: $tType,Y3: set @ ( coinductive_llist @ A )] :
% 2.26/1.39 ( ( coinductive_lSup @ A @ ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ Y3 @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ) )
% 2.26/1.39 = ( coinductive_lSup @ A @ Y3 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_148_lstrict__prefix__code_I2_J,axiom,
% 2.26/1.39 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_149_lstrict__prefix__code_I3_J,axiom,
% 2.26/1.39 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.26/1.39 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_150_member__remove,axiom,
% 2.26/1.39 ! [A: $tType,X: A,Y: A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ X @ ( remove @ A @ Y @ A2 ) )
% 2.26/1.39 = ( ( member @ A @ X @ A2 )
% 2.26/1.39 & ( X != Y ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_151_lstrict__prefix__code_I4_J,axiom,
% 2.26/1.39 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 2.26/1.39 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 2.26/1.39 = ( ( X = Y )
% 2.26/1.39 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_152_lstrict__prefix__code_I1_J,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_153_lSup__empty,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( coinductive_lSup @ A @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) )
% 2.26/1.39 = ( coinductive_LNil @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_154_lSup__singleton,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lSup @ A @ ( insert @ ( coinductive_llist @ A ) @ Xs @ ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) )
% 2.26/1.39 = Xs ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_155_llist__less__induct,axiom,
% 2.26/1.39 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ! [Xs3: coinductive_llist @ A] :
% 2.26/1.39 ( ! [Ys2: coinductive_llist @ A] :
% 2.26/1.39 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 2.26/1.39 => ( P @ Ys2 ) )
% 2.26/1.39 => ( P @ Xs3 ) )
% 2.26/1.39 => ( P @ Xs ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_156_lSup__insert__LNil,axiom,
% 2.26/1.39 ! [A: $tType,Y3: set @ ( coinductive_llist @ A )] :
% 2.26/1.39 ( ( coinductive_lSup @ A @ ( insert @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ Y3 ) )
% 2.26/1.39 = ( coinductive_lSup @ A @ Y3 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_157_llast__singleton,axiom,
% 2.26/1.39 ! [A: $tType,X: A] :
% 2.26/1.39 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 2.26/1.39 = X ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_158_totally__bounded__empty,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( topolo47006728_space @ A @ ( type2 @ A ) )
% 2.26/1.39 => ( topolo406746546ounded @ A @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_159_pairwise__singleton,axiom,
% 2.26/1.39 ! [A: $tType,P: A > A > $o,A2: A] : ( pairwise @ A @ P @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_160_llast__LCons2,axiom,
% 2.26/1.39 ! [A: $tType,X: A,Y: A,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 2.26/1.39 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_161_pairwise__def,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( pairwise @ A )
% 2.26/1.39 = ( ^ [R2: A > A > $o,S2: set @ A] :
% 2.26/1.39 ! [X4: A] :
% 2.26/1.39 ( ( member @ A @ X4 @ S2 )
% 2.26/1.39 => ! [Y4: A] :
% 2.26/1.39 ( ( member @ A @ Y4 @ S2 )
% 2.26/1.39 => ( ( X4 != Y4 )
% 2.26/1.39 => ( R2 @ X4 @ Y4 ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_162_pairwise__empty,axiom,
% 2.26/1.39 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_163_pairwise__insert,axiom,
% 2.26/1.39 ! [A: $tType,R: A > A > $o,X: A,S: set @ A] :
% 2.26/1.39 ( ( pairwise @ A @ R @ ( insert @ A @ X @ S ) )
% 2.26/1.39 = ( ! [Y4: A] :
% 2.26/1.39 ( ( ( member @ A @ Y4 @ S )
% 2.26/1.39 & ( Y4 != X ) )
% 2.26/1.39 => ( ( R @ X @ Y4 )
% 2.26/1.39 & ( R @ Y4 @ X ) ) )
% 2.26/1.39 & ( pairwise @ A @ R @ S ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_164_llast__lappend__LCons,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ Xs )
% 2.26/1.39 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 2.26/1.39 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_165_fin__Int__inf,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 = ( bot_bot @ ( set @ ( coinductive_llist @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_166_fin__Un__inf,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.26/1.39 = ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_167_Int__iff,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = ( ( member @ A @ C @ A2 )
% 2.26/1.39 & ( member @ A @ C @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_168_IntI,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ A2 )
% 2.26/1.39 => ( ( member @ A @ C @ B2 )
% 2.26/1.39 => ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_169_Un__iff,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = ( ( member @ A @ C @ A2 )
% 2.26/1.39 | ( member @ A @ C @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_170_UnCI,axiom,
% 2.26/1.39 ! [A: $tType,C: A,B2: set @ A,A2: set @ A] :
% 2.26/1.39 ( ( ~ ( member @ A @ C @ B2 )
% 2.26/1.39 => ( member @ A @ C @ A2 ) )
% 2.26/1.39 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_171_Int__UNIV,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 2.26/1.39 = ( top_top @ ( set @ A ) ) )
% 2.26/1.39 = ( ( A2
% 2.26/1.39 = ( top_top @ ( set @ A ) ) )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_172_Un__empty,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( ( A2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_173_Int__insert__left__if0,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,C4: set @ A,B2: set @ A] :
% 2.26/1.39 ( ~ ( member @ A @ A3 @ C4 )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_174_Int__insert__left__if1,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,C4: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ A3 @ C4 )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 2.26/1.39 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_175_insert__inter__insert,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A2 ) @ ( insert @ A @ A3 @ B2 ) )
% 2.26/1.39 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_176_Int__insert__right__if0,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ~ ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_177_Int__insert__right__if1,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 2.26/1.39 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_178_Un__insert__left,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 2.26/1.39 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_179_Un__insert__right,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,A3: A,B2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 2.26/1.39 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_180_Un__Diff__cancel,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_181_Un__Diff__cancel2,axiom,
% 2.26/1.39 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) @ A2 )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ B2 @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_182_lfinite__LCons,axiom,
% 2.26/1.39 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.26/1.39 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_183_lfinite__code_I2_J,axiom,
% 2.26/1.39 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.26/1.39 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 2.26/1.39 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_184_lfinite__code_I1_J,axiom,
% 2.26/1.39 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_185_lfinite__lappend,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.26/1.39 = ( ( coinductive_lfinite @ A @ Xs )
% 2.26/1.39 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_186_insert__disjoint_I1_J,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A2 ) @ B2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( ~ ( member @ A @ A3 @ B2 )
% 2.26/1.39 & ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_187_insert__disjoint_I2_J,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( bot_bot @ ( set @ A ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ A2 ) @ B2 ) )
% 2.26/1.39 = ( ~ ( member @ A @ A3 @ B2 )
% 2.26/1.39 & ( ( bot_bot @ ( set @ A ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_188_disjoint__insert_I1_J,axiom,
% 2.26/1.39 ! [A: $tType,B2: set @ A,A3: A,A2: set @ A] :
% 2.26/1.39 ( ( ( inf_inf @ ( set @ A ) @ B2 @ ( insert @ A @ A3 @ A2 ) )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( ~ ( member @ A @ A3 @ B2 )
