%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PRO019^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 09:28:07 AM UTC 2026
% Result : Theorem 3.00s 1.60s
% Output : Refutation 3.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PRO019^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n014.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:29:42 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : PRO019^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.46 % Domain : Processes
% 0.19/0.46 % Problem : Process algebra 25
% 0.19/0.46 % Version : [Bla16] axioms : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.19/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.19/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bla16]
% 0.19/0.46 % Names : process__25.p [Bla16]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.19/0.46 % Syntax : Number of formulae : 328 ( 152 unt; 44 typ; 0 def)
% 0.19/0.46 % Number of atoms : 698 ( 354 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 10 ( 2 avg)
% 0.19/0.46 % Number of connectives : 4525 ( 60 ~; 14 |; 63 &;4096 @)
% 0.19/0.46 % ( 0 <=>; 292 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 31 ( 8 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 512 ( 512 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 46 ( 43 usr; 3 con; 0-14 aty)
% 0.19/0.46 % Number of variables : 1359 ( 48 ^;1236 !; 24 ?;1359 :)
% 0.19/0.46 % ( 51 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.46 % SPC : TH1_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.19/0.46 % 2016-07-13 14:39:38.993
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 %----Could-be-implicit typings (4)
% 0.19/0.46 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 0.19/0.46 proces634752977rocess: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Set_Oset,type,
% 0.19/0.46 set: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_itself,type,
% 0.19/0.46 itself: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_tf_a,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 %----Explicit typings (40)
% 0.19/0.46 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.19/0.46 bounded_lattice:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_HOL_Otype,type,
% 0.19/0.46 type:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Lattices_Olattice,type,
% 0.19/0.46 lattice:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Complete__Lattices_OInf,type,
% 0.19/0.46 complete_Inf:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Complete__Lattices_OSup,type,
% 0.19/0.46 complete_Sup:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.19/0.46 semilattice_sup:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.19/0.46 bounded_lattice_bot:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 0.19/0.46 comple187826305attice:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.19/0.46 bounde1808546759up_bot:
% 0.19/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_BNF__Def_Oeq__onp,type,
% 0.19/0.46 bNF_eq_onp:
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_BNF__Def_Ovimage2p,type,
% 0.19/0.46 bNF_vimage2p:
% 0.19/0.46 !>[A: $tType,D: $tType,B: $tType,E: $tType,C: $tType] : ( ( A > D ) > ( B > E ) > ( D > E > C ) > A > B > C ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Complete__Lattices_OInf__class_OInf,type,
% 0.19/0.46 complete_Inf_Inf:
% 0.19/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Complete__Lattices_OSup__class_OSup,type,
% 0.19/0.46 complete_Sup_Sup:
% 0.19/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Fun_Ocomp,type,
% 0.19/0.46 comp:
% 0.19/0.46 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Fun_Oid,type,
% 0.19/0.46 id:
% 0.19/0.46 !>[A: $tType] : ( A > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_If,type,
% 0.19/0.46 if:
% 0.19/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.19/0.46 sup_sup:
% 0.19/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.19/0.46 bot_bot:
% 0.19/0.46 !>[A: $tType] : A ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 0.19/0.46 proces1525233512Action:
% 0.19/0.46 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 0.19/0.46 proces1915862579Choice:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 0.19/0.46 proces1406508781rocess:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 0.19/0.46 proces979765041_ch1Of:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 0.19/0.46 proces988026546_ch2Of:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 0.19/0.46 proces1778668539contOf:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 0.19/0.46 proces894737309rocess:
% 0.19/0.46 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 0.19/0.46 proces10484146Action:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 0.19/0.46 proces401113213Choice:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
% 0.19/0.46 proces370407749rocess:
% 0.19/0.46 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
% 0.19/0.46 proces1205983068rocess:
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 0.19/0.46 proces745025900prefOf:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 0.19/0.46 proces749077512rocess:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Oset__process,type,
% 0.19/0.46 proces1148692671rocess:
% 0.19/0.46 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Pure_Otype,type,
% 0.19/0.46 type2:
% 0.19/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OBall,type,
% 0.19/0.46 ball:
% 0.19/0.46 !>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect,type,
% 0.19/0.46 collect:
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_Obind,type,
% 0.19/0.46 bind:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > ( set @ B ) ) > ( set @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_Oimage,type,
% 0.19/0.46 image:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_Oinsert,type,
% 0.19/0.46 insert:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member,type,
% 0.19/0.46 member:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_p,type,
% 0.19/0.46 p: proces634752977rocess @ a ).
% 0.19/0.46
% 0.19/0.46 %----Relevant facts (256)
% 0.19/0.46 thf(fact_0_process_Odistinct__disc_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces401113213Choice @ A @ Process )
% 0.19/0.46 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.distinct_disc(2)
% 0.19/0.46 thf(fact_1_process_Odistinct__disc_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces10484146Action @ A @ Process )
% 0.19/0.46 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.distinct_disc(1)
% 0.19/0.46 thf(fact_2_process_Oexhaust__disc,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.46 ( ~ ( proces10484146Action @ A @ Process )
% 0.19/0.46 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.exhaust_disc
% 0.19/0.46 thf(fact_3_process_Ocorec__disc__iff_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
% 0.19/0.46 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.46 = ( ~ ( P @ A2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.corec_disc_iff(2)
% 0.19/0.46 thf(fact_4_process_Ocorec__disc__iff_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
% 0.19/0.46 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.46 = ( P @ A2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.corec_disc_iff(1)
% 0.19/0.46 thf(fact_5_process_Omap__disc__iff_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.19/0.46 = ( proces401113213Choice @ A @ A2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.map_disc_iff(2)
% 0.19/0.46 thf(fact_6_process_Omap__disc__iff_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.19/0.46 = ( proces10484146Action @ A @ A2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.map_disc_iff(1)
% 0.19/0.46 thf(fact_7_process_Ocorec__disc_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.19/0.46 ( ~ ( P @ A2 )
% 0.19/0.46 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.corec_disc(2)
% 0.19/0.46 thf(fact_8_process_Ocorec__disc_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.19/0.46 ( ( P @ A2 )
% 0.19/0.46 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.corec_disc(1)
% 0.19/0.46 thf(fact_9_process_Odisc_I4_J,axiom,
% 0.19/0.46 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.disc(4)
% 0.19/0.46 thf(fact_10_process_Odisc_I3_J,axiom,
% 0.19/0.46 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 0.19/0.46 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.disc(3)
% 0.19/0.46 thf(fact_11_process_OdiscI_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.19/0.46 ( ( Process
% 0.19/0.46 = ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.19/0.46 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.discI(2)
% 0.19/0.46 thf(fact_12_isChoice__def,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( proces401113213Choice @ A )
% 0.19/0.46 = ( ^ [Process2: proces634752977rocess @ A] :
% 0.19/0.46 ? [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.19/0.46 ( Process2
% 0.19/0.46 = ( proces1915862579Choice @ A @ X212 @ X222 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % isChoice_def
% 0.19/0.46 thf(fact_13_process_Odisc_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.19/0.46 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.disc(2)
% 0.19/0.46 thf(fact_14_process_Odisc_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.disc(1)
% 0.19/0.46 thf(fact_15_process_Oinject_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 0.19/0.46 ( ( ( proces1915862579Choice @ A @ X21 @ X22 )
% 0.19/0.46 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.inject(2)
% 0.19/0.46 thf(fact_16_process_Oinject_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,X11: A,X12: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 0.19/0.46 ( ( ( proces1525233512Action @ A @ X11 @ X12 )
% 0.19/0.46 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 0.19/0.46 = ( ( X11 = Y11 )
% 0.19/0.46 & ( X12 = Y12 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.inject(1)
% 0.19/0.46 thf(fact_17_process_Ocorec_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.19/0.46 ( ~ ( P @ A2 )
% 0.19/0.46 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 0.19/0.46 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A2 ) @ ( G211 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A2 ) @ ( G221 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.corec(2)
% 0.19/0.46 thf(fact_18_process_Ocorec_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.19/0.46 ( ( P @ A2 )
% 0.19/0.46 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 0.19/0.46 = ( proces1525233512Action @ A @ ( G11 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A2 ) @ ( G121 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.corec(1)
% 0.19/0.46 thf(fact_19_process_Osimps_I16_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces370407749rocess @ A @ B @ F @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.19/0.46 = ( proces1915862579Choice @ B @ ( proces370407749rocess @ A @ B @ F @ X21 ) @ ( proces370407749rocess @ A @ B @ F @ X22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.simps(16)
% 0.19/0.46 thf(fact_20_process_Osimps_I15_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,X11: A,X12: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces370407749rocess @ A @ B @ F @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.19/0.46 = ( proces1525233512Action @ B @ ( F @ X11 ) @ ( proces370407749rocess @ A @ B @ F @ X12 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.simps(15)
% 0.19/0.46 thf(fact_21_process_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,X11: A,X12: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces1525233512Action @ A @ X11 @ X12 )
% 0.19/0.46 != ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.distinct(1)
% 0.19/0.46 thf(fact_22_process_Oexhaust,axiom,
% 0.19/0.46 ! [A: $tType,Y: proces634752977rocess @ A] :
% 0.19/0.46 ( ! [X112: A,X122: proces634752977rocess @ A] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( proces1525233512Action @ A @ X112 @ X122 ) )
% 0.19/0.46 => ~ ! [X213: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( proces1915862579Choice @ A @ X213 @ X223 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.exhaust
% 0.19/0.46 thf(fact_23_isAction__def,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( proces10484146Action @ A )
% 0.19/0.46 = ( ^ [Process2: proces634752977rocess @ A] :
% 0.19/0.46 ? [X113: A,X123: proces634752977rocess @ A] :
% 0.19/0.46 ( Process2
% 0.19/0.46 = ( proces1525233512Action @ A @ X113 @ X123 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % isAction_def
% 0.19/0.46 thf(fact_24_process_OdiscI_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A,X11: A,X12: proces634752977rocess @ A] :
% 0.19/0.46 ( ( Process
% 0.19/0.46 = ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.19/0.46 => ( proces10484146Action @ A @ Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.discI(1)
% 0.19/0.46 thf(fact_25_process_Omap__sel_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.19/0.46 ( ( proces10484146Action @ A @ A2 )
% 0.19/0.46 => ( ( proces745025900prefOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.19/0.46 = ( F @ ( proces745025900prefOf @ A @ A2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.map_sel(1)
% 0.19/0.46 thf(fact_26_process_Omap__sel_I3_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.19/0.46 ( ( proces401113213Choice @ A @ A2 )
% 0.19/0.46 => ( ( proces979765041_ch1Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.19/0.46 = ( proces370407749rocess @ A @ B @ F @ ( proces979765041_ch1Of @ A @ A2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.map_sel(3)
% 0.19/0.46 thf(fact_27_process_Omap__sel_I4_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.19/0.46 ( ( proces401113213Choice @ A @ A2 )
% 0.19/0.46 => ( ( proces988026546_ch2Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.19/0.46 = ( proces370407749rocess @ A @ B @ F @ ( proces988026546_ch2Of @ A @ A2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.map_sel(4)
% 0.19/0.46 thf(fact_28_process_Omap__sel_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 0.19/0.46 ( ( proces10484146Action @ A @ A2 )
% 0.19/0.46 => ( ( proces1778668539contOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.19/0.46 = ( proces370407749rocess @ A @ B @ F @ ( proces1778668539contOf @ A @ A2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.map_sel(2)
% 0.19/0.46 thf(fact_29_process_Oset__cases,axiom,
% 0.19/0.46 ! [A: $tType,E2: A,A2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( member @ A @ E2 @ ( proces1148692671rocess @ A @ A2 ) )
% 0.19/0.46 => ( ! [Z2: proces634752977rocess @ A] :
% 0.19/0.46 ( A2
% 0.19/0.46 != ( proces1525233512Action @ A @ E2 @ Z2 ) )
% 0.19/0.46 => ( ! [Z1: A,Z2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( A2
% 0.19/0.46 = ( proces1525233512Action @ A @ Z1 @ Z2 ) )
% 0.19/0.46 => ~ ( member @ A @ E2 @ ( proces1148692671rocess @ A @ Z2 ) ) )
% 0.19/0.46 => ( ! [Z1: proces634752977rocess @ A] :
% 0.19/0.46 ( ? [Z2: proces634752977rocess @ A] :
% 0.19/0.46 ( A2
% 0.19/0.46 = ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
% 0.19/0.46 => ~ ( member @ A @ E2 @ ( proces1148692671rocess @ A @ Z1 ) ) )
% 0.19/0.46 => ~ ! [Z1: proces634752977rocess @ A,Z2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( A2
% 0.19/0.46 = ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
% 0.19/0.46 => ~ ( member @ A @ E2 @ ( proces1148692671rocess @ A @ Z2 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.set_cases
% 0.19/0.46 thf(fact_30_process_Oset__induct,axiom,
% 0.19/0.46 ! [A: $tType,X: A,A2: proces634752977rocess @ A,P2: A > ( proces634752977rocess @ A ) > $o] :
% 0.19/0.46 ( ( member @ A @ X @ ( proces1148692671rocess @ A @ A2 ) )
% 0.19/0.46 => ( ! [Z1: A,Z2: proces634752977rocess @ A] : ( P2 @ Z1 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) )
% 0.19/0.46 => ( ! [Z1: A,Z2: proces634752977rocess @ A,Xa: A] :
% 0.19/0.46 ( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ Z2 ) )
% 0.19/0.46 => ( ( P2 @ Xa @ Z2 )
% 0.19/0.46 => ( P2 @ Xa @ ( proces1525233512Action @ A @ Z1 @ Z2 ) ) ) )
% 0.19/0.46 => ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xb: A] :
% 0.19/0.46 ( ( member @ A @ Xb @ ( proces1148692671rocess @ A @ Z1a ) )
% 0.19/0.46 => ( ( P2 @ Xb @ Z1a )
% 0.19/0.46 => ( P2 @ Xb @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
% 0.19/0.46 => ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xc: A] :
% 0.19/0.46 ( ( member @ A @ Xc @ ( proces1148692671rocess @ A @ Z2a ) )
% 0.19/0.46 => ( ( P2 @ Xc @ Z2a )
% 0.19/0.46 => ( P2 @ Xc @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
% 0.19/0.46 => ( P2 @ X @ A2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.set_induct
% 0.19/0.46 thf(fact_31_process_Opred__inject_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,P2: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces1205983068rocess @ A @ P2 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
% 0.19/0.46 = ( ( proces1205983068rocess @ A @ P2 @ A2 )
% 0.19/0.46 & ( proces1205983068rocess @ A @ P2 @ Aa2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.pred_inject(2)
% 0.19/0.46 thf(fact_32_process_Opred__inject_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,P2: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces1205983068rocess @ A @ P2 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
% 0.19/0.46 = ( ( P2 @ A2 )
% 0.19/0.46 & ( proces1205983068rocess @ A @ P2 @ Aa2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.pred_inject(1)
% 0.19/0.46 thf(fact_33_process_Osimps_I6_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.19/0.46 = ( F2 @ X21 @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.simps(6)
% 0.19/0.46 thf(fact_34_process_Osimps_I5_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X12: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.19/0.46 = ( F1 @ X11 @ X12 ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.simps(5)
% 0.19/0.46 thf(fact_35_process_Ocollapse_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces10484146Action @ A @ Process )
% 0.19/0.46 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 0.19/0.46 = Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.collapse(1)
% 0.19/0.46 thf(fact_36_process_Ocollapse_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.46 ( ( proces401113213Choice @ A @ Process )
% 0.19/0.46 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 0.19/0.46 = Process ) ) ).