% 2.26/1.39 & ( ( inf_inf @ ( set @ A ) @ B2 @ A2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_189_disjoint__insert_I2_J,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B3: A,B2: set @ A] :
% 2.26/1.39 ( ( ( bot_bot @ ( set @ A ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ B2 ) ) )
% 2.26/1.39 = ( ~ ( member @ A @ B3 @ A2 )
% 2.26/1.39 & ( ( bot_bot @ ( set @ A ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_190_Diff__disjoint,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ A2 ) )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_191_Int__left__commute,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ B2 @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_192_Un__left__commute,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_193_Un__Int__distrib2,axiom,
% 2.26/1.39 ! [A: $tType,B2: set @ A,C4: set @ A,A2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) @ A2 )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ B2 @ A2 ) @ ( sup_sup @ ( set @ A ) @ C4 @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_194_Int__left__absorb,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_195_Int__Un__distrib2,axiom,
% 2.26/1.39 ! [A: $tType,B2: set @ A,C4: set @ A,A2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) @ A2 )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B2 @ A2 ) @ ( inf_inf @ ( set @ A ) @ C4 @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_196_Un__left__absorb,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_197_Un__Int__distrib,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_198_Int__Un__distrib,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_199_Un__Int__crazy,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) @ ( inf_inf @ ( set @ A ) @ C4 @ A2 ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) @ ( sup_sup @ ( set @ A ) @ C4 @ A2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_200_Int__commute,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) )
% 2.26/1.39 = ( ^ [A7: set @ A,B5: set @ A] : ( inf_inf @ ( set @ A ) @ B5 @ A7 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_201_Un__commute,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) )
% 2.26/1.39 = ( ^ [A7: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A7 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_202_Int__absorb,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ A2 @ A2 )
% 2.26/1.39 = A2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_203_Un__absorb,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 2.26/1.39 = A2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_204_Int__assoc,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_205_Un__assoc,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_206_ball__Un,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 2.26/1.39 ( ( ! [X4: A] :
% 2.26/1.39 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 => ( P @ X4 ) ) )
% 2.26/1.39 = ( ! [X4: A] :
% 2.26/1.39 ( ( member @ A @ X4 @ A2 )
% 2.26/1.39 => ( P @ X4 ) )
% 2.26/1.39 & ! [X4: A] :
% 2.26/1.39 ( ( member @ A @ X4 @ B2 )
% 2.26/1.39 => ( P @ X4 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_207_bex__Un,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 2.26/1.39 ( ( ? [X4: A] :
% 2.26/1.39 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 & ( P @ X4 ) ) )
% 2.26/1.39 = ( ? [X4: A] :
% 2.26/1.39 ( ( member @ A @ X4 @ A2 )
% 2.26/1.39 & ( P @ X4 ) )
% 2.26/1.39 | ? [X4: A] :
% 2.26/1.39 ( ( member @ A @ X4 @ B2 )
% 2.26/1.39 & ( P @ X4 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_208_IntD2,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 => ( member @ A @ C @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_209_IntD1,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 => ( member @ A @ C @ A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_210_UnI2,axiom,
% 2.26/1.39 ! [A: $tType,C: A,B2: set @ A,A2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ B2 )
% 2.26/1.39 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_211_UnI1,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ A2 )
% 2.26/1.39 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_212_IntE,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 => ~ ( ( member @ A @ C @ A2 )
% 2.26/1.39 => ~ ( member @ A @ C @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_213_UnE,axiom,
% 2.26/1.39 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 => ( ~ ( member @ A @ C @ A2 )
% 2.26/1.39 => ( member @ A @ C @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_214_Int__insert__left,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,C4: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( member @ A @ A3 @ C4 )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 2.26/1.39 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) )
% 2.26/1.39 & ( ~ ( member @ A @ A3 @ C4 )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_215_Int__insert__right,axiom,
% 2.26/1.39 ! [A: $tType,A3: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 2.26/1.39 = ( insert @ A @ A3 @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) )
% 2.26/1.39 & ( ~ ( member @ A @ A3 @ A2 )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_216_Int__UNIV__right,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 2.26/1.39 = A2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_217_Int__UNIV__left,axiom,
% 2.26/1.39 ! [A: $tType,B2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 2.26/1.39 = B2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_218_disjoint__iff__not__equal,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( ! [X4: A] :
% 2.26/1.39 ( ( member @ A @ X4 @ A2 )
% 2.26/1.39 => ! [Y4: A] :
% 2.26/1.39 ( ( member @ A @ Y4 @ B2 )
% 2.26/1.39 => ( X4 != Y4 ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_219_Int__empty__right,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_220_Int__empty__left,axiom,
% 2.26/1.39 ! [A: $tType,B2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_221_Int__emptyI,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ! [X3: A] :
% 2.26/1.39 ( ( member @ A @ X3 @ A2 )
% 2.26/1.39 => ~ ( member @ A @ X3 @ B2 ) )
% 2.26/1.39 => ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_222_Un__UNIV__right,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 2.26/1.39 = ( top_top @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_223_Un__UNIV__left,axiom,
% 2.26/1.39 ! [A: $tType,B2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B2 )
% 2.26/1.39 = ( top_top @ ( set @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_224_Un__empty__right,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = A2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_225_Un__empty__left,axiom,
% 2.26/1.39 ! [A: $tType,B2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 2.26/1.39 = B2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_226_lappend__inf,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.26/1.39 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.26/1.39 = Xs ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_227_lfinite__LNil,axiom,
% 2.26/1.39 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_228_lfinite__LConsI,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ Xs )
% 2.26/1.39 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_229_lfinite__lSupD,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ ( coinductive_llist @ A )] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ ( coinductive_lSup @ A @ A2 ) )
% 2.26/1.39 => ! [X5: coinductive_llist @ A] :
% 2.26/1.39 ( ( member @ ( coinductive_llist @ A ) @ X5 @ A2 )
% 2.26/1.39 => ( coinductive_lfinite @ A @ X5 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_230_lstrict__prefix__lfinite1,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.26/1.39 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 2.26/1.39 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_231_Diff__Int__distrib2,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_232_Diff__Int__distrib,axiom,
% 2.26/1.39 ! [A: $tType,C4: set @ A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( inf_inf @ ( set @ A ) @ C4 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ C4 @ A2 ) @ ( inf_inf @ ( set @ A ) @ C4 @ B2 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_233_Diff__Diff__Int,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_234_Un__Diff__Int,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = A2 ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_235_Diff__Int2,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,C4: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) )
% 2.26/1.39 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ C4 ) @ B2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_236_Int__Diff,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ A2 @ ( minus_minus @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_237_Diff__Int,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ A2 @ ( inf_inf @ ( set @ A ) @ B2 @ C4 ) )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( minus_minus @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_238_Un__Diff,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ C4 ) @ ( minus_minus @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_239_Diff__Un,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.26/1.39 ( ( minus_minus @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 2.26/1.39 = ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( minus_minus @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_240_lfinite_Ocases,axiom,
% 2.26/1.39 ! [A: $tType,A3: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ A3 )
% 2.26/1.39 => ( ( A3
% 2.26/1.39 != ( coinductive_LNil @ A ) )
% 2.26/1.39 => ~ ! [Xs3: coinductive_llist @ A] :
% 2.26/1.39 ( ? [X3: A] :
% 2.26/1.39 ( A3
% 2.26/1.39 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 2.26/1.39 => ~ ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_241_lfinite_Osimps,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( coinductive_lfinite @ A )
% 2.26/1.39 = ( ^ [A5: coinductive_llist @ A] :
% 2.26/1.39 ( ( A5
% 2.26/1.39 = ( coinductive_LNil @ A ) )
% 2.26/1.39 | ? [Xs4: coinductive_llist @ A,X4: A] :
% 2.26/1.39 ( ( A5
% 2.26/1.39 = ( coinductive_LCons @ A @ X4 @ Xs4 ) )
% 2.26/1.39 & ( coinductive_lfinite @ A @ Xs4 ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_242_lfinite_Oinducts,axiom,
% 2.26/1.39 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ X )
% 2.26/1.39 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.26/1.39 => ( ! [Xs3: coinductive_llist @ A,X3: A] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.26/1.39 => ( ( P @ Xs3 )
% 2.26/1.39 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) )
% 2.26/1.39 => ( P @ X ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_243_singleton__Un__iff,axiom,
% 2.26/1.39 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.26/1.39 = ( ( ( A2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.26/1.39 | ( ( A2
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 | ( ( A2
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_244_Un__singleton__iff,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A,X: A] :
% 2.26/1.39 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 = ( ( ( A2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.26/1.39 | ( ( A2
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 | ( ( A2
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.26/1.39 & ( B2
% 2.26/1.39 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_245_insert__is__Un,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( insert @ A )
% 2.26/1.39 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_246_Diff__triv,axiom,
% 2.26/1.39 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.26/1.39 ( ( ( inf_inf @ ( set @ A ) @ A2 @ B2 )
% 2.26/1.39 = ( bot_bot @ ( set @ A ) ) )
% 2.26/1.39 => ( ( minus_minus @ ( set @ A ) @ A2 @ B2 )
% 2.26/1.39 = A2 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_247_lfinite__rev__induct,axiom,
% 2.26/1.39 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ Xs )
% 2.26/1.39 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.26/1.39 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.26/1.39 => ( ( P @ Xs3 )
% 2.26/1.39 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 2.26/1.39 => ( P @ Xs ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_248_llimit__induct,axiom,
% 2.26/1.39 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.26/1.39 ( ( P @ ( coinductive_LNil @ A ) )
% 2.26/1.39 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 2.26/1.39 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.26/1.39 => ( ( P @ Xs3 )
% 2.26/1.39 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) )
% 2.26/1.39 => ( ( ! [Ys2: coinductive_llist @ A] :
% 2.26/1.39 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs )
% 2.26/1.39 => ( P @ Ys2 ) )
% 2.26/1.39 => ( P @ Xs ) )
% 2.26/1.39 => ( P @ Xs ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_249_sup__top__right,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.26/1.39 => ! [X: A] :
% 2.26/1.39 ( ( sup_sup @ A @ X @ ( top_top @ A ) )
% 2.26/1.39 = ( top_top @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_250_sup__top__left,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.26/1.39 => ! [X: A] :
% 2.26/1.39 ( ( sup_sup @ A @ ( top_top @ A ) @ X )
% 2.26/1.39 = ( top_top @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_251_sup__bot_Oright__neutral,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.26/1.39 => ! [A3: A] :
% 2.26/1.39 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 2.26/1.39 = A3 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_252_inf__bot__left,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.26/1.39 => ! [X: A] :
% 2.26/1.39 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 2.26/1.39 = ( bot_bot @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_253_inf__bot__right,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.26/1.39 => ! [X: A] :
% 2.26/1.39 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 2.26/1.39 = ( bot_bot @ A ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_254_inf__eq__top__iff,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.26/1.39 => ! [X: A,Y: A] :
% 2.26/1.39 ( ( ( inf_inf @ A @ X @ Y )
% 2.26/1.39 = ( top_top @ A ) )
% 2.26/1.39 = ( ( X
% 2.26/1.39 = ( top_top @ A ) )
% 2.26/1.39 & ( Y
% 2.26/1.39 = ( top_top @ A ) ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(fact_255_inf__top_Oleft__neutral,axiom,
% 2.26/1.39 ! [A: $tType] :
% 2.26/1.39 ( ( bounde1561333602nf_top @ A @ ( type2 @ A ) )
% 2.26/1.39 => ! [A3: A] :
% 2.26/1.39 ( ( inf_inf @ A @ ( top_top @ A ) @ A3 )
% 2.26/1.39 = A3 ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.26/1.39 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.26/1.39 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.26/1.39 ! [A8: $tType,A9: $tType] :
% 2.26/1.39 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.26/1.39 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 2.26/1.39 ! [A8: $tType,A9: $tType] :
% 2.26/1.39 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.26/1.39 => ( bounde1808546759up_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_fun___Lattices_Obounded__semilattice__inf__top,axiom,
% 2.26/1.39 ! [A8: $tType,A9: $tType] :
% 2.26/1.39 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.26/1.39 => ( bounde1561333602nf_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 2.26/1.39 ! [A8: $tType,A9: $tType] :
% 2.26/1.39 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.26/1.39 => ( bounded_lattice_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 2.26/1.39 ! [A8: $tType,A9: $tType] :
% 2.26/1.39 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.26/1.39 => ( bounded_lattice_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_fun___Orderings_Otop,axiom,
% 2.26/1.39 ! [A8: $tType,A9: $tType] :
% 2.26/1.39 ( ( top @ A9 @ ( type2 @ A9 ) )
% 2.26/1.39 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_fun___Orderings_Obot,axiom,
% 2.26/1.39 ! [A8: $tType,A9: $tType] :
% 2.26/1.39 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 2.26/1.39 => ( bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 2.26/1.39 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_4,axiom,
% 2.26/1.39 ! [A8: $tType] : ( bounde1561333602nf_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5,axiom,
% 2.26/1.39 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6,axiom,
% 2.26/1.39 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_Set_Oset___Orderings_Otop_7,axiom,
% 2.26/1.39 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_Set_Oset___Orderings_Obot_8,axiom,
% 2.26/1.39 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_9,axiom,
% 2.26/1.39 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_10,axiom,
% 2.26/1.39 bounde1561333602nf_top @ $o @ ( type2 @ $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_11,axiom,
% 2.26/1.39 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12,axiom,
% 2.26/1.39 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_HOL_Obool___Orderings_Otop_13,axiom,
% 2.26/1.39 top @ $o @ ( type2 @ $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(tcon_HOL_Obool___Orderings_Obot_14,axiom,
% 2.26/1.39 bot @ $o @ ( type2 @ $o ) ).