% 0.19/0.46
% 0.19/0.46 % process.collapse(2)
% 0.19/0.46 thf(fact_37_process_Ocase__eq__if,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( proces1406508781rocess @ A @ B )
% 0.19/0.46 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process2: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process2 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process2 ) @ ( proces1778668539contOf @ A @ Process2 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process2 ) @ ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.case_eq_if
% 0.19/0.47 thf(fact_38_process_Opred__mono__strong,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o,X: proces634752977rocess @ A,Pa: A > $o] :
% 0.19/0.47 ( ( proces1205983068rocess @ A @ P2 @ X )
% 0.19/0.47 => ( ! [Z: A] :
% 0.19/0.47 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 0.19/0.47 => ( ( P2 @ Z )
% 0.19/0.47 => ( Pa @ Z ) ) )
% 0.19/0.47 => ( proces1205983068rocess @ A @ Pa @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.pred_mono_strong
% 0.19/0.47 thf(fact_39_process_Opred__cong,axiom,
% 0.19/0.47 ! [A: $tType,X: proces634752977rocess @ A,Ya: proces634752977rocess @ A,P2: A > $o,Pa: A > $o] :
% 0.19/0.47 ( ( X = Ya )
% 0.19/0.47 => ( ! [Z: A] :
% 0.19/0.47 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ Ya ) )
% 0.19/0.47 => ( ( P2 @ Z )
% 0.19/0.47 = ( Pa @ Z ) ) )
% 0.19/0.47 => ( ( proces1205983068rocess @ A @ P2 @ X )
% 0.19/0.47 = ( proces1205983068rocess @ A @ Pa @ Ya ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.pred_cong
% 0.19/0.47 thf(fact_40_process_Osplit__sel__asm,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,P2: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( P2 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.19/0.47 = ( ~ ( ( ( Process
% 0.19/0.47 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.19/0.47 & ~ ( P2 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.19/0.47 | ( ( Process
% 0.19/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.19/0.47 & ~ ( P2 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.split_sel_asm
% 0.19/0.47 thf(fact_41_process_Osplit__sel,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,P2: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( P2 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.19/0.47 = ( ( ( Process
% 0.19/0.47 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.19/0.47 => ( P2 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.19/0.47 & ( ( Process
% 0.19/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.19/0.47 => ( P2 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.split_sel
% 0.19/0.47 thf(fact_42_process_Oexhaust__sel,axiom,
% 0.19/0.47 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.19/0.47 ( ( Process
% 0.19/0.47 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.19/0.47 => ( Process
% 0.19/0.47 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.exhaust_sel
% 0.19/0.47 thf(fact_43_process_Oexpand,axiom,
% 0.19/0.47 ! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.19/0.47 ( ( ( proces10484146Action @ A @ Process )
% 0.19/0.47 = ( proces10484146Action @ A @ Process3 ) )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ Process )
% 0.19/0.47 => ( ( proces10484146Action @ A @ Process3 )
% 0.19/0.47 => ( ( ( proces745025900prefOf @ A @ Process )
% 0.19/0.47 = ( proces745025900prefOf @ A @ Process3 ) )
% 0.19/0.47 & ( ( proces1778668539contOf @ A @ Process )
% 0.19/0.47 = ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
% 0.19/0.47 => ( ( ( proces401113213Choice @ A @ Process )
% 0.19/0.47 => ( ( proces401113213Choice @ A @ Process3 )
% 0.19/0.47 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 0.19/0.47 = ( proces979765041_ch1Of @ A @ Process3 ) )
% 0.19/0.47 & ( ( proces988026546_ch2Of @ A @ Process )
% 0.19/0.47 = ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
% 0.19/0.47 => ( Process = Process3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.expand
% 0.19/0.47 thf(fact_44_process_Ocoinduct,axiom,
% 0.19/0.47 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.19/0.47 ( ( R @ Process @ Process3 )
% 0.19/0.47 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 0.19/0.47 ( ( R @ Process4 @ Process5 )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 = ( proces10484146Action @ A @ Process5 ) )
% 0.19/0.47 & ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 => ( ( proces10484146Action @ A @ Process5 )
% 0.19/0.47 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 0.19/0.47 = ( proces745025900prefOf @ A @ Process5 ) )
% 0.19/0.47 & ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ Process4 )
% 0.19/0.47 => ( ( proces401113213Choice @ A @ Process5 )
% 0.19/0.47 => ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 0.19/0.47 & ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
% 0.19/0.47 => ( Process = Process3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.coinduct
% 0.19/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,P2: A > $o] :
% 0.19/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.19/0.47 = ( P2 @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % mem_Collect_eq
% 0.19/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A] :
% 0.19/0.47 ( ( collect @ A
% 0.19/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.19/0.47 = A3 ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_mem_eq
% 0.19/0.47 thf(fact_47_Collect__cong,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.19/0.47 ( ! [X3: A] :
% 0.19/0.47 ( ( P2 @ X3 )
% 0.19/0.47 = ( Q @ X3 ) )
% 0.19/0.47 => ( ( collect @ A @ P2 )
% 0.19/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_cong
% 0.19/0.47 thf(fact_48_ext,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.19/0.47 ( ! [X3: A] :
% 0.19/0.47 ( ( F @ X3 )
% 0.19/0.47 = ( G @ X3 ) )
% 0.19/0.47 => ( F = G ) ) ).
% 0.19/0.47
% 0.19/0.47 % ext
% 0.19/0.47 thf(fact_49_process_Ocoinduct__strong,axiom,
% 0.19/0.47 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.19/0.47 ( ( R @ Process @ Process3 )
% 0.19/0.47 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 0.19/0.47 ( ( R @ Process4 @ Process5 )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 = ( proces10484146Action @ A @ Process5 ) )
% 0.19/0.47 & ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 => ( ( proces10484146Action @ A @ Process5 )
% 0.19/0.47 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 0.19/0.47 = ( proces745025900prefOf @ A @ Process5 ) )
% 0.19/0.47 & ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
% 0.19/0.47 | ( ( proces1778668539contOf @ A @ Process4 )
% 0.19/0.47 = ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ Process4 )
% 0.19/0.47 => ( ( proces401113213Choice @ A @ Process5 )
% 0.19/0.47 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 0.19/0.47 | ( ( proces979765041_ch1Of @ A @ Process4 )
% 0.19/0.47 = ( proces979765041_ch1Of @ A @ Process5 ) ) )
% 0.19/0.47 & ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
% 0.19/0.47 | ( ( proces988026546_ch2Of @ A @ Process4 )
% 0.19/0.47 = ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
% 0.19/0.47 => ( Process = Process3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.coinduct_strong
% 0.19/0.47 thf(fact_50_process_Oset__sel_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,A2: proces634752977rocess @ A,X: A] :
% 0.19/0.47 ( ( proces10484146Action @ A @ A2 )
% 0.19/0.47 => ( ( member @ A @ X @ ( proces1148692671rocess @ A @ ( proces1778668539contOf @ A @ A2 ) ) )
% 0.19/0.47 => ( member @ A @ X @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_sel(2)
% 0.19/0.47 thf(fact_51_process_Oset__sel_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,A2: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces10484146Action @ A @ A2 )
% 0.19/0.47 => ( member @ A @ ( proces745025900prefOf @ A @ A2 ) @ ( proces1148692671rocess @ A @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_sel(1)
% 0.19/0.47 thf(fact_52_process_Oset__sel_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,A2: proces634752977rocess @ A,Xb2: A] :
% 0.19/0.47 ( ( proces401113213Choice @ A @ A2 )
% 0.19/0.47 => ( ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ ( proces988026546_ch2Of @ A @ A2 ) ) )
% 0.19/0.47 => ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_sel(4)
% 0.19/0.47 thf(fact_53_process_Oset__sel_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,A2: proces634752977rocess @ A,Xa2: A] :
% 0.19/0.47 ( ( proces401113213Choice @ A @ A2 )
% 0.19/0.47 => ( ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ ( proces979765041_ch1Of @ A @ A2 ) ) )
% 0.19/0.47 => ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_sel(3)
% 0.19/0.47 thf(fact_54_process_Oinj__map__strong,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,X: proces634752977rocess @ A,Xa2: proces634752977rocess @ A,F: A > B,Fa: A > B] :
% 0.19/0.47 ( ! [Z: A,Za: A] :
% 0.19/0.47 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 0.19/0.47 => ( ( member @ A @ Za @ ( proces1148692671rocess @ A @ Xa2 ) )
% 0.19/0.47 => ( ( ( F @ Z )
% 0.19/0.47 = ( Fa @ Za ) )
% 0.19/0.47 => ( Z = Za ) ) ) )
% 0.19/0.47 => ( ( ( proces370407749rocess @ A @ B @ F @ X )
% 0.19/0.47 = ( proces370407749rocess @ A @ B @ Fa @ Xa2 ) )
% 0.19/0.47 => ( X = Xa2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.inj_map_strong
% 0.19/0.47 thf(fact_55_process_Omap__cong0,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,X: proces634752977rocess @ A,F: A > B,G: A > B] :
% 0.19/0.47 ( ! [Z: A] :
% 0.19/0.47 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 0.19/0.47 => ( ( F @ Z )
% 0.19/0.47 = ( G @ Z ) ) )
% 0.19/0.47 => ( ( proces370407749rocess @ A @ B @ F @ X )
% 0.19/0.47 = ( proces370407749rocess @ A @ B @ G @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.map_cong0
% 0.19/0.47 thf(fact_56_process_Omap__cong,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,X: proces634752977rocess @ A,Ya: proces634752977rocess @ A,F: A > B,G: A > B] :
% 0.19/0.47 ( ( X = Ya )
% 0.19/0.47 => ( ! [Z: A] :
% 0.19/0.47 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ Ya ) )
% 0.19/0.47 => ( ( F @ Z )
% 0.19/0.47 = ( G @ Z ) ) )
% 0.19/0.47 => ( ( proces370407749rocess @ A @ B @ F @ X )
% 0.19/0.47 = ( proces370407749rocess @ A @ B @ G @ Ya ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.map_cong
% 0.19/0.47 thf(fact_57_process_Oset__intros_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,A1: A,A22: proces634752977rocess @ A] : ( member @ A @ A1 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_intros(1)
% 0.19/0.47 thf(fact_58_process_Oset__intros_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,X: A,A22: proces634752977rocess @ A,A1: A] :
% 0.19/0.47 ( ( member @ A @ X @ ( proces1148692671rocess @ A @ A22 ) )
% 0.19/0.47 => ( member @ A @ X @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_intros(2)
% 0.19/0.47 thf(fact_59_process_Oset__intros_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,Xa2: A,A1a: proces634752977rocess @ A,A2a: proces634752977rocess @ A] :
% 0.19/0.47 ( ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ A1a ) )
% 0.19/0.47 => ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_intros(3)
% 0.19/0.47 thf(fact_60_process_Oset__intros_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,Xb2: A,A2a: proces634752977rocess @ A,A1a: proces634752977rocess @ A] :
% 0.19/0.47 ( ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ A2a ) )
% 0.19/0.47 => ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_intros(4)
% 0.19/0.47 thf(fact_61_process_Osel_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.19/0.47 = X12 ) ).
% 0.19/0.47
% 0.19/0.47 % process.sel(2)
% 0.19/0.47 thf(fact_62_process_Osel_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.19/0.47 = X21 ) ).
% 0.19/0.47
% 0.19/0.47 % process.sel(3)
% 0.19/0.47 thf(fact_63_process_Osel_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.19/0.47 = X22 ) ).
% 0.19/0.47
% 0.19/0.47 % process.sel(4)
% 0.19/0.47 thf(fact_64_process_Osel_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.19/0.47 = X11 ) ).
% 0.19/0.47
% 0.19/0.47 % process.sel(1)
% 0.19/0.47 thf(fact_65_process_Ocorec__sel_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q12: C > $o,G11: C > A,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.19/0.47 ( ( P @ A2 )
% 0.19/0.47 => ( ( ( Q12 @ A2 )
% 0.19/0.47 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.47 = ( G121 @ A2 ) ) )
% 0.19/0.47 & ( ~ ( Q12 @ A2 )
% 0.19/0.47 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.47 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_sel(2)
% 0.19/0.47 thf(fact_66_process_Ocorec__sel_I3_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q21: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.19/0.47 ( ~ ( P @ A2 )
% 0.19/0.47 => ( ( ( Q21 @ A2 )
% 0.19/0.47 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.47 = ( G211 @ A2 ) ) )
% 0.19/0.47 & ( ~ ( Q21 @ A2 )
% 0.19/0.47 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.47 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_sel(3)
% 0.19/0.47 thf(fact_67_process_Ocorec__sel_I4_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q22: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.19/0.47 ( ~ ( P @ A2 )
% 0.19/0.47 => ( ( ( Q22 @ A2 )
% 0.19/0.47 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.47 = ( G221 @ A2 ) ) )
% 0.19/0.47 & ( ~ ( Q22 @ A2 )
% 0.19/0.47 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.47 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_sel(4)
% 0.19/0.47 thf(fact_68_process_Ocorec__sel_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 0.19/0.47 ( ( P @ A2 )
% 0.19/0.47 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 0.19/0.47 = ( G11 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.corec_sel(1)
% 0.19/0.47 thf(fact_69_process_Orel__coinduct,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,P2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X: proces634752977rocess @ A,Y: proces634752977rocess @ B,R: A > B > $o] :
% 0.19/0.47 ( ( P2 @ X @ Y )
% 0.19/0.47 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
% 0.19/0.47 ( ( P2 @ Process4 @ Process5 )
% 0.19/0.47 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 = ( proces10484146Action @ B @ Process5 ) )
% 0.19/0.47 & ( ( proces10484146Action @ A @ Process4 )
% 0.19/0.47 => ( ( proces10484146Action @ B @ Process5 )
% 0.19/0.47 => ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
% 0.19/0.47 & ( P2 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ Process4 )
% 0.19/0.47 => ( ( proces401113213Choice @ B @ Process5 )
% 0.19/0.47 => ( ( P2 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
% 0.19/0.47 & ( P2 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
% 0.19/0.47 => ( proces749077512rocess @ A @ B @ R @ X @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_coinduct
% 0.19/0.47 thf(fact_70_process_Orel__sel,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B )
% 0.19/0.47 = ( ^ [R2: A > B > $o,A4: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 0.19/0.47 ( ( ( proces10484146Action @ A @ A4 )
% 0.19/0.47 = ( proces10484146Action @ B @ B2 ) )
% 0.19/0.47 & ( ( proces10484146Action @ A @ A4 )
% 0.19/0.47 => ( ( proces10484146Action @ B @ B2 )
% 0.19/0.47 => ( ( R2 @ ( proces745025900prefOf @ A @ A4 ) @ ( proces745025900prefOf @ B @ B2 ) )
% 0.19/0.47 & ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A4 ) @ ( proces1778668539contOf @ B @ B2 ) ) ) ) )
% 0.19/0.47 & ( ( proces401113213Choice @ A @ A4 )
% 0.19/0.47 => ( ( proces401113213Choice @ B @ B2 )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A4 ) @ ( proces979765041_ch1Of @ B @ B2 ) )
% 0.19/0.47 & ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A4 ) @ ( proces988026546_ch2Of @ B @ B2 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_sel
% 0.19/0.47 thf(fact_71_process_Osimps_I21_J,axiom,
% 0.19/0.47 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 0.19/0.47 = ( insert @ A @ X11 @ ( proces1148692671rocess @ A @ X12 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.simps(21)
% 0.19/0.47 thf(fact_72_process_Osimps_I22_J,axiom,
% 0.19/0.47 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ ( proces1148692671rocess @ A @ X21 ) @ ( proces1148692671rocess @ A @ X22 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.simps(22)
% 0.19/0.47 thf(fact_73_process_Opred__map,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,Q: B > $o,F: A > B,X: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1205983068rocess @ B @ Q @ ( proces370407749rocess @ A @ B @ F @ X ) )
% 0.19/0.47 = ( proces1205983068rocess @ A @ ( comp @ B @ $o @ A @ Q @ F ) @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.pred_map
% 0.19/0.47 thf(fact_74_process_Opred__set,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces1205983068rocess @ A )
% 0.19/0.47 = ( ^ [P3: A > $o,X2: proces634752977rocess @ A] :
% 0.19/0.47 ! [Y2: A] :
% 0.19/0.47 ( ( member @ A @ Y2 @ ( proces1148692671rocess @ A @ X2 ) )
% 0.19/0.47 => ( P3 @ Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.pred_set
% 0.19/0.47 thf(fact_75_process_Oset__map,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F: A > B,V: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces1148692671rocess @ B @ ( proces370407749rocess @ A @ B @ F @ V ) )
% 0.19/0.47 = ( image @ A @ B @ F @ ( proces1148692671rocess @ A @ V ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.set_map
% 0.19/0.47 thf(fact_76_process_Orel__cases,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B3: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B3 )
% 0.19/0.47 => ( ! [X1: A,X23: proces634752977rocess @ A] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces1525233512Action @ A @ X1 @ X23 ) )
% 0.19/0.47 => ! [Y1: B,Y23: proces634752977rocess @ B] :
% 0.19/0.47 ( ( B3
% 0.19/0.47 = ( proces1525233512Action @ B @ Y1 @ Y23 ) )
% 0.19/0.47 => ( ( R @ X1 @ Y1 )
% 0.19/0.47 => ~ ( proces749077512rocess @ A @ B @ R @ X23 @ Y23 ) ) ) )
% 0.19/0.47 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 0.19/0.47 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 0.19/0.47 ( ( B3
% 0.19/0.47 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 0.19/0.47 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_cases
% 0.19/0.47 thf(fact_77_process_Orel__distinct_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.19/0.47 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_distinct(1)
% 0.19/0.47 thf(fact_78_process_Orel__inject_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 0.19/0.47 = ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 0.19/0.47 & ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_inject(2)
% 0.19/0.47 thf(fact_79_process_Orel__inject_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 0.19/0.47 = ( ( R @ X11 @ Y11 )
% 0.19/0.47 & ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_inject(1)
% 0.19/0.47 thf(fact_80_process_Orel__eq,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ A
% 0.19/0.47 @ ^ [Y3: A,Z3: A] : ( Y3 = Z3 ) )
% 0.19/0.47 = ( ^ [Y3: proces634752977rocess @ A,Z3: proces634752977rocess @ A] : ( Y3 = Z3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_eq
% 0.19/0.47 thf(fact_81_process_Orel__refl,axiom,
% 0.19/0.47 ! [B: $tType,Ra: B > B > $o,X: proces634752977rocess @ B] :
% 0.19/0.47 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 0.19/0.47 => ( proces749077512rocess @ B @ B @ Ra @ X @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_refl
% 0.19/0.47 thf(fact_82_process_Omap__o__corec,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: C > $o,Ga: C > A,Gb: C > $o,Gc: C > ( proces634752977rocess @ A ),Gd: C > C,Ge: C > $o,Gf: C > ( proces634752977rocess @ A ),Gg: C > C,Gh: C > $o,Gi: C > ( proces634752977rocess @ A ),Gj: C > C] :
% 0.19/0.47 ( ( comp @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ ( proces370407749rocess @ A @ B @ F ) @ ( proces894737309rocess @ C @ A @ G @ Ga @ Gb @ Gc @ Gd @ Ge @ Gf @ Gg @ Gh @ Gi @ Gj ) )
% 0.19/0.47 = ( proces894737309rocess @ C @ B @ G @ ( comp @ A @ B @ C @ F @ Ga ) @ Gb @ ( comp @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ ( proces370407749rocess @ A @ B @ F ) @ Gc ) @ Gd @ Ge @ ( comp @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ ( proces370407749rocess @ A @ B @ F ) @ Gf ) @ Gg @ Gh @ ( comp @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ ( proces370407749rocess @ A @ B @ F ) @ Gi ) @ Gj ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.map_o_corec
% 0.19/0.47 thf(fact_83_process_Orel__cong,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X: proces634752977rocess @ A,Ya: proces634752977rocess @ A,Y: proces634752977rocess @ B,Xa2: proces634752977rocess @ B,R: A > B > $o,Ra: A > B > $o] :
% 0.19/0.47 ( ( X = Ya )
% 0.19/0.47 => ( ( Y = Xa2 )
% 0.19/0.47 => ( ! [Z: A,Yb: B] :
% 0.19/0.47 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ Ya ) )
% 0.19/0.47 => ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Xa2 ) )
% 0.19/0.47 => ( ( R @ Z @ Yb )
% 0.19/0.47 = ( Ra @ Z @ Yb ) ) ) )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X @ Y )
% 0.19/0.47 = ( proces749077512rocess @ A @ B @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_cong
% 0.19/0.47 thf(fact_84_process_Orel__mono__strong,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X: proces634752977rocess @ A,Y: proces634752977rocess @ B,Ra: A > B > $o] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ X @ Y )
% 0.19/0.47 => ( ! [Z: A,Yb: B] :
% 0.19/0.47 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 0.19/0.47 => ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Y ) )
% 0.19/0.47 => ( ( R @ Z @ Yb )
% 0.19/0.47 => ( Ra @ Z @ Yb ) ) ) )
% 0.19/0.47 => ( proces749077512rocess @ A @ B @ Ra @ X @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_mono_strong
% 0.19/0.47 thf(fact_85_process_Orel__refl__strong,axiom,
% 0.19/0.47 ! [A: $tType,X: proces634752977rocess @ A,Ra: A > A > $o] :
% 0.19/0.47 ( ! [Z: A] :
% 0.19/0.47 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 0.19/0.47 => ( Ra @ Z @ Z ) )
% 0.19/0.47 => ( proces749077512rocess @ A @ A @ Ra @ X @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_refl_strong
% 0.19/0.47 thf(fact_86_process_Orel__intros_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X22: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 )
% 0.19/0.47 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_intros(2)
% 0.19/0.47 thf(fact_87_process_Orel__intros_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X12: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 0.19/0.47 ( ( R @ X11 @ Y11 )
% 0.19/0.47 => ( ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 )
% 0.19/0.47 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_intros(1)
% 0.19/0.47 thf(fact_88_process_Omap__comp,axiom,
% 0.19/0.47 ! [B: $tType,C: $tType,A: $tType,G: B > C,F: A > B,V: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces370407749rocess @ B @ C @ G @ ( proces370407749rocess @ A @ B @ F @ V ) )
% 0.19/0.47 = ( proces370407749rocess @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.map_comp
% 0.19/0.47 thf(fact_89_process_Orel__distinct_I2_J,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X12: proces634752977rocess @ B] :
% 0.19/0.47 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X12 ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_distinct(2)
% 0.19/0.47 thf(fact_90_Un__insert__left,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,B4: set @ A,C2: set @ A] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B4 ) @ C2 )
% 0.19/0.47 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B4 @ C2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_insert_left
% 0.19/0.47 thf(fact_91_Un__insert__right,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,A2: A,B4: set @ A] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B4 ) )
% 0.19/0.47 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_insert_right
% 0.19/0.47 thf(fact_92_image__insert,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: B > A,A2: B,B4: set @ B] :
% 0.19/0.47 ( ( image @ B @ A @ F @ ( insert @ B @ A2 @ B4 ) )
% 0.19/0.47 = ( insert @ A @ ( F @ A2 ) @ ( image @ B @ A @ F @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_insert
% 0.19/0.47 thf(fact_93_insert__image,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,X: A,A3: set @ A,F: A > B] :
% 0.19/0.47 ( ( member @ A @ X @ A3 )
% 0.19/0.47 => ( ( insert @ B @ ( F @ X ) @ ( image @ A @ B @ F @ A3 ) )
% 0.19/0.47 = ( image @ A @ B @ F @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_image