% 2.26/1.39
% 2.26/1.39 thf(conj_0,conjecture,
% 2.26/1.39 member @ ( coinductive_llist @ a ) @ sa @ ( lList21612149805nflsts @ a @ a2 ) ).
% 2.26/1.39 ------------------------
% 2.50/1.42 % (12074)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_11852 for (2999ds/27Mi)
% 2.50/1.42 % (12072)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/183Mi)
% 2.50/1.42 % (12073)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_11852 for (2999ds/4Mi)
% 2.50/1.42 % (12075)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/2Mi)
% 2.50/1.42 % (12078)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/18Mi)
% 2.50/1.42 % (12075)Instruction limit reached!
% 2.50/1.42 % (12075)------------------------------
% 2.50/1.42 % (12075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.42 % (12075)Termination reason: Unknown
% 2.50/1.42 % (12075)Termination phase: shuffling
% 2.50/1.42
% 2.50/1.42 % (12075)Memory used [KB]: 1279
% 2.50/1.42 % (12075)Time elapsed: 0.002 s
% 2.50/1.42 % (12075)Instructions burned: 2 (million)
% 2.50/1.42 % (12075)------------------------------
% 2.50/1.42 % (12075)------------------------------
% 2.50/1.42 % (12073)Instruction limit reached!
% 2.50/1.42 % (12073)------------------------------
% 2.50/1.42 % (12073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.42 % (12073)Termination reason: Unknown
% 2.50/1.42 % (12073)Termination phase: shuffling
% 2.50/1.42
% 2.50/1.42 % (12073)Memory used [KB]: 1407
% 2.50/1.42 % (12073)Time elapsed: 0.003 s
% 2.50/1.42 % (12073)Instructions burned: 6 (million)
% 2.50/1.42 % (12073)------------------------------
% 2.50/1.42 % (12073)------------------------------
% 2.50/1.43 % (12076)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_11852 for (2999ds/2Mi)
% 2.50/1.43 % (12076)Instruction limit reached!
% 2.50/1.43 % (12076)------------------------------
% 2.50/1.43 % (12076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.43 % (12076)Termination reason: Unknown
% 2.50/1.43 % (12076)Termination phase: shuffling
% 2.50/1.43
% 2.50/1.43 % (12076)Memory used [KB]: 1279
% 2.50/1.43 % (12076)Time elapsed: 0.003 s
% 2.50/1.43 % (12076)Instructions burned: 2 (million)
% 2.50/1.43 % (12076)------------------------------
% 2.50/1.43 % (12076)------------------------------
% 2.50/1.43 % (12078)Instruction limit reached!
% 2.50/1.43 % (12078)------------------------------
% 2.50/1.43 % (12078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.43 % (12078)Termination reason: Unknown
% 2.50/1.43 % (12078)Termination phase: Property scanning
% 2.50/1.43
% 2.50/1.43 % (12078)Memory used [KB]: 1535
% 2.50/1.43 % (12078)Time elapsed: 0.008 s
% 2.50/1.43 % (12078)Instructions burned: 21 (million)
% 2.50/1.43 % (12078)------------------------------
% 2.50/1.43 % (12078)------------------------------
% 2.50/1.43 % (12077)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_11852 for (2999ds/275Mi)
% 2.50/1.43 % (12074)Instruction limit reached!
% 2.50/1.43 % (12074)------------------------------
% 2.50/1.43 % (12074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.43 % (12074)Termination reason: Unknown
% 2.50/1.43 % (12074)Termination phase: Property scanning
% 2.50/1.43
% 2.50/1.43 % (12074)Memory used [KB]: 1535
% 2.50/1.43 % (12074)Time elapsed: 0.010 s
% 2.50/1.43 % (12074)Instructions burned: 29 (million)
% 2.50/1.43 % (12074)------------------------------
% 2.50/1.43 % (12074)------------------------------
% 2.50/1.43 % (12079)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/3Mi)
% 2.50/1.43 % (12080)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_11852 for (2999ds/37Mi)
% 2.50/1.43 % (12079)Instruction limit reached!
% 2.50/1.43 % (12079)------------------------------
% 2.50/1.43 % (12079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.43 % (12079)Termination reason: Unknown
% 2.50/1.43 % (12079)Termination phase: shuffling
% 2.50/1.43
% 2.50/1.43 % (12079)Memory used [KB]: 1279
% 2.50/1.43 % (12079)Time elapsed: 0.002 s
% 2.50/1.43 % (12079)Instructions burned: 3 (million)
% 2.50/1.43 % (12079)------------------------------
% 2.50/1.43 % (12079)------------------------------
% 2.50/1.44 % (12083)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_11852 for (2999ds/3Mi)
% 2.50/1.44 % (12083)Instruction limit reached!
% 2.50/1.44 % (12083)------------------------------
% 2.50/1.44 % (12083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.44 % (12083)Termination reason: Unknown
% 2.50/1.44 % (12083)Termination phase: shuffling
% 2.50/1.44
% 2.50/1.44 % (12083)Memory used [KB]: 1279
% 2.50/1.44 % (12083)Time elapsed: 0.002 s
% 2.50/1.44 % (12083)Instructions burned: 3 (million)
% 2.50/1.44 % (12083)------------------------------
% 2.50/1.44 % (12083)------------------------------
% 2.50/1.44 % (12087)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_11852 for (2999ds/1041Mi)
% 2.50/1.44 % (12089)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/7Mi)
% 2.50/1.45 % (12080)Instruction limit reached!