% 0.19/0.47 thf(fact_94_Ball__image__comp,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,G: A > $o] :
% 0.19/0.47 ( ( ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ ( image @ B @ A @ F @ A3 ) )
% 0.19/0.47 => ( G @ X2 ) ) )
% 0.19/0.47 = ( ! [X2: B] :
% 0.19/0.47 ( ( member @ B @ X2 @ A3 )
% 0.19/0.47 => ( comp @ A @ $o @ B @ G @ F @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Ball_image_comp
% 0.19/0.47 thf(fact_95_UnCI,axiom,
% 0.19/0.47 ! [A: $tType,C3: A,B4: set @ A,A3: set @ A] :
% 0.19/0.47 ( ( ~ ( member @ A @ C3 @ B4 )
% 0.19/0.47 => ( member @ A @ C3 @ A3 ) )
% 0.19/0.47 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UnCI
% 0.19/0.47 thf(fact_96_image__eqI,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,B3: A,F: B > A,X: B,A3: set @ B] :
% 0.19/0.47 ( ( B3
% 0.19/0.47 = ( F @ X ) )
% 0.19/0.47 => ( ( member @ B @ X @ A3 )
% 0.19/0.47 => ( member @ A @ B3 @ ( image @ B @ A @ F @ A3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_eqI
% 0.19/0.47 thf(fact_97_insert__absorb2,axiom,
% 0.19/0.47 ! [A: $tType,X: A,A3: set @ A] :
% 0.19/0.47 ( ( insert @ A @ X @ ( insert @ A @ X @ A3 ) )
% 0.19/0.47 = ( insert @ A @ X @ A3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_absorb2
% 0.19/0.47 thf(fact_98_insert__iff,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.19/0.47 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 0.19/0.47 = ( ( A2 = B3 )
% 0.19/0.47 | ( member @ A @ A2 @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_iff
% 0.19/0.47 thf(fact_99_insertCI,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 0.19/0.47 ( ( ~ ( member @ A @ A2 @ B4 )
% 0.19/0.47 => ( A2 = B3 ) )
% 0.19/0.47 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insertCI
% 0.19/0.47 thf(fact_100_Un__iff,axiom,
% 0.19/0.47 ! [A: $tType,C3: A,A3: set @ A,B4: set @ A] :
% 0.19/0.47 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 0.19/0.47 = ( ( member @ A @ C3 @ A3 )
% 0.19/0.47 | ( member @ A @ C3 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_iff
% 0.19/0.47 thf(fact_101_rev__image__eqI,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,X: A,A3: set @ A,B3: B,F: A > B] :
% 0.19/0.47 ( ( member @ A @ X @ A3 )
% 0.19/0.47 => ( ( B3
% 0.19/0.47 = ( F @ X ) )
% 0.19/0.47 => ( member @ B @ B3 @ ( image @ A @ B @ F @ A3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rev_image_eqI
% 0.19/0.47 thf(fact_102_ball__imageD,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P2: A > $o] :
% 0.19/0.47 ( ! [X3: A] :
% 0.19/0.47 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A3 ) )
% 0.19/0.47 => ( P2 @ X3 ) )
% 0.19/0.47 => ! [X4: B] :
% 0.19/0.47 ( ( member @ B @ X4 @ A3 )
% 0.19/0.47 => ( P2 @ ( F @ X4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ball_imageD
% 0.19/0.47 thf(fact_103_image__cong,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,M: set @ A,N: set @ A,F: A > B,G: A > B] :
% 0.19/0.47 ( ( M = N )
% 0.19/0.47 => ( ! [X3: A] :
% 0.19/0.47 ( ( member @ A @ X3 @ N )
% 0.19/0.47 => ( ( F @ X3 )
% 0.19/0.47 = ( G @ X3 ) ) )
% 0.19/0.47 => ( ( image @ A @ B @ F @ M )
% 0.19/0.47 = ( image @ A @ B @ G @ N ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_cong
% 0.19/0.47 thf(fact_104_bex__imageD,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P2: A > $o] :
% 0.19/0.47 ( ? [X4: A] :
% 0.19/0.47 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A3 ) )
% 0.19/0.47 & ( P2 @ X4 ) )
% 0.19/0.47 => ? [X3: B] :
% 0.19/0.47 ( ( member @ B @ X3 @ A3 )
% 0.19/0.47 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bex_imageD
% 0.19/0.47 thf(fact_105_image__iff,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Z4: A,F: B > A,A3: set @ B] :
% 0.19/0.47 ( ( member @ A @ Z4 @ ( image @ B @ A @ F @ A3 ) )
% 0.19/0.47 = ( ? [X2: B] :
% 0.19/0.47 ( ( member @ B @ X2 @ A3 )
% 0.19/0.47 & ( Z4
% 0.19/0.47 = ( F @ X2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_iff
% 0.19/0.47 thf(fact_106_imageI,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,X: A,A3: set @ A,F: A > B] :
% 0.19/0.47 ( ( member @ A @ X @ A3 )
% 0.19/0.47 => ( member @ B @ ( F @ X ) @ ( image @ A @ B @ F @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % imageI
% 0.19/0.47 thf(fact_107_mk__disjoint__insert,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.19/0.47 ( ( member @ A @ A2 @ A3 )
% 0.19/0.47 => ? [B5: set @ A] :
% 0.19/0.47 ( ( A3
% 0.19/0.47 = ( insert @ A @ A2 @ B5 ) )
% 0.19/0.47 & ~ ( member @ A @ A2 @ B5 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % mk_disjoint_insert
% 0.19/0.47 thf(fact_108_insert__commute,axiom,
% 0.19/0.47 ! [A: $tType,X: A,Y: A,A3: set @ A] :
% 0.19/0.47 ( ( insert @ A @ X @ ( insert @ A @ Y @ A3 ) )
% 0.19/0.47 = ( insert @ A @ Y @ ( insert @ A @ X @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_commute
% 0.19/0.47 thf(fact_109_insert__eq__iff,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,A3: set @ A,B3: A,B4: set @ A] :
% 0.19/0.47 ( ~ ( member @ A @ A2 @ A3 )
% 0.19/0.47 => ( ~ ( member @ A @ B3 @ B4 )
% 0.19/0.47 => ( ( ( insert @ A @ A2 @ A3 )
% 0.19/0.47 = ( insert @ A @ B3 @ B4 ) )
% 0.19/0.47 = ( ( ( A2 = B3 )
% 0.19/0.47 => ( A3 = B4 ) )
% 0.19/0.47 & ( ( A2 != B3 )
% 0.19/0.47 => ? [C4: set @ A] :
% 0.19/0.47 ( ( A3
% 0.19/0.47 = ( insert @ A @ B3 @ C4 ) )
% 0.19/0.47 & ~ ( member @ A @ B3 @ C4 )
% 0.19/0.47 & ( B4
% 0.19/0.47 = ( insert @ A @ A2 @ C4 ) )
% 0.19/0.47 & ~ ( member @ A @ A2 @ C4 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_eq_iff
% 0.19/0.47 thf(fact_110_insert__absorb,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.19/0.47 ( ( member @ A @ A2 @ A3 )
% 0.19/0.47 => ( ( insert @ A @ A2 @ A3 )
% 0.19/0.47 = A3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_absorb
% 0.19/0.47 thf(fact_111_insert__ident,axiom,
% 0.19/0.47 ! [A: $tType,X: A,A3: set @ A,B4: set @ A] :
% 0.19/0.47 ( ~ ( member @ A @ X @ A3 )
% 0.19/0.47 => ( ~ ( member @ A @ X @ B4 )
% 0.19/0.47 => ( ( ( insert @ A @ X @ A3 )
% 0.19/0.47 = ( insert @ A @ X @ B4 ) )
% 0.19/0.47 = ( A3 = B4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_ident
% 0.19/0.47 thf(fact_112_Set_Oset__insert,axiom,
% 0.19/0.47 ! [A: $tType,X: A,A3: set @ A] :
% 0.19/0.47 ( ( member @ A @ X @ A3 )
% 0.19/0.47 => ~ ! [B5: set @ A] :
% 0.19/0.47 ( ( A3
% 0.19/0.47 = ( insert @ A @ X @ B5 ) )
% 0.19/0.47 => ( member @ A @ X @ B5 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Set.set_insert
% 0.19/0.47 thf(fact_113_insertI2,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 0.19/0.47 ( ( member @ A @ A2 @ B4 )
% 0.19/0.47 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insertI2
% 0.19/0.47 thf(fact_114_insertI1,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,B4: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % insertI1
% 0.19/0.47 thf(fact_115_insertE,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.19/0.47 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 0.19/0.47 => ( ( A2 != B3 )
% 0.19/0.47 => ( member @ A @ A2 @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insertE
% 0.19/0.47 thf(fact_116_comp__apply__eq,axiom,
% 0.19/0.47 ! [B: $tType,D: $tType,A: $tType,C: $tType,F: B > A,G: C > B,X: C,H: D > A,K: C > D] :
% 0.19/0.47 ( ( ( F @ ( G @ X ) )
% 0.19/0.47 = ( H @ ( K @ X ) ) )
% 0.19/0.47 => ( ( comp @ B @ A @ C @ F @ G @ X )
% 0.19/0.47 = ( comp @ D @ A @ C @ H @ K @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_apply_eq
% 0.19/0.47 thf(fact_117_Ball__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ball @ A )
% 0.19/0.47 = ( ^ [A5: set @ A,P3: A > $o] :
% 0.19/0.47 ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ A5 )
% 0.19/0.47 => ( P3 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Ball_def
% 0.19/0.47 thf(fact_118_Un__left__commute,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C2: set @ A] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B4 @ C2 ) )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A3 @ C2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_left_commute
% 0.19/0.47 thf(fact_119_Un__left__absorb,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_left_absorb
% 0.19/0.47 thf(fact_120_Un__commute,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.19/0.47 = ( ^ [A5: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A5 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_commute
% 0.19/0.47 thf(fact_121_Un__absorb,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.19/0.47 = A3 ) ).
% 0.19/0.47
% 0.19/0.47 % Un_absorb
% 0.19/0.47 thf(fact_122_Un__assoc,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C2: set @ A] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) @ C2 )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B4 @ C2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_assoc
% 0.19/0.47 thf(fact_123_ball__Un,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,P2: A > $o] :
% 0.19/0.47 ( ( ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 0.19/0.47 => ( P2 @ X2 ) ) )
% 0.19/0.47 = ( ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ A3 )
% 0.19/0.47 => ( P2 @ X2 ) )
% 0.19/0.47 & ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ B4 )
% 0.19/0.47 => ( P2 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ball_Un
% 0.19/0.47 thf(fact_124_bex__Un,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,P2: A > $o] :
% 0.19/0.47 ( ( ? [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 0.19/0.47 & ( P2 @ X2 ) ) )
% 0.19/0.47 = ( ? [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ A3 )
% 0.19/0.47 & ( P2 @ X2 ) )
% 0.19/0.47 | ? [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ B4 )
% 0.19/0.47 & ( P2 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bex_Un
% 0.19/0.47 thf(fact_125_UnI2,axiom,
% 0.19/0.47 ! [A: $tType,C3: A,B4: set @ A,A3: set @ A] :
% 0.19/0.47 ( ( member @ A @ C3 @ B4 )
% 0.19/0.47 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UnI2
% 0.19/0.47 thf(fact_126_UnI1,axiom,
% 0.19/0.47 ! [A: $tType,C3: A,A3: set @ A,B4: set @ A] :
% 0.19/0.47 ( ( member @ A @ C3 @ A3 )
% 0.19/0.47 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UnI1
% 0.19/0.47 thf(fact_127_UnE,axiom,
% 0.19/0.47 ! [A: $tType,C3: A,A3: set @ A,B4: set @ A] :
% 0.19/0.47 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 0.19/0.47 => ( ~ ( member @ A @ C3 @ A3 )
% 0.19/0.47 => ( member @ A @ C3 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UnE
% 0.19/0.47 thf(fact_128_image__Un,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,B4: set @ B] :
% 0.19/0.47 ( ( image @ B @ A @ F @ ( sup_sup @ ( set @ B ) @ A3 @ B4 ) )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ ( image @ B @ A @ F @ A3 ) @ ( image @ B @ A @ F @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_Un
% 0.19/0.47 thf(fact_129_not__False__in__image__Ball,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o,A3: set @ A] :
% 0.19/0.47 ( ( ~ ( member @ $o @ $false @ ( image @ A @ $o @ P2 @ A3 ) ) )
% 0.19/0.47 = ( ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ A3 )
% 0.19/0.47 => ( P2 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_False_in_image_Ball
% 0.19/0.47 thf(fact_130_comp__apply,axiom,
% 0.19/0.47 ! [C: $tType,A: $tType,B: $tType] :
% 0.19/0.47 ( ( comp @ B @ A @ C )
% 0.19/0.47 = ( ^ [F3: B > A,G2: C > B,X2: C] : ( F3 @ ( G2 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_apply
% 0.19/0.47 thf(fact_131_sup_Oright__idem,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A2: A,B3: A] :
% 0.19/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ B3 )
% 0.19/0.47 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup.right_idem
% 0.19/0.47 thf(fact_132_sup__left__idem,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A,Y: A] :
% 0.19/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.19/0.47 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_left_idem
% 0.19/0.47 thf(fact_133_sup_Oleft__idem,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A2: A,B3: A] :
% 0.19/0.47 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) )
% 0.19/0.47 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup.left_idem
% 0.19/0.47 thf(fact_134_sup__apply,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.19/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.19/0.47 = ( ^ [F3: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F3 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_apply
% 0.19/0.47 thf(fact_135_sup_Oidem,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A2: A] :
% 0.19/0.47 ( ( sup_sup @ A @ A2 @ A2 )
% 0.19/0.47 = A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup.idem
% 0.19/0.47 thf(fact_136_sup__idem,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A] :
% 0.19/0.47 ( ( sup_sup @ A @ X @ X )
% 0.19/0.47 = X ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_idem
% 0.19/0.47 thf(fact_137_Inf_OINF__cong,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,A3: set @ B,B4: set @ B,C2: B > A,D2: B > A,Inf: ( set @ A ) > A] :
% 0.19/0.47 ( ( A3 = B4 )
% 0.19/0.47 => ( ! [X3: B] :
% 0.19/0.47 ( ( member @ B @ X3 @ B4 )
% 0.19/0.47 => ( ( C2 @ X3 )
% 0.19/0.47 = ( D2 @ X3 ) ) )
% 0.19/0.47 => ( ( Inf @ ( image @ B @ A @ C2 @ A3 ) )
% 0.19/0.47 = ( Inf @ ( image @ B @ A @ D2 @ B4 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Inf.INF_cong
% 0.19/0.47 thf(fact_138_Sup_OSUP__cong,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,A3: set @ B,B4: set @ B,C2: B > A,D2: B > A,Sup: ( set @ A ) > A] :
% 0.19/0.47 ( ( A3 = B4 )
% 0.19/0.47 => ( ! [X3: B] :
% 0.19/0.47 ( ( member @ B @ X3 @ B4 )
% 0.19/0.47 => ( ( C2 @ X3 )
% 0.19/0.47 = ( D2 @ X3 ) ) )
% 0.19/0.47 => ( ( Sup @ ( image @ B @ A @ C2 @ A3 ) )
% 0.19/0.47 = ( Sup @ ( image @ B @ A @ D2 @ B4 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup.SUP_cong
% 0.19/0.47 thf(fact_139_inf__sup__aci_I8_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( lattice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A,Y: A] :
% 0.19/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.19/0.47 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % inf_sup_aci(8)
% 0.19/0.47 thf(fact_140_inf__sup__aci_I7_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( lattice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A,Y: A,Z4: A] :
% 0.19/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z4 ) )
% 0.19/0.47 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % inf_sup_aci(7)
% 0.19/0.47 thf(fact_141_inf__sup__aci_I6_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( lattice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A,Y: A,Z4: A] :
% 0.19/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z4 )
% 0.19/0.47 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % inf_sup_aci(6)
% 0.19/0.47 thf(fact_142_inf__sup__aci_I5_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( lattice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ( ( sup_sup @ A )
% 0.19/0.47 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % inf_sup_aci(5)
% 0.19/0.47 thf(fact_143_sup__fun__def,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.19/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.19/0.47 = ( ^ [F3: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F3 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_fun_def
% 0.19/0.47 thf(fact_144_sup_Oassoc,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.19/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ C3 )
% 0.19/0.47 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup.assoc
% 0.19/0.47 thf(fact_145_sup__assoc,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A,Y: A,Z4: A] :
% 0.19/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z4 )
% 0.19/0.47 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_assoc
% 0.19/0.47 thf(fact_146_sup_Ocommute,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ( ( sup_sup @ A )
% 0.19/0.47 = ( ^ [A4: A,B2: A] : ( sup_sup @ A @ B2 @ A4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup.commute
% 0.19/0.47 thf(fact_147_sup__commute,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ( ( sup_sup @ A )
% 0.19/0.47 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_commute
% 0.19/0.47 thf(fact_148_sup_Oleft__commute,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.19/0.47 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A2 @ C3 ) )
% 0.19/0.47 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup.left_commute
% 0.19/0.47 thf(fact_149_sup__left__commute,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A,Y: A,Z4: A] :
% 0.19/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z4 ) )
% 0.19/0.47 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_left_commute
% 0.19/0.47 thf(fact_150_comp__def,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.19/0.47 ( ( comp @ B @ C @ A )
% 0.19/0.47 = ( ^ [F3: B > C,G2: A > B,X2: A] : ( F3 @ ( G2 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_def
% 0.19/0.47 thf(fact_151_comp__assoc,axiom,
% 0.19/0.47 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H: A > C] :
% 0.19/0.47 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H )
% 0.19/0.47 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_assoc
% 0.19/0.47 thf(fact_152_comp__eq__dest,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B3: A > C,C3: D > B,D3: A > D,V: A] :
% 0.19/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B3 )
% 0.19/0.47 = ( comp @ D @ B @ A @ C3 @ D3 ) )
% 0.19/0.47 => ( ( A2 @ ( B3 @ V ) )
% 0.19/0.47 = ( C3 @ ( D3 @ V ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_eq_dest
% 0.19/0.47 thf(fact_153_comp__eq__elim,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B3: A > C,C3: D > B,D3: A > D] :
% 0.19/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B3 )
% 0.19/0.47 = ( comp @ D @ B @ A @ C3 @ D3 ) )
% 0.19/0.47 => ! [V2: A] :
% 0.19/0.47 ( ( A2 @ ( B3 @ V2 ) )
% 0.19/0.47 = ( C3 @ ( D3 @ V2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_eq_elim
% 0.19/0.47 thf(fact_154_comp__eq__dest__lhs,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B3: A > C,C3: A > B,V: A] :
% 0.19/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B3 )
% 0.19/0.47 = C3 )
% 0.19/0.47 => ( ( A2 @ ( B3 @ V ) )
% 0.19/0.47 = ( C3 @ V ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_eq_dest_lhs
% 0.19/0.47 thf(fact_155_image__comp,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,C: $tType,F: B > A,G: C > B,R3: set @ C] :
% 0.19/0.47 ( ( image @ B @ A @ F @ ( image @ C @ B @ G @ R3 ) )
% 0.19/0.47 = ( image @ C @ A @ ( comp @ B @ A @ C @ F @ G ) @ R3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_comp
% 0.19/0.47 thf(fact_156_image__eq__imp__comp,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: B > A,A3: set @ B,G: C > A,B4: set @ C,H: A > D] :
% 0.19/0.47 ( ( ( image @ B @ A @ F @ A3 )
% 0.19/0.47 = ( image @ C @ A @ G @ B4 ) )
% 0.19/0.47 => ( ( image @ B @ D @ ( comp @ A @ D @ B @ H @ F ) @ A3 )
% 0.19/0.47 = ( image @ C @ D @ ( comp @ A @ D @ C @ H @ G ) @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_eq_imp_comp
% 0.19/0.47 thf(fact_157_Inf_OINF__image,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,C: $tType,Inf: ( set @ A ) > A,G: B > A,F: C > B,A3: set @ C] :
% 0.19/0.47 ( ( Inf @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A3 ) ) )
% 0.19/0.47 = ( Inf @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Inf.INF_image
% 0.19/0.47 thf(fact_158_Sup_OSUP__image,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,C: $tType,Sup: ( set @ A ) > A,G: B > A,F: C > B,A3: set @ C] :
% 0.19/0.47 ( ( Sup @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A3 ) ) )
% 0.19/0.47 = ( Sup @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup.SUP_image
% 0.19/0.47 thf(fact_159_ball__reg,axiom,
% 0.19/0.47 ! [A: $tType,R: set @ A,P2: A > $o,Q: A > $o] :
% 0.19/0.47 ( ! [X3: A] :
% 0.19/0.47 ( ( member @ A @ X3 @ R )
% 0.19/0.47 => ( ( P2 @ X3 )
% 0.19/0.47 => ( Q @ X3 ) ) )
% 0.19/0.47 => ( ! [X3: A] :
% 0.19/0.47 ( ( member @ A @ X3 @ R )
% 0.19/0.47 => ( P2 @ X3 ) )
% 0.19/0.47 => ! [X4: A] :
% 0.19/0.47 ( ( member @ A @ X4 @ R )
% 0.19/0.47 => ( Q @ X4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ball_reg
% 0.19/0.47 thf(fact_160_comp__cong,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,D: $tType,A: $tType,E: $tType,F: B > A,G: C > B,X: C,F4: D > A,G3: E > D,X5: E] :
% 0.19/0.47 ( ( ( F @ ( G @ X ) )
% 0.19/0.47 = ( F4 @ ( G3 @ X5 ) ) )
% 0.19/0.47 => ( ( comp @ B @ A @ C @ F @ G @ X )
% 0.19/0.47 = ( comp @ D @ A @ E @ F4 @ G3 @ X5 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_cong
% 0.19/0.47 thf(fact_161_fun_Omap__comp,axiom,
% 0.19/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 0.19/0.47 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 0.19/0.47 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.19/0.47
% 0.19/0.47 % fun.map_comp
% 0.19/0.47 thf(fact_162_type__copy__map__cong0,axiom,
% 0.19/0.47 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X: C,N: D > A,H: C > D,F: A > E] :
% 0.19/0.47 ( ( ( M @ ( G @ X ) )
% 0.19/0.47 = ( N @ ( H @ X ) ) )
% 0.19/0.47 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F @ M ) @ G @ X )
% 0.19/0.47 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F @ N ) @ H @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % type_copy_map_cong0
% 0.19/0.47 thf(fact_163_rewriteR__comp__comp2,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R1: D > B,R22: A > D,F: B > E,L: D > E] :
% 0.19/0.47 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.19/0.47 = ( comp @ D @ B @ A @ R1 @ R22 ) )
% 0.19/0.47 => ( ( ( comp @ B @ E @ D @ F @ R1 )
% 0.19/0.47 = L )
% 0.19/0.47 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H )
% 0.19/0.47 = ( comp @ D @ E @ A @ L @ R22 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rewriteR_comp_comp2
% 0.19/0.47 thf(fact_164_rewriteL__comp__comp2,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H: E > A,R3: E > D] :
% 0.19/0.47 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.19/0.47 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.19/0.47 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 0.19/0.47 = R3 )
% 0.19/0.47 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H ) )
% 0.19/0.47 = ( comp @ D @ B @ E @ L1 @ R3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rewriteL_comp_comp2
% 0.19/0.47 thf(fact_165_rewriteR__comp__comp,axiom,
% 0.19/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R3: A > B,F: B > D] :
% 0.19/0.47 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.19/0.47 = R3 )
% 0.19/0.47 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H )
% 0.19/0.47 = ( comp @ B @ D @ A @ F @ R3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rewriteR_comp_comp
% 0.19/0.47 thf(fact_166_rewriteL__comp__comp,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H: D > A] :
% 0.19/0.47 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.19/0.47 = L )
% 0.19/0.47 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H ) )
% 0.19/0.47 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rewriteL_comp_comp
% 0.19/0.47 thf(fact_167_process_Opred__rel,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces1205983068rocess @ A )
% 0.19/0.47 = ( ^ [P3: A > $o,X2: proces634752977rocess @ A] : ( proces749077512rocess @ A @ A @ ( bNF_eq_onp @ A @ P3 ) @ X2 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.pred_rel
% 0.19/0.47 thf(fact_168_Sup__insert,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A2: A,A3: set @ A] :
% 0.19/0.47 ( ( complete_Sup_Sup @ A @ ( insert @ A @ A2 @ A3 ) )
% 0.19/0.47 = ( sup_sup @ A @ A2 @ ( complete_Sup_Sup @ A @ A3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup_insert
% 0.19/0.47 thf(fact_169_SUP__image,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,C: $tType] :
% 0.19/0.47 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [G: B > A,F: C > B,A3: set @ C] :
% 0.19/0.47 ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A3 ) ) )
% 0.19/0.47 = ( complete_Sup_Sup @ A @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % SUP_image
% 0.19/0.47 thf(fact_170_Union__Un__distrib,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ ( set @ A ),B4: set @ ( set @ A )] :
% 0.19/0.47 ( ( complete_Sup_Sup @ ( set @ A ) @ ( sup_sup @ ( set @ ( set @ A ) ) @ A3 @ B4 ) )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ ( complete_Sup_Sup @ ( set @ A ) @ A3 ) @ ( complete_Sup_Sup @ ( set @ A ) @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Union_Un_distrib
% 0.19/0.47 thf(fact_171_SUP__cong,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A3: set @ B,B4: set @ B,C2: B > A,D2: B > A] :
% 0.19/0.47 ( ( A3 = B4 )
% 0.19/0.47 => ( ! [X3: B] :
% 0.19/0.47 ( ( member @ B @ X3 @ B4 )
% 0.19/0.47 => ( ( C2 @ X3 )
% 0.19/0.47 = ( D2 @ X3 ) ) )
% 0.19/0.47 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ C2 @ A3 ) )
% 0.19/0.47 = ( complete_Sup_Sup @ A @ ( image @ B @ A @ D2 @ B4 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % SUP_cong