% 2.50/1.45 % (12080)------------------------------
% 2.50/1.45 % (12080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.45 % (12080)Termination reason: Unknown
% 2.50/1.45 % (12080)Termination phase: Property scanning
% 2.50/1.45
% 2.50/1.45 % (12080)Memory used [KB]: 2046
% 2.50/1.45 % (12080)Time elapsed: 0.012 s
% 2.50/1.45 % (12080)Instructions burned: 40 (million)
% 2.50/1.45 % (12080)------------------------------
% 2.50/1.45 % (12080)------------------------------
% 2.50/1.45 % (12081)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_11852 for (2999ds/15Mi)
% 2.50/1.45 % (12089)Instruction limit reached!
% 2.50/1.45 % (12089)------------------------------
% 2.50/1.45 % (12089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.45 % (12089)Termination reason: Unknown
% 2.50/1.45 % (12089)Termination phase: shuffling
% 2.50/1.45
% 2.50/1.45 % (12089)Memory used [KB]: 1407
% 2.50/1.45 % (12089)Time elapsed: 0.004 s
% 2.50/1.45 % (12089)Instructions burned: 8 (million)
% 2.50/1.45 % (12089)------------------------------
% 2.50/1.45 % (12089)------------------------------
% 2.50/1.45 % (12096)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/16Mi)
% 2.50/1.45 % (12101)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/3Mi)
% 2.50/1.45 % (12081)Instruction limit reached!
% 2.50/1.45 % (12081)------------------------------
% 2.50/1.45 % (12081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.45 % (12081)Termination reason: Unknown
% 2.50/1.45 % (12081)Termination phase: shuffling
% 2.50/1.45
% 2.50/1.45 % (12081)Memory used [KB]: 1535
% 2.50/1.45 % (12081)Time elapsed: 0.010 s
% 2.50/1.45 % (12081)Instructions burned: 16 (million)
% 2.50/1.45 % (12081)------------------------------
% 2.50/1.45 % (12081)------------------------------
% 2.50/1.46 % (12101)Instruction limit reached!
% 2.50/1.46 % (12101)------------------------------
% 2.50/1.46 % (12101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.46 % (12101)Termination reason: Unknown
% 2.50/1.46 % (12101)Termination phase: shuffling
% 2.50/1.46
% 2.50/1.46 % (12101)Memory used [KB]: 1279
% 2.50/1.46 % (12101)Time elapsed: 0.002 s
% 2.50/1.46 % (12101)Instructions burned: 3 (million)
% 2.50/1.46 % (12101)------------------------------
% 2.50/1.46 % (12101)------------------------------
% 2.50/1.46 % (12096)Instruction limit reached!
% 2.50/1.46 % (12096)------------------------------
% 2.50/1.46 % (12096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.46 % (12096)Termination reason: Unknown
% 2.50/1.46 % (12096)Termination phase: Property scanning
% 2.50/1.46
% 2.50/1.46 % (12096)Memory used [KB]: 1535
% 2.50/1.46 % (12096)Time elapsed: 0.007 s
% 2.50/1.46 % (12096)Instructions burned: 18 (million)
% 2.50/1.46 % (12096)------------------------------
% 2.50/1.46 % (12096)------------------------------
% 2.50/1.46 % (12102)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/3Mi)
% 2.50/1.46 % (12102)Instruction limit reached!
% 2.50/1.46 % (12102)------------------------------
% 2.50/1.46 % (12102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.46 % (12102)Termination reason: Unknown
% 2.50/1.46 % (12102)Termination phase: shuffling
% 2.50/1.46
% 2.50/1.46 % (12102)Memory used [KB]: 1279
% 2.50/1.46 % (12102)Time elapsed: 0.002 s
% 2.50/1.46 % (12102)Instructions burned: 3 (million)
% 2.50/1.46 % (12102)------------------------------
% 2.50/1.46 % (12102)------------------------------
% 2.50/1.46 % (12105)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/3Mi)
% 2.50/1.47 % (12103)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/7Mi)
% 2.50/1.47 % (12106)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/4Mi)
% 2.50/1.47 % (12105)Instruction limit reached!
% 2.50/1.47 % (12105)------------------------------
% 2.50/1.47 % (12105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.47 % (12105)Termination reason: Unknown
% 2.50/1.47 % (12105)Termination phase: shuffling
% 2.50/1.47
% 2.50/1.47 % (12105)Memory used [KB]: 1279
% 2.50/1.47 % (12105)Time elapsed: 0.002 s
% 2.50/1.47 % (12105)Instructions burned: 4 (million)
% 2.50/1.47 % (12105)------------------------------
% 2.50/1.47 % (12105)------------------------------
% 2.50/1.47 % (12107)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/18Mi)
% 2.50/1.47 % (12106)Instruction limit reached!
% 2.50/1.47 % (12106)------------------------------
% 2.50/1.47 % (12106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.47 % (12106)Termination reason: Unknown
% 2.50/1.47 % (12106)Termination phase: shuffling
% 2.50/1.47
% 2.50/1.47 % (12106)Memory used [KB]: 1407
% 2.50/1.47 % (12106)Time elapsed: 0.003 s
% 2.50/1.47 % (12106)Instructions burned: 6 (million)
% 2.50/1.47 % (12106)------------------------------
% 2.50/1.47 % (12106)------------------------------
% 2.50/1.47 % (12103)Instruction limit reached!
% 2.50/1.47 % (12103)------------------------------
% 2.50/1.47 % (12103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.47 % (12103)Termination reason: Unknown
% 2.50/1.47 % (12103)Termination phase: shuffling
% 2.50/1.47
% 2.50/1.47 % (12103)Memory used [KB]: 1407
% 2.50/1.47 % (12103)Time elapsed: 0.004 s
% 2.50/1.47 % (12103)Instructions burned: 9 (million)
% 2.50/1.47 % (12103)------------------------------
% 2.50/1.47 % (12103)------------------------------
% 2.50/1.47 % (12077)Refutation not found, incomplete strategy
% 2.50/1.47 % (12077)------------------------------
% 2.50/1.47 % (12077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.47 % (12077)Termination reason: Refutation not found, incomplete strategy
% 2.50/1.47
% 2.50/1.47
% 2.50/1.47 % (12077)Memory used [KB]: 6652
% 2.50/1.47 % (12077)Time elapsed: 0.042 s
% 2.50/1.47 % (12077)Instructions burned: 88 (million)
% 2.50/1.47 % (12077)------------------------------
% 2.50/1.47 % (12077)------------------------------
% 2.50/1.47 % (12107)Instruction limit reached!