% 0.19/0.47 thf(fact_172_process_Orel__eq__onp,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o] :
% 0.19/0.47 ( ( proces749077512rocess @ A @ A @ ( bNF_eq_onp @ A @ P2 ) )
% 0.19/0.47 = ( bNF_eq_onp @ ( proces634752977rocess @ A ) @ ( proces1205983068rocess @ A @ P2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.rel_eq_onp
% 0.19/0.47 thf(fact_173_eq__onp__eqD,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o,Q: A > A > $o,X: A] :
% 0.19/0.47 ( ( ( bNF_eq_onp @ A @ P2 )
% 0.19/0.47 = Q )
% 0.19/0.47 => ( ( P2 @ X )
% 0.19/0.47 = ( Q @ X @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % eq_onp_eqD
% 0.19/0.47 thf(fact_174_eq__onp__mono0,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,P2: A > $o,Q: A > $o] :
% 0.19/0.47 ( ! [X3: A] :
% 0.19/0.47 ( ( member @ A @ X3 @ A3 )
% 0.19/0.47 => ( ( P2 @ X3 )
% 0.19/0.47 => ( Q @ X3 ) ) )
% 0.19/0.47 => ! [X4: A] :
% 0.19/0.47 ( ( member @ A @ X4 @ A3 )
% 0.19/0.47 => ! [Xa3: A] :
% 0.19/0.47 ( ( member @ A @ Xa3 @ A3 )
% 0.19/0.47 => ( ( bNF_eq_onp @ A @ P2 @ X4 @ Xa3 )
% 0.19/0.47 => ( bNF_eq_onp @ A @ Q @ X4 @ Xa3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % eq_onp_mono0
% 0.19/0.47 thf(fact_175_eq__onp__to__eq,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o,X: A,Y: A] :
% 0.19/0.47 ( ( bNF_eq_onp @ A @ P2 @ X @ Y )
% 0.19/0.47 => ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % eq_onp_to_eq
% 0.19/0.47 thf(fact_176_eq__onp__same__args,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o,X: A] :
% 0.19/0.47 ( ( bNF_eq_onp @ A @ P2 @ X @ X )
% 0.19/0.47 = ( P2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % eq_onp_same_args
% 0.19/0.47 thf(fact_177_Union__insert,axiom,
% 0.19/0.47 ! [A: $tType,A2: set @ A,B4: set @ ( set @ A )] :
% 0.19/0.47 ( ( complete_Sup_Sup @ ( set @ A ) @ ( insert @ ( set @ A ) @ A2 @ B4 ) )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ ( complete_Sup_Sup @ ( set @ A ) @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Union_insert
% 0.19/0.47 thf(fact_178_Sup__union__distrib,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A3: set @ A,B4: set @ A] :
% 0.19/0.47 ( ( complete_Sup_Sup @ A @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 0.19/0.47 = ( sup_sup @ A @ ( complete_Sup_Sup @ A @ A3 ) @ ( complete_Sup_Sup @ A @ B4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup_union_distrib
% 0.19/0.47 thf(fact_179_Union__image__insert,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: B > ( set @ A ),A2: B,B4: set @ B] :
% 0.19/0.47 ( ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ ( insert @ B @ A2 @ B4 ) ) )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ ( F @ A2 ) @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ B4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Union_image_insert
% 0.19/0.47 thf(fact_180_vimage2p__comp,axiom,
% 0.19/0.47 ! [E: $tType,D: $tType,F5: $tType,A: $tType,C: $tType,B: $tType,G4: $tType,F1: F5 > A,F2: D > F5,G1: G4 > B,G22: E > G4] :
% 0.19/0.47 ( ( bNF_vimage2p @ D @ A @ E @ B @ C @ ( comp @ F5 @ A @ D @ F1 @ F2 ) @ ( comp @ G4 @ B @ E @ G1 @ G22 ) )
% 0.19/0.47 = ( comp @ ( F5 > G4 > C ) @ ( D > E > C ) @ ( A > B > C ) @ ( bNF_vimage2p @ D @ F5 @ E @ G4 @ C @ F2 @ G22 ) @ ( bNF_vimage2p @ F5 @ A @ G4 @ B @ C @ F1 @ G1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % vimage2p_comp
% 0.19/0.47 thf(fact_181_INF__image,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,C: $tType] :
% 0.19/0.47 ( ( complete_Inf @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [G: B > A,F: C > B,A3: set @ C] :
% 0.19/0.47 ( ( complete_Inf_Inf @ A @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A3 ) ) )
% 0.19/0.47 = ( complete_Inf_Inf @ A @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % INF_image
% 0.19/0.47 thf(fact_182_SUP__id__eq,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A3: set @ A] :
% 0.19/0.47 ( ( complete_Sup_Sup @ A @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 0.19/0.47 = ( complete_Sup_Sup @ A @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % SUP_id_eq
% 0.19/0.47 thf(fact_183_UN__ball__bex__simps_I3_J,axiom,
% 0.19/0.47 ! [D: $tType,A3: set @ ( set @ D ),P2: D > $o] :
% 0.19/0.47 ( ( ? [X2: D] :
% 0.19/0.47 ( ( member @ D @ X2 @ ( complete_Sup_Sup @ ( set @ D ) @ A3 ) )
% 0.19/0.47 & ( P2 @ X2 ) ) )
% 0.19/0.47 = ( ? [X2: set @ D] :
% 0.19/0.47 ( ( member @ ( set @ D ) @ X2 @ A3 )
% 0.19/0.47 & ? [Y2: D] :
% 0.19/0.47 ( ( member @ D @ Y2 @ X2 )
% 0.19/0.47 & ( P2 @ Y2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UN_ball_bex_simps(3)
% 0.19/0.47 thf(fact_184_UN__ball__bex__simps_I1_J,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ ( set @ A ),P2: A > $o] :
% 0.19/0.47 ( ( ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ ( complete_Sup_Sup @ ( set @ A ) @ A3 ) )
% 0.19/0.47 => ( P2 @ X2 ) ) )
% 0.19/0.47 = ( ! [X2: set @ A] :
% 0.19/0.47 ( ( member @ ( set @ A ) @ X2 @ A3 )
% 0.19/0.47 => ! [Y2: A] :
% 0.19/0.47 ( ( member @ A @ Y2 @ X2 )
% 0.19/0.47 => ( P2 @ Y2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UN_ball_bex_simps(1)
% 0.19/0.47 thf(fact_185_UnionI,axiom,
% 0.19/0.47 ! [A: $tType,X6: set @ A,C2: set @ ( set @ A ),A3: A] :
% 0.19/0.47 ( ( member @ ( set @ A ) @ X6 @ C2 )
% 0.19/0.47 => ( ( member @ A @ A3 @ X6 )
% 0.19/0.47 => ( member @ A @ A3 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UnionI
% 0.19/0.47 thf(fact_186_Union__iff,axiom,
% 0.19/0.47 ! [A: $tType,A3: A,C2: set @ ( set @ A )] :
% 0.19/0.47 ( ( member @ A @ A3 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) )
% 0.19/0.47 = ( ? [X2: set @ A] :
% 0.19/0.47 ( ( member @ ( set @ A ) @ X2 @ C2 )
% 0.19/0.47 & ( member @ A @ A3 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Union_iff
% 0.19/0.47 thf(fact_187_id__apply,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( id @ A )
% 0.19/0.47 = ( ^ [X2: A] : X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % id_apply
% 0.19/0.47 thf(fact_188_image__id,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( image @ A @ A @ ( id @ A ) )
% 0.19/0.47 = ( id @ ( set @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_id
% 0.19/0.47 thf(fact_189_ball__UN,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,B4: B > ( set @ A ),A3: set @ B,P2: A > $o] :
% 0.19/0.47 ( ( ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B4 @ A3 ) ) )
% 0.19/0.47 => ( P2 @ X2 ) ) )
% 0.19/0.47 = ( ! [X2: B] :
% 0.19/0.47 ( ( member @ B @ X2 @ A3 )
% 0.19/0.47 => ! [Y2: A] :
% 0.19/0.47 ( ( member @ A @ Y2 @ ( B4 @ X2 ) )
% 0.19/0.47 => ( P2 @ Y2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ball_UN
% 0.19/0.47 thf(fact_190_bex__UN,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,B4: B > ( set @ A ),A3: set @ B,P2: A > $o] :
% 0.19/0.47 ( ( ? [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B4 @ A3 ) ) )
% 0.19/0.47 & ( P2 @ X2 ) ) )
% 0.19/0.47 = ( ? [X2: B] :
% 0.19/0.47 ( ( member @ B @ X2 @ A3 )
% 0.19/0.47 & ? [Y2: A] :
% 0.19/0.47 ( ( member @ A @ Y2 @ ( B4 @ X2 ) )
% 0.19/0.47 & ( P2 @ Y2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bex_UN
% 0.19/0.47 thf(fact_191_UN__ball__bex__simps_I2_J,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,B4: B > ( set @ C ),A3: set @ B,P2: C > $o] :
% 0.19/0.47 ( ( ! [X2: C] :
% 0.19/0.47 ( ( member @ C @ X2 @ ( complete_Sup_Sup @ ( set @ C ) @ ( image @ B @ ( set @ C ) @ B4 @ A3 ) ) )
% 0.19/0.47 => ( P2 @ X2 ) ) )
% 0.19/0.47 = ( ! [X2: B] :
% 0.19/0.47 ( ( member @ B @ X2 @ A3 )
% 0.19/0.47 => ! [Y2: C] :
% 0.19/0.47 ( ( member @ C @ Y2 @ ( B4 @ X2 ) )
% 0.19/0.47 => ( P2 @ Y2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UN_ball_bex_simps(2)
% 0.19/0.47 thf(fact_192_UN__ball__bex__simps_I4_J,axiom,
% 0.19/0.47 ! [F5: $tType,E: $tType,B4: E > ( set @ F5 ),A3: set @ E,P2: F5 > $o] :
% 0.19/0.47 ( ( ? [X2: F5] :
% 0.19/0.47 ( ( member @ F5 @ X2 @ ( complete_Sup_Sup @ ( set @ F5 ) @ ( image @ E @ ( set @ F5 ) @ B4 @ A3 ) ) )
% 0.19/0.47 & ( P2 @ X2 ) ) )
% 0.19/0.47 = ( ? [X2: E] :
% 0.19/0.47 ( ( member @ E @ X2 @ A3 )
% 0.19/0.47 & ? [Y2: F5] :
% 0.19/0.47 ( ( member @ F5 @ Y2 @ ( B4 @ X2 ) )
% 0.19/0.47 & ( P2 @ Y2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UN_ball_bex_simps(4)
% 0.19/0.47 thf(fact_193_fun_Omap__id,axiom,
% 0.19/0.47 ! [A: $tType,D: $tType,T: D > A] :
% 0.19/0.47 ( ( comp @ A @ A @ D @ ( id @ A ) @ T )
% 0.19/0.47 = T ) ).
% 0.19/0.47
% 0.19/0.47 % fun.map_id
% 0.19/0.47 thf(fact_194_id__comp,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,G: A > B] :
% 0.19/0.47 ( ( comp @ B @ B @ A @ ( id @ B ) @ G )
% 0.19/0.47 = G ) ).
% 0.19/0.47
% 0.19/0.47 % id_comp
% 0.19/0.47 thf(fact_195_comp__id,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F: A > B] :
% 0.19/0.47 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 0.19/0.47 = F ) ).
% 0.19/0.47
% 0.19/0.47 % comp_id
% 0.19/0.47 thf(fact_196_INF__id__eq,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( complete_Inf @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A3: set @ A] :
% 0.19/0.47 ( ( complete_Inf_Inf @ A @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 0.19/0.47 = ( complete_Inf_Inf @ A @ A3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % INF_id_eq
% 0.19/0.47 thf(fact_197_UnionE,axiom,
% 0.19/0.47 ! [A: $tType,A3: A,C2: set @ ( set @ A )] :
% 0.19/0.47 ( ( member @ A @ A3 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) )
% 0.19/0.47 => ~ ! [X7: set @ A] :
% 0.19/0.47 ( ( member @ A @ A3 @ X7 )
% 0.19/0.47 => ~ ( member @ ( set @ A ) @ X7 @ C2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % UnionE
% 0.19/0.47 thf(fact_198_fun_Omap__id0,axiom,
% 0.19/0.47 ! [A: $tType,D: $tType] :
% 0.19/0.47 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 0.19/0.47 = ( id @ ( D > A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fun.map_id0
% 0.19/0.47 thf(fact_199_process_Omap__id0,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( proces370407749rocess @ A @ A @ ( id @ A ) )
% 0.19/0.47 = ( id @ ( proces634752977rocess @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % process.map_id0
% 0.19/0.47 thf(fact_200_process_Omap__id,axiom,
% 0.19/0.47 ! [A: $tType,T: proces634752977rocess @ A] :
% 0.19/0.47 ( ( proces370407749rocess @ A @ A @ ( id @ A ) @ T )
% 0.19/0.47 = T ) ).
% 0.19/0.47
% 0.19/0.47 % process.map_id
% 0.19/0.47 thf(fact_201_Inf_OINF__id__eq,axiom,
% 0.19/0.47 ! [A: $tType,Inf: ( set @ A ) > A,A3: set @ A] :
% 0.19/0.47 ( ( Inf @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 0.19/0.47 = ( Inf @ A3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Inf.INF_id_eq
% 0.19/0.47 thf(fact_202_Sup_OSUP__id__eq,axiom,
% 0.19/0.47 ! [A: $tType,Sup: ( set @ A ) > A,A3: set @ A] :
% 0.19/0.47 ( ( Sup @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 0.19/0.47 = ( Sup @ A3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup.SUP_id_eq
% 0.19/0.47 thf(fact_203_INF__cong,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( complete_Inf @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A3: set @ B,B4: set @ B,C2: B > A,D2: B > A] :
% 0.19/0.47 ( ( A3 = B4 )
% 0.19/0.47 => ( ! [X3: B] :
% 0.19/0.47 ( ( member @ B @ X3 @ B4 )
% 0.19/0.47 => ( ( C2 @ X3 )
% 0.19/0.47 = ( D2 @ X3 ) ) )
% 0.19/0.47 => ( ( complete_Inf_Inf @ A @ ( image @ B @ A @ C2 @ A3 ) )
% 0.19/0.47 = ( complete_Inf_Inf @ A @ ( image @ B @ A @ D2 @ B4 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % INF_cong
% 0.19/0.47 thf(fact_204_eq__id__iff,axiom,
% 0.19/0.47 ! [A: $tType,F: A > A] :
% 0.19/0.47 ( ( ! [X2: A] :
% 0.19/0.47 ( ( F @ X2 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 = ( F
% 0.19/0.47 = ( id @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % eq_id_iff
% 0.19/0.47 thf(fact_205_id__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( id @ A )
% 0.19/0.47 = ( ^ [X2: A] : X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % id_def
% 0.19/0.47 thf(fact_206_comp__eq__id__dest,axiom,
% 0.19/0.47 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B3: A > C,C3: A > B,V: A] :
% 0.19/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B3 )
% 0.19/0.47 = ( comp @ B @ B @ A @ ( id @ B ) @ C3 ) )
% 0.19/0.47 => ( ( A2 @ ( B3 @ V ) )
% 0.19/0.47 = ( C3 @ V ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % comp_eq_id_dest
% 0.19/0.47 thf(fact_207_pointfree__idE,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F: B > A,G: A > B,X: A] :
% 0.19/0.47 ( ( ( comp @ B @ A @ A @ F @ G )
% 0.19/0.47 = ( id @ A ) )
% 0.19/0.47 => ( ( F @ ( G @ X ) )
% 0.19/0.47 = X ) ) ).