% 2.50/1.47 % (12107)------------------------------
% 2.50/1.47 % (12107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.47 % (12107)Termination reason: Unknown
% 2.50/1.47 % (12107)Termination phase: Property scanning
% 2.50/1.47
% 2.50/1.47 % (12107)Memory used [KB]: 1535
% 2.50/1.47 % (12107)Time elapsed: 0.007 s
% 2.50/1.47 % (12107)Instructions burned: 19 (million)
% 2.50/1.47 % (12107)------------------------------
% 2.50/1.47 % (12107)------------------------------
% 2.50/1.48 % (12112)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/710Mi)
% 2.50/1.48 % (12114)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/6Mi)
% 2.50/1.48 % (12115)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/902Mi)
% 2.50/1.48 % (12072)Instruction limit reached!
% 2.50/1.48 % (12072)------------------------------
% 2.50/1.48 % (12072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.48 % (12072)Termination reason: Unknown
% 2.50/1.48 % (12072)Termination phase: Saturation
% 2.50/1.48
% 2.50/1.48 % (12072)Memory used [KB]: 7036
% 2.50/1.48 % (12072)Time elapsed: 0.056 s
% 2.50/1.48 % (12072)Instructions burned: 183 (million)
% 2.50/1.48 % (12072)------------------------------
% 2.50/1.48 % (12072)------------------------------
% 2.50/1.48 % (12114)Instruction limit reached!
% 2.50/1.48 % (12114)------------------------------
% 2.50/1.48 % (12114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.48 % (12114)Termination reason: Unknown
% 2.50/1.48 % (12114)Termination phase: shuffling
% 2.50/1.48
% 2.50/1.48 % (12114)Memory used [KB]: 1407
% 2.50/1.48 % (12114)Time elapsed: 0.003 s
% 2.50/1.48 % (12114)Instructions burned: 6 (million)
% 2.50/1.48 % (12114)------------------------------
% 2.50/1.48 % (12114)------------------------------
% 2.50/1.48 % (12119)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/21Mi)
% 2.50/1.48 % (12120)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/5Mi)
% 2.50/1.48 % (12120)Instruction limit reached!
% 2.50/1.48 % (12120)------------------------------
% 2.50/1.48 % (12120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.48 % (12120)Termination reason: Unknown
% 2.50/1.48 % (12120)Termination phase: shuffling
% 2.50/1.48
% 2.50/1.48 % (12120)Memory used [KB]: 1407
% 2.50/1.48 % (12120)Time elapsed: 0.003 s
% 2.50/1.48 % (12120)Instructions burned: 6 (million)
% 2.50/1.48 % (12120)------------------------------
% 2.50/1.48 % (12120)------------------------------
% 2.50/1.49 % (12124)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/6Mi)
% 2.50/1.49 % (12126)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/377Mi)
% 2.50/1.49 % (12124)Instruction limit reached!
% 2.50/1.49 % (12124)------------------------------
% 2.50/1.49 % (12124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.49 % (12124)Termination reason: Unknown
% 2.50/1.49 % (12124)Termination phase: shuffling
% 2.50/1.49
% 2.50/1.49 % (12124)Memory used [KB]: 1407
% 2.50/1.49 % (12124)Time elapsed: 0.003 s
% 2.50/1.49 % (12124)Instructions burned: 6 (million)
% 2.50/1.49 % (12124)------------------------------
% 2.50/1.49 % (12124)------------------------------
% 2.50/1.49 % (12119)Instruction limit reached!
% 2.50/1.49 % (12119)------------------------------
% 2.50/1.49 % (12119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.49 % (12119)Termination reason: Unknown
% 2.50/1.49 % (12119)Termination phase: shuffling
% 2.50/1.49
% 2.50/1.49 % (12119)Memory used [KB]: 1663
% 2.50/1.49 % (12119)Time elapsed: 0.009 s
% 2.50/1.49 % (12119)Instructions burned: 23 (million)
% 2.50/1.49 % (12119)------------------------------
% 2.50/1.49 % (12119)------------------------------
% 2.50/1.49 % (12129)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/779Mi)
% 2.50/1.50 % (12131)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/879Mi)
% 2.50/1.51 % (12130)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_11852 for (2999ds/19Mi)
% 2.50/1.52 % (12130)Instruction limit reached!
% 2.50/1.52 % (12130)------------------------------
% 2.50/1.52 % (12130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.52 % (12130)Termination reason: Unknown
% 2.50/1.52 % (12130)Termination phase: shuffling
% 2.50/1.52
% 2.50/1.52 % (12130)Memory used [KB]: 1663
% 2.50/1.52 % (12130)Time elapsed: 0.012 s
% 2.50/1.52 % (12130)Instructions burned: 19 (million)
% 2.50/1.52 % (12130)------------------------------
% 2.50/1.52 % (12130)------------------------------
% 2.50/1.52 % (12115)Refutation not found, incomplete strategy
% 2.50/1.52 % (12115)------------------------------
% 2.50/1.52 % (12115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.52 % (12115)Termination reason: Refutation not found, incomplete strategy
% 2.50/1.52
% 2.50/1.52
% 2.50/1.52 % (12115)Memory used [KB]: 6908
% 2.50/1.52 % (12115)Time elapsed: 0.042 s
% 2.50/1.52 % (12115)Instructions burned: 127 (million)
% 2.50/1.52 % (12115)------------------------------
% 2.50/1.52 % (12115)------------------------------
% 2.50/1.53 % (12147)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11852 for (2998ds/3Mi)
% 2.50/1.53 % (12147)Instruction limit reached!
% 2.50/1.53 % (12147)------------------------------
% 2.50/1.53 % (12147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.53 % (12147)Termination reason: Unknown
% 2.50/1.53 % (12147)Termination phase: shuffling
% 2.50/1.53
% 2.50/1.53 % (12147)Memory used [KB]: 1279
% 2.50/1.53 % (12147)Time elapsed: 0.003 s
% 2.50/1.53 % (12147)Instructions burned: 3 (million)
% 2.50/1.53 % (12147)------------------------------
% 2.50/1.53 % (12147)------------------------------
% 2.50/1.53 % (12144)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_11852 for (2998ds/17Mi)
% 2.50/1.54 % (12149)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_11852 for (2998ds/30Mi)
% 2.50/1.54 % (12144)Instruction limit reached!