% 0.19/0.47
% 0.19/0.47 % pointfree_idE
% 0.19/0.47 thf(fact_208_member__bind,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X: A,P2: set @ B,F: B > ( set @ A )] :
% 0.19/0.47 ( ( member @ A @ X @ ( bind @ B @ A @ P2 @ F ) )
% 0.19/0.47 = ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ P2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % member_bind
% 0.19/0.47 thf(fact_209_Sup__SUP__eq,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( complete_Sup_Sup @ ( A > $o ) )
% 0.19/0.47 = ( ^ [S: set @ ( A > $o ),X2: A] : ( member @ A @ X2 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ ( A > $o ) @ ( set @ A ) @ ( collect @ A ) @ S ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup_SUP_eq
% 0.19/0.47 thf(fact_210_Union__image__empty,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,A3: set @ A,F: B > ( set @ A )] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ ( bot_bot @ ( set @ B ) ) ) ) )
% 0.19/0.47 = A3 ) ).
% 0.19/0.47
% 0.19/0.47 % Union_image_empty
% 0.19/0.47 thf(fact_211_empty__iff,axiom,
% 0.19/0.47 ! [A: $tType,C3: A] :
% 0.19/0.47 ~ ( member @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % empty_iff
% 0.19/0.47 thf(fact_212_all__not__in__conv,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A] :
% 0.19/0.47 ( ( ! [X2: A] :
% 0.19/0.47 ~ ( member @ A @ X2 @ A3 ) )
% 0.19/0.47 = ( A3
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % all_not_in_conv
% 0.19/0.47 thf(fact_213_Collect__empty__eq,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o] :
% 0.19/0.47 ( ( ( collect @ A @ P2 )
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 = ( ! [X2: A] :
% 0.19/0.47 ~ ( P2 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_empty_eq
% 0.19/0.47 thf(fact_214_empty__Collect__eq,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o] :
% 0.19/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.19/0.47 = ( collect @ A @ P2 ) )
% 0.19/0.47 = ( ! [X2: A] :
% 0.19/0.47 ~ ( P2 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % empty_Collect_eq
% 0.19/0.47 thf(fact_215_Sup1__I,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o,A3: set @ ( A > $o ),A2: A] :
% 0.19/0.47 ( ( member @ ( A > $o ) @ P2 @ A3 )
% 0.19/0.47 => ( ( P2 @ A2 )
% 0.19/0.47 => ( complete_Sup_Sup @ ( A > $o ) @ A3 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup1_I
% 0.19/0.47 thf(fact_216_image__empty,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F: B > A] :
% 0.19/0.47 ( ( image @ B @ A @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_empty
% 0.19/0.47 thf(fact_217_empty__is__image,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B] :
% 0.19/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.19/0.47 = ( image @ B @ A @ F @ A3 ) )
% 0.19/0.47 = ( A3
% 0.19/0.47 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % empty_is_image
% 0.19/0.47 thf(fact_218_image__is__empty,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B] :
% 0.19/0.47 ( ( ( image @ B @ A @ F @ A3 )
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 = ( A3
% 0.19/0.47 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_is_empty
% 0.19/0.47 thf(fact_219_sup__bot_Oright__neutral,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A2: A] :
% 0.19/0.47 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.19/0.47 = A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_bot.right_neutral
% 0.19/0.47 thf(fact_220_sup__bot_Oleft__neutral,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A2: A] :
% 0.19/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.19/0.47 = A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_bot.left_neutral
% 0.19/0.47 thf(fact_221_sup__eq__bot__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A,Y: A] :
% 0.19/0.47 ( ( ( sup_sup @ A @ X @ Y )
% 0.19/0.47 = ( bot_bot @ A ) )
% 0.19/0.47 = ( ( X
% 0.19/0.47 = ( bot_bot @ A ) )
% 0.19/0.47 & ( Y
% 0.19/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_eq_bot_iff
% 0.19/0.47 thf(fact_222_bot__eq__sup__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A,Y: A] :
% 0.19/0.47 ( ( ( bot_bot @ A )
% 0.19/0.47 = ( sup_sup @ A @ X @ Y ) )
% 0.19/0.47 = ( ( X
% 0.19/0.47 = ( bot_bot @ A ) )
% 0.19/0.47 & ( Y
% 0.19/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bot_eq_sup_iff
% 0.19/0.47 thf(fact_223_Sup__bot__conv_I2_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A3: set @ A] :
% 0.19/0.47 ( ( ( bot_bot @ A )
% 0.19/0.47 = ( complete_Sup_Sup @ A @ A3 ) )
% 0.19/0.47 = ( ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ A3 )
% 0.19/0.47 => ( X2
% 0.19/0.47 = ( bot_bot @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup_bot_conv(2)
% 0.19/0.47 thf(fact_224_Sup__bot__conv_I1_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [A3: set @ A] :
% 0.19/0.47 ( ( ( complete_Sup_Sup @ A @ A3 )
% 0.19/0.47 = ( bot_bot @ A ) )
% 0.19/0.47 = ( ! [X2: A] :
% 0.19/0.47 ( ( member @ A @ X2 @ A3 )
% 0.19/0.47 => ( X2
% 0.19/0.47 = ( bot_bot @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup_bot_conv(1)
% 0.19/0.47 thf(fact_225_singletonI,axiom,
% 0.19/0.47 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % singletonI
% 0.19/0.47 thf(fact_226_ball__empty,axiom,
% 0.19/0.47 ! [A: $tType,P2: A > $o,X4: A] :
% 0.19/0.47 ( ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 => ( P2 @ X4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % ball_empty
% 0.19/0.47 thf(fact_227_Un__empty,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.19/0.47 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B4 )
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 = ( ( A3
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 & ( B4
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_empty
% 0.19/0.47 thf(fact_228_empty__bind,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType,F: B > ( set @ A )] :
% 0.19/0.47 ( ( bind @ B @ A @ ( bot_bot @ ( set @ B ) ) @ F )
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % empty_bind
% 0.19/0.47 thf(fact_229_Sup__empty,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ( ( complete_Sup_Sup @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 = ( bot_bot @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup_empty
% 0.19/0.47 thf(fact_230_Sup1__E,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ ( A > $o ),A2: A] :
% 0.19/0.47 ( ( complete_Sup_Sup @ ( A > $o ) @ A3 @ A2 )
% 0.19/0.47 => ~ ! [P4: A > $o] :
% 0.19/0.47 ( ( member @ ( A > $o ) @ P4 @ A3 )
% 0.19/0.47 => ~ ( P4 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sup1_E
% 0.19/0.47 thf(fact_231_Union__empty,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( complete_Sup_Sup @ ( set @ A ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) )
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Union_empty
% 0.19/0.47 thf(fact_232_Union__empty__conv,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ ( set @ A )] :
% 0.19/0.47 ( ( ( complete_Sup_Sup @ ( set @ A ) @ A3 )
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 = ( ! [X2: set @ A] :
% 0.19/0.47 ( ( member @ ( set @ A ) @ X2 @ A3 )
% 0.19/0.47 => ( X2
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Union_empty_conv
% 0.19/0.47 thf(fact_233_empty__Union__conv,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ ( set @ A )] :
% 0.19/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.19/0.47 = ( complete_Sup_Sup @ ( set @ A ) @ A3 ) )
% 0.19/0.47 = ( ! [X2: set @ A] :
% 0.19/0.47 ( ( member @ ( set @ A ) @ X2 @ A3 )
% 0.19/0.47 => ( X2
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % empty_Union_conv
% 0.19/0.47 thf(fact_234_sup__bot__right,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A] :
% 0.19/0.47 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.19/0.47 = X ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_bot_right
% 0.19/0.47 thf(fact_235_sup__bot__left,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [X: A] :
% 0.19/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.19/0.47 = X ) ) ).
% 0.19/0.47
% 0.19/0.47 % sup_bot_left
% 0.19/0.47 thf(fact_236_Un__empty__right,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 = A3 ) ).
% 0.19/0.47
% 0.19/0.47 % Un_empty_right
% 0.19/0.47 thf(fact_237_Un__empty__left,axiom,
% 0.19/0.47 ! [A: $tType,B4: set @ A] :
% 0.19/0.47 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 0.19/0.47 = B4 ) ).
% 0.19/0.47
% 0.19/0.47 % Un_empty_left
% 0.19/0.47 thf(fact_238_image__bind,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,F: B > A,A3: set @ C,G: C > ( set @ B )] :
% 0.19/0.47 ( ( image @ B @ A @ F @ ( bind @ C @ B @ A3 @ G ) )
% 0.19/0.47 = ( bind @ C @ A @ A3 @ ( comp @ ( set @ B ) @ ( set @ A ) @ C @ ( image @ B @ A @ F ) @ G ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % image_bind
% 0.19/0.47 thf(fact_239_bind__image,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,C: $tType,F: C > B,A3: set @ C,G: B > ( set @ A )] :
% 0.19/0.47 ( ( bind @ B @ A @ ( image @ C @ B @ F @ A3 ) @ G )
% 0.19/0.47 = ( bind @ C @ A @ A3 @ ( comp @ B @ ( set @ A ) @ C @ G @ F ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bind_image
% 0.19/0.47 thf(fact_240_singletonD,axiom,
% 0.19/0.47 ! [A: $tType,B3: A,A2: A] :
% 0.19/0.47 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 => ( B3 = A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % singletonD
% 0.19/0.47 thf(fact_241_singleton__iff,axiom,
% 0.19/0.47 ! [A: $tType,B3: A,A2: A] :
% 0.19/0.47 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 = ( B3 = A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % singleton_iff
% 0.19/0.47 thf(fact_242_doubleton__eq__iff,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,B3: A,C3: A,D3: A] :
% 0.19/0.47 ( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 = ( insert @ A @ C3 @ ( insert @ A @ D3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.19/0.47 = ( ( ( A2 = C3 )
% 0.19/0.47 & ( B3 = D3 ) )
% 0.19/0.47 | ( ( A2 = D3 )
% 0.19/0.47 & ( B3 = C3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % doubleton_eq_iff
% 0.19/0.47 thf(fact_243_insert__not__empty,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.19/0.47 ( ( insert @ A @ A2 @ A3 )
% 0.19/0.47 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_not_empty
% 0.19/0.47 thf(fact_244_singleton__inject,axiom,
% 0.19/0.47 ! [A: $tType,A2: A,B3: A] :
% 0.19/0.47 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 => ( A2 = B3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % singleton_inject
% 0.19/0.47 thf(fact_245_Inf__INT__eq,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( complete_Inf_Inf @ ( A > $o ) )
% 0.19/0.47 = ( ^ [S: set @ ( A > $o ),X2: A] : ( member @ A @ X2 @ ( complete_Inf_Inf @ ( set @ A ) @ ( image @ ( A > $o ) @ ( set @ A ) @ ( collect @ A ) @ S ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Inf_INT_eq
% 0.19/0.47 thf(fact_246_emptyE,axiom,
% 0.19/0.47 ! [A: $tType,A2: A] :
% 0.19/0.47 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % emptyE
% 0.19/0.47 thf(fact_247_equals0D,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,A2: A] :
% 0.19/0.47 ( ( A3
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % equals0D
% 0.19/0.47 thf(fact_248_equals0I,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A] :
% 0.19/0.47 ( ! [Y4: A] :
% 0.19/0.47 ~ ( member @ A @ Y4 @ A3 )
% 0.19/0.47 => ( A3
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % equals0I
% 0.19/0.47 thf(fact_249_ex__in__conv,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A] :
% 0.19/0.47 ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.19/0.47 = ( A3
% 0.19/0.47 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ex_in_conv
% 0.19/0.47 thf(fact_250_SUP__eq__const,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [I: set @ B,F: B > A,X: A] :
% 0.19/0.47 ( ( I
% 0.19/0.47 != ( bot_bot @ ( set @ B ) ) )
% 0.19/0.47 => ( ! [I2: B] :
% 0.19/0.47 ( ( member @ B @ I2 @ I )
% 0.19/0.47 => ( ( F @ I2 )
% 0.19/0.47 = X ) )
% 0.19/0.47 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ I ) )
% 0.19/0.47 = X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % SUP_eq_const
% 0.19/0.47 thf(fact_251_INF__eq__const,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.19/0.47 => ! [I: set @ B,F: B > A,X: A] :
% 0.19/0.47 ( ( I
% 0.19/0.47 != ( bot_bot @ ( set @ B ) ) )
% 0.19/0.47 => ( ! [I2: B] :
% 0.19/0.47 ( ( member @ B @ I2 @ I )
% 0.19/0.47 => ( ( F @ I2 )
% 0.19/0.47 = X ) )
% 0.19/0.47 => ( ( complete_Inf_Inf @ A @ ( image @ B @ A @ F @ I ) )
% 0.19/0.47 = X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % INF_eq_const
% 0.19/0.47 thf(fact_252_singleton__Un__iff,axiom,
% 0.19/0.47 ! [A: $tType,X: A,A3: set @ A,B4: set @ A] :
% 0.19/0.47 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 = ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 0.19/0.47 = ( ( ( A3
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 & ( B4
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.19/0.47 | ( ( A3
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 & ( B4
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 | ( ( A3
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 & ( B4
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % singleton_Un_iff
% 0.19/0.47 thf(fact_253_Un__singleton__iff,axiom,
% 0.19/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,X: A] :
% 0.19/0.47 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B4 )
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 = ( ( ( A3
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47 & ( B4
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.19/0.47 | ( ( A3
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 & ( B4
% 0.19/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 | ( ( A3
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47 & ( B4
% 0.19/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Un_singleton_iff
% 0.19/0.47 thf(fact_254_insert__is__Un,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( insert @ A )
% 0.19/0.47 = ( ^ [A4: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % insert_is_Un
% 0.19/0.47 thf(fact_255_bind__UNION,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( bind @ B @ A )
% 0.19/0.47 = ( ^ [A5: set @ B,F3: B > ( set @ A )] : ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F3 @ A5 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bind_UNION
% 0.19/0.47
% 0.19/0.47 %----Type constructors (24)
% 0.19/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.19/0.47 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.19/0.47 ! [A6: $tType] : ( bounded_lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.19/0.47 ! [A6: $tType,A7: $tType] :
% 0.19/0.47 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.19/0.47 => ( bounded_lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.19/0.47 ! [A6: $tType,A7: $tType] :
% 0.19/0.47 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.19/0.47 => ( bounde1808546759up_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 0.19/0.47 ! [A6: $tType,A7: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A7 @ ( type2 @ A7 ) )
% 0.19/0.47 => ( comple187826305attice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.19/0.47 ! [A6: $tType,A7: $tType] :
% 0.19/0.47 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.19/0.47 => ( bounded_lattice_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.19/0.47 ! [A6: $tType,A7: $tType] :
% 0.19/0.47 ( ( semilattice_sup @ A7 @ ( type2 @ A7 ) )
% 0.19/0.47 => ( semilattice_sup @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_fun___Complete__Lattices_OSup,axiom,
% 0.19/0.47 ! [A6: $tType,A7: $tType] :
% 0.19/0.47 ( ( complete_Sup @ A7 @ ( type2 @ A7 ) )
% 0.19/0.47 => ( complete_Sup @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_fun___Complete__Lattices_OInf,axiom,
% 0.19/0.47 ! [A6: $tType,A7: $tType] :
% 0.19/0.47 ( ( complete_Inf @ A7 @ ( type2 @ A7 ) )
% 0.19/0.47 => ( complete_Inf @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.19/0.47 ! [A6: $tType,A7: $tType] :
% 0.19/0.47 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 0.19/0.47 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 0.19/0.47 ! [A6: $tType] : ( bounde1808546759up_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_4,axiom,
% 0.19/0.47 ! [A6: $tType] : ( comple187826305attice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_5,axiom,
% 0.19/0.47 ! [A6: $tType] : ( bounded_lattice_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_6,axiom,
% 0.19/0.47 ! [A6: $tType] : ( semilattice_sup @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_Set_Oset___Complete__Lattices_OSup_7,axiom,
% 0.19/0.47 ! [A6: $tType] : ( complete_Sup @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_Set_Oset___Complete__Lattices_OInf_8,axiom,
% 0.19/0.47 ! [A6: $tType] : ( complete_Inf @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_Set_Oset___Lattices_Olattice_9,axiom,
% 0.19/0.47 ! [A6: $tType] : ( lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_10,axiom,
% 0.19/0.47 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_11,axiom,
% 0.19/0.47 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12,axiom,
% 0.19/0.47 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_13,axiom,
% 0.19/0.47 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_HOL_Obool___Complete__Lattices_OSup_14,axiom,
% 0.19/0.47 complete_Sup @ $o @ ( type2 @ $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_HOL_Obool___Complete__Lattices_OInf_15,axiom,
% 0.19/0.47 complete_Inf @ $o @ ( type2 @ $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(tcon_HOL_Obool___Lattices_Olattice_16,axiom,
% 0.19/0.47 lattice @ $o @ ( type2 @ $o ) ).
% 0.19/0.47
% 0.19/0.47 %----Helper facts (3)
% 0.19/0.47 thf(help_If_3_1_T,axiom,
% 0.19/0.47 ! [P2: $o] :
% 0.19/0.47 ( ( P2 = $true )
% 0.19/0.47 | ( P2 = $false ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(help_If_2_1_T,axiom,
% 0.19/0.47 ! [A: $tType,X: A,Y: A] :
% 0.19/0.47 ( ( if @ A @ $false @ X @ Y )
% 0.19/0.47 = Y ) ).
% 0.19/0.47
% 0.19/0.47 thf(help_If_1_1_T,axiom,
% 0.19/0.47 ! [A: $tType,X: A,Y: A] :
% 0.19/0.47 ( ( if @ A @ $true @ X @ Y )
% 0.19/0.47 = X ) ).
% 0.19/0.47
% 0.19/0.47 %----Conjectures (1)
% 0.19/0.47 thf(conj_0,conjecture,
% 0.19/0.47 ( ( proces10484146Action @ a @ p )
% 0.19/0.47 | ( proces401113213Choice @ a @ p ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 2.93/1.51 ---- Embedded in THF ---
% 2.93/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.93/1.51 %%% Generated on Tue Feb 24 11:29:43 EST 2026
% 2.93/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.93/1.51 %%% Logic specification used:
% 2.93/1.51 %%% thf(spec, logic, $$dhol).
% 2.93/1.51
% 2.93/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lJEBhRXwsb/DTF2DTF10395.p
% 2.93/1.51 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess, type, proces634752977rocess: ($tType > $tType)).
% 2.93/1.51 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.93/1.51 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.93/1.51 thf(ty_tf_a, type, a: $tType).
% 2.93/1.51 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_cl_Complete__Lattices_OInf, type, complete_Inf: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_cl_Complete__Lattices_OSup, type, complete_Sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_cl_Complete__Lattices_Ocomplete__lattice, type, comple187826305attice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.93/1.51 thf(sy_c_BNF__Def_Oeq__onp, type, bNF_eq_onp: (!> [A:$tType]: (((A > $o) > (A > (A > $o)))))).
% 2.93/1.51 thf(sy_c_BNF__Def_Ovimage2p, type, bNF_vimage2p: (!> [A:$tType,D:$tType,B:$tType,E:$tType,C:$tType]: (((A > D) > ((B > E) > ((D > (E > C)) > (A > (B > C)))))))).
% 2.93/1.51 thf(sy_c_Complete__Lattices_OInf__class_OInf, type, complete_Inf_Inf: (!> [A:$tType]: (((set @ A) > A)))).
% 2.93/1.51 thf(sy_c_Complete__Lattices_OSup__class_OSup, type, complete_Sup_Sup: (!> [A:$tType]: (((set @ A) > A)))).
% 2.93/1.51 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 2.93/1.51 thf(sy_c_Fun_Oid, type, id: (!> [A:$tType]: ((A > A)))).
% 2.93/1.51 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.93/1.51 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.93/1.51 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction, type, proces1525233512Action: (!> [A:$tType]: ((A > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice, type, proces1915862579Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process, type, proces1406508781rocess: (!> [A:$tType,B:$tType]: (((A > ((proces634752977rocess @ A) > B)) > (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)) > ((proces634752977rocess @ A) > B)))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of, type, proces979765041_ch1Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of, type, proces988026546_ch2Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf, type, proces1778668539contOf: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process, type, proces894737309rocess: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))))))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction, type, proces10484146Action: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice, type, proces401113213Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process, type, proces370407749rocess: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((proces634752977rocess @ A) > (proces634752977rocess @ Aa)))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process, type, proces1205983068rocess: (!> [A:$tType]: (((A > $o) > ((proces634752977rocess @ A) > $o))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf, type, proces745025900prefOf: (!> [A:$tType]: (((proces634752977rocess @ A) > A)))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process, type, proces749077512rocess: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)))))).
% 2.93/1.51 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Oset__process, type, proces1148692671rocess: (!> [A:$tType]: (((proces634752977rocess @ A) > (set @ A))))).
% 2.93/1.51 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.93/1.51 thf(sy_c_Set_OBall, type, ball: (!> [A:$tType]: (((set @ A) > ((A > $o) > $o))))).
% 2.93/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.93/1.51 thf(sy_c_Set_Obind, type, bind: (!> [A:$tType,B:$tType]: (((set @ A) > ((A > (set @ B)) > (set @ B)))))).
% 2.93/1.51 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 2.93/1.51 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.93/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.93/1.51 thf(sy_v_p, type, p: (proces634752977rocess @ a)).
% 2.93/1.51 thf(fact_0_process_Odistinct__disc_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => (~ (((proces10484146Action @ A) @ Process))))))).
% 2.93/1.51 thf(fact_1_process_Odistinct__disc_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => (~ (((proces401113213Choice @ A) @ Process))))))).
% 2.93/1.51 thf(fact_2_process_Oexhaust__disc, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((~ (((proces10484146Action @ A) @ Process))) => ((proces401113213Choice @ A) @ Process))))).
% 2.93/1.51 thf(fact_3_process_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C),A2:C]: ((((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (~ ((P @ A2))))))).
% 2.93/1.51 thf(fact_4_process_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C),A2:C]: ((((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (P @ A2))))).
% 2.93/1.51 thf(fact_5_process_Omap__disc__iff_I2_J, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(proces634752977rocess @ A)]: ((((proces401113213Choice @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((proces401113213Choice @ A) @ A2))))).
% 2.93/1.51 thf(fact_6_process_Omap__disc__iff_I1_J, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(proces634752977rocess @ A)]: ((((proces10484146Action @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((proces10484146Action @ A) @ A2))))).
% 2.93/1.51 thf(fact_7_process_Ocorec__disc_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => ((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)))))).
% 2.93/1.51 thf(fact_8_process_Ocorec__disc_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => ((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)))))).
% 2.93/1.51 thf(fact_9_process_Odisc_I4_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: (((proces401113213Choice @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22))))).
% 2.93/1.51 thf(fact_10_process_Odisc_I3_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: ((~ (((proces401113213Choice @ A) @ (((proces1525233512Action @ A) @ X11) @ X12))))))).
% 2.93/1.51 thf(fact_11_process_OdiscI_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: (((Process = (((proces1915862579Choice @ A) @ X21) @ X22)) => ((proces401113213Choice @ A) @ Process))))).
% 2.93/1.51 thf(fact_12_isChoice__def, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = (^ [Process2:(proces634752977rocess @ A)]: ((? [X212:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: ((Process2 = (((proces1915862579Choice @ A) @ X212) @ X222)))))))))).
% 2.93/1.51 thf(fact_13_process_Odisc_I2_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((~ (((proces10484146Action @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22))))))).
% 2.93/1.51 thf(fact_14_process_Odisc_I1_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: (((proces10484146Action @ A) @ (((proces1525233512Action @ A) @ X11) @ X12))))).
% 2.93/1.51 thf(fact_15_process_Oinject_I2_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A)]: ((((((proces1915862579Choice @ A) @ X21) @ X22) = (((proces1915862579Choice @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.93/1.51 thf(fact_16_process_Oinject_I1_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A),Y11:A,Y12:(proces634752977rocess @ A)]: ((((((proces1525233512Action @ A) @ X11) @ X12) = (((proces1525233512Action @ A) @ Y11) @ Y12)) = ((X11 = Y11) & (X12 = Y12)))))).
% 2.93/1.51 thf(fact_17_process_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2) = (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q21 @ A2)) @ (G211 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G212 @ A2)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q22 @ A2)) @ (G221 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G222 @ A2))))))))).
% 2.93/1.51 thf(fact_18_process_Ocorec_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2) = (((proces1525233512Action @ A) @ (G11 @ A2)) @ ((((if @ (proces634752977rocess @ A)) @ (Q12 @ A2)) @ (G121 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G122 @ A2))))))))).
% 2.93/1.51 thf(fact_19_process_Osimps_I16_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ A) @ B) @ F) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = (((proces1915862579Choice @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ X21)) @ ((((proces370407749rocess @ A) @ B) @ F) @ X22)))))).
% 2.93/1.51 thf(fact_20_process_Osimps_I15_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X11:A,X12:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ A) @ B) @ F) @ (((proces1525233512Action @ A) @ X11) @ X12)) = (((proces1525233512Action @ B) @ (F @ X11)) @ ((((proces370407749rocess @ A) @ B) @ F) @ X12)))))).
% 2.93/1.51 thf(fact_21_process_Odistinct_I1_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: (((((proces1525233512Action @ A) @ X11) @ X12) != (((proces1915862579Choice @ A) @ X21) @ X22))))).
% 2.93/1.51 thf(fact_22_process_Oexhaust, axiom, (! [A:$tType,Y:(proces634752977rocess @ A)]: (((! [X112:A,X122:(proces634752977rocess @ A)]: ((Y != (((proces1525233512Action @ A) @ X112) @ X122)))) => (~ ((! [X213:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((Y != (((proces1915862579Choice @ A) @ X213) @ X223)))))))))).
% 2.93/1.51 thf(fact_23_isAction__def, axiom, (! [A:$tType]: (((proces10484146Action @ A) = (^ [Process2:(proces634752977rocess @ A)]: ((? [X113:A,X123:(proces634752977rocess @ A)]: ((Process2 = (((proces1525233512Action @ A) @ X113) @ X123)))))))))).
% 2.93/1.51 thf(fact_24_process_OdiscI_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X11:A,X12:(proces634752977rocess @ A)]: (((Process = (((proces1525233512Action @ A) @ X11) @ X12)) => ((proces10484146Action @ A) @ Process))))).
% 2.93/1.51 thf(fact_25_process_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces10484146Action @ A) @ A2) => (((proces745025900prefOf @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = (F @ ((proces745025900prefOf @ A) @ A2))))))).
% 2.93/1.51 thf(fact_26_process_Omap__sel_I3_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces401113213Choice @ A) @ A2) => (((proces979765041_ch1Of @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((((proces370407749rocess @ A) @ B) @ F) @ ((proces979765041_ch1Of @ A) @ A2))))))).
% 2.93/1.51 thf(fact_27_process_Omap__sel_I4_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces401113213Choice @ A) @ A2) => (((proces988026546_ch2Of @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((((proces370407749rocess @ A) @ B) @ F) @ ((proces988026546_ch2Of @ A) @ A2))))))).
% 2.93/1.51 thf(fact_28_process_Omap__sel_I2_J, axiom, (! [B:$tType,A:$tType,A2:(proces634752977rocess @ A),F:(A > B)]: ((((proces10484146Action @ A) @ A2) => (((proces1778668539contOf @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((((proces370407749rocess @ A) @ B) @ F) @ ((proces1778668539contOf @ A) @ A