% 2.50/1.54 % (12144)------------------------------
% 2.50/1.54 % (12144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.54 % (12144)Termination reason: Unknown
% 2.50/1.54 % (12144)Termination phase: shuffling
% 2.50/1.54
% 2.50/1.54 % (12144)Memory used [KB]: 1535
% 2.50/1.54 % (12144)Time elapsed: 0.011 s
% 2.50/1.54 % (12144)Instructions burned: 18 (million)
% 2.50/1.54 % (12144)------------------------------
% 2.50/1.54 % (12144)------------------------------
% 2.50/1.55 % (12149)Instruction limit reached!
% 2.50/1.55 % (12149)------------------------------
% 2.50/1.55 % (12149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.55 % (12149)Termination reason: Unknown
% 2.50/1.55 % (12149)Termination phase: Property scanning
% 2.50/1.55
% 2.50/1.55 % (12149)Memory used [KB]: 1663
% 2.50/1.55 % (12149)Time elapsed: 0.011 s
% 2.50/1.55 % (12149)Instructions burned: 30 (million)
% 2.50/1.55 % (12149)------------------------------
% 2.50/1.55 % (12149)------------------------------
% 2.50/1.56 % (12156)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_11852 for (2998ds/127Mi)
% 2.50/1.56 % (12160)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_11852 for (2998ds/100Mi)
% 2.50/1.57 % (12129)First to succeed.
% 2.50/1.57 % (12129)Refutation found. Thanks to Tanya!
% 2.50/1.57 % SZS status Theorem for DTF2THF_11852
% 2.50/1.57 % SZS output start Proof for DTF2THF_11852
% 2.50/1.57 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.50/1.57 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 2.50/1.57 thf(type_def_8, type, set: ($tType) > $tType).
% 2.50/1.57 thf(type_def_9, type, a: $tType).
% 2.50/1.57 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 2.50/1.57 thf(func_def_1, type, set: ($tType) > $tType).
% 2.50/1.57 thf(func_def_2, type, itself: ($tType) > $tType).
% 2.50/1.57 thf(func_def_3, type, a: $tType).
% 2.50/1.57 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_6, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_7, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_8, type, bounded_lattice_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_9, type, bounded_lattice_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_10, type, topolo890362671_space: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_11, type, topolo47006728_space: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_12, type, bounde1561333602nf_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_13, type, bounde1808546759up_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.57 thf(func_def_14, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.50/1.57 thf(func_def_15, type, coinductive_gen_lset: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ X0)).
% 2.50/1.57 thf(func_def_16, type, coinductive_lSup: !>[X0: $tType]:(set @ coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_17, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_18, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 2.50/1.57 thf(func_def_19, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.50/1.57 thf(func_def_20, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_21, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_22, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 2.50/1.57 thf(func_def_23, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.50/1.57 thf(func_def_24, type, lList2435255213lllsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_25, type, lList2236698231inlsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_26, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0)).
% 2.50/1.57 thf(func_def_27, type, lList22096119349pslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_28, type, lList21612149805nflsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_29, type, lList21148268032oslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_30, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.50/1.57 thf(func_def_31, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.50/1.57 thf(func_def_32, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.50/1.57 thf(func_def_33, type, top_top: !>[X0: $tType]:(X0)).
% 2.50/1.57 thf(func_def_34, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.50/1.57 thf(func_def_35, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.50/1.57 thf(func_def_36, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.50/1.57 thf(func_def_37, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 2.50/1.57 thf(func_def_38, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 2.50/1.57 thf(func_def_39, type, pairwise: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 2.50/1.57 thf(func_def_40, type, remove: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.50/1.57 thf(func_def_41, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 2.50/1.57 thf(func_def_42, type, topolo406746546ounded: !>[X0: $tType]:(set @ X0 > $o)).
% 2.50/1.57 thf(func_def_43, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.50/1.57 thf(func_def_44, type, a2: set @ a).
% 2.50/1.57 thf(func_def_45, type, l: coinductive_llist @ a).
% 2.50/1.57 thf(func_def_46, type, r: coinductive_llist @ a).
% 2.50/1.57 thf(func_def_47, type, sa: coinductive_llist @ a).
% 2.50/1.57 thf(func_def_66, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.50/1.57 thf(func_def_67, type, sK2: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 2.50/1.57 thf(func_def_68, type, sK3: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.50/1.57 thf(func_def_69, type, sK4: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_70, type, sK5: !>[X0: $tType]:(set @ X0 > X0)).
% 2.50/1.57 thf(func_def_71, type, sK6: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_72, type, sK7: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 2.50/1.57 thf(func_def_73, type, sK8: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_74, type, sK9: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.50/1.57 thf(func_def_75, type, sK10: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 2.50/1.57 thf(func_def_76, type, sK11: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.50/1.57 thf(func_def_77, type, sK12: !>[X0: $tType]:((X0 > $o) > set @ X0 > set @ X0 > X0)).
% 2.50/1.57 thf(func_def_78, type, sK13: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.50/1.57 thf(func_def_79, type, sK14: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 2.50/1.57 thf(func_def_80, type, sK15: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 2.50/1.57 thf(func_def_81, type, sK16: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 2.50/1.57 thf(func_def_82, type, sK17: !>[X0: $tType]:(set @ X0 > X0)).
% 2.50/1.57 thf(func_def_83, type, ph18: !>[X0: $tType]:(X0)).
% 2.50/1.57 thf(f2534,plain,(
% 2.50/1.57 $false),
% 2.50/1.57 inference(trivial_inequality_removal,[status(thm)],[f2533])).
% 2.50/1.57 thf(f2533,plain,(
% 2.50/1.57 ($true = $false)),
% 2.50/1.57 inference(forward_demodulation,[status(thm)],[f2532,f2297])).
% 2.50/1.57 thf(f2297,plain,(
% 2.50/1.57 ((member @ coinductive_llist @ a @ sa @ (lList21612149805nflsts @ a @ a2)) = $false)),
% 2.50/1.57 inference(not_proxy_clausification,[status(thm)],[f1102])).
% 2.50/1.57 thf(f1102,plain,(
% 2.50/1.57 ((~ (member @ coinductive_llist @ a @ sa @ (lList21612149805nflsts @ a @ a2))) = $true)),
% 2.50/1.57 inference(cnf_transformation,[status(thm)],[f666])).
% 2.50/1.57 thf(f666,plain,(
% 2.50/1.57 ((~ (member @ coinductive_llist @ a @ sa @ (lList21612149805nflsts @ a @ a2))) = $true)),
% 2.50/1.57 inference(fool_elimination,[status(thm)],[f665])).
% 2.50/1.57 thf(f665,plain,(
% 2.50/1.57 ~(member @ coinductive_llist @ a @ sa @ (lList21612149805nflsts @ a @ a2))),
% 2.50/1.57 inference(rectify,[status(thm)],[f279])).
% 2.50/1.57 thf(f279,negated_conjecture,(
% 2.50/1.57 ~(member @ coinductive_llist @ a @ sa @ (lList21612149805nflsts @ a @ a2))),
% 2.50/1.57 inference(negated_conjecture,[status(cth)],[f278])).
% 2.50/1.57 thf(f278,conjecture,(
% 2.50/1.57 (member @ coinductive_llist @ a @ sa @ (lList21612149805nflsts @ a @ a2))),
% 2.50/1.57 file('/export/starexec/sandbox2/tmp/tmp.vlkqeUQ3AI/DTF2THF_11852.p',conj_0)).
% 2.50/1.57 thf(f2532,plain,(
% 2.50/1.57 ((member @ coinductive_llist @ a @ sa @ (lList21612149805nflsts @ a @ a2)) = $true)),
% 2.50/1.57 inference(forward_demodulation,[status(thm)],[f1154,f1329])).
% 2.50/1.57 thf(f1329,plain,(
% 2.50/1.57 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ coinductive_LNil @ X0 @ X1) = X1)) )),
% 2.50/1.57 inference(equality_proxy_clausification,[status(thm)],[f1328])).
% 2.50/1.57 thf(f1328,plain,(
% 2.50/1.57 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = ((coinductive_lappend @ X0 @ coinductive_LNil @ X0 @ X1) = X1))) )),
% 2.50/1.57 inference(beta_eta_normalization,[status(thm)],[f1327])).
% 2.50/1.57 thf(f1327,plain,(
% 2.50/1.57 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((^[Y0 : coinductive_llist @ X0]: ((coinductive_lappend @ X0 @ coinductive_LNil @ X0 @ Y0) = Y0)) @ X1) = $true)) )),
% 2.50/1.57 inference(pi_clausification,[status(thm)],[f1034])).
% 2.50/1.57 thf(f1034,plain,(
% 2.50/1.57 ( ! [X0 : $tType] : (((!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: ((coinductive_lappend @ X0 @ coinductive_LNil @ X0 @ Y0) = Y0))) = $true)) )),
% 2.50/1.57 inference(cnf_transformation,[status(thm)],[f871])).
% 2.50/1.57 thf(f871,plain,(
% 2.50/1.57 ! [X0 : $tType] : ((!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: ((coinductive_lappend @ X0 @ coinductive_LNil @ X0 @ Y0) = Y0))) = $true)),
% 2.50/1.57 inference(closure,[status(thm)],[f284])).
% 2.50/1.57 thf(f284,plain,(
% 2.50/1.57 ( ! [X0 : $tType] : (((!! @ coinductive_llist @ X0 @ (^[Y0 : coinductive_llist @ X0]: ((coinductive_lappend @ X0 @ coinductive_LNil @ X0 @ Y0) = Y0))) = $true)) )),
% 2.50/1.57 inference(fool_elimination,[status(thm)],[f283])).
% 2.50/1.57 thf(f283,plain,(
% 2.50/1.57 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ coinductive_LNil @ X0 @ X1) = X1)),
% 2.50/1.57 inference(rectify,[status(thm)],[f43])).
% 2.50/1.57 thf(f43,axiom,(
% 2.50/1.57 ! [X0 : $tType,X23 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ coinductive_LNil @ X0 @ X23) = X23)),
% 2.50/1.57 file('/export/starexec/sandbox2/tmp/tmp.vlkqeUQ3AI/DTF2THF_11852.p',fact_42_lappend__code_I1_J)).
% 2.50/1.57 thf(f1154,plain,(
% 2.50/1.57 ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ coinductive_LNil @ a @ sa) @ (lList21612149805nflsts @ a @ a2)) = $true)),
% 2.50/1.57 inference(definition_unfolding,[status(thm)],[f1111,f1072])).
% 2.50/1.57 thf(f1072,plain,(
% 2.50/1.57 (l = coinductive_LNil @ a)),
% 2.50/1.57 inference(cnf_transformation,[status(thm)],[f478])).
% 2.50/1.57 thf(f478,plain,(
% 2.50/1.57 (l = coinductive_LNil @ a)),
% 2.50/1.57 inference(fool_elimination,[status(thm)],[f14])).
% 2.50/1.57 thf(f14,axiom,(
% 2.50/1.57 (l = coinductive_LNil @ a)),
% 2.50/1.57 file('/export/starexec/sandbox2/tmp/tmp.vlkqeUQ3AI/DTF2THF_11852.p',fact_13_LNil__fin_Ohyps)).
% 2.50/1.57 thf(f1111,plain,(
% 2.50/1.57 ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ l @ sa) @ (lList21612149805nflsts @ a @ a2)) = $true)),
% 2.50/1.57 inference(cnf_transformation,[status(thm)],[f554])).
% 2.50/1.57 thf(f554,plain,(
% 2.50/1.57 ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ l @ sa) @ (lList21612149805nflsts @ a @ a2)) = $true)),
% 2.50/1.57 inference(fool_elimination,[status(thm)],[f553])).
% 2.50/1.57 thf(f553,plain,(
% 2.50/1.57 (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ l @ sa) @ (lList21612149805nflsts @ a @ a2))),
% 2.50/1.57 inference(rectify,[status(thm)],[f1])).
% 2.50/1.57 thf(f1,axiom,(
% 2.50/1.57 (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ l @ sa) @ (lList21612149805nflsts @ a @ a2))),
% 2.50/1.57 file('/export/starexec/sandbox2/tmp/tmp.vlkqeUQ3AI/DTF2THF_11852.p',fact_0_LNil__fin_Oprems)).
% 2.50/1.57 % SZS output end Proof for DTF2THF_11852
% 2.50/1.57 % (12129)------------------------------
% 2.50/1.57 % (12129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.57 % (12129)Termination reason: Refutation
% 2.50/1.57
% 2.50/1.57 % (12129)Memory used [KB]: 7291
% 2.50/1.57 % (12129)Time elapsed: 0.075 s
% 2.50/1.57 % (12129)Instructions burned: 247 (million)
% 2.50/1.57 % (12129)------------------------------
% 2.50/1.57 % (12129)------------------------------
% 2.50/1.57 % (12057)Success in time 0.158 s
%------------------------------------------------------------------------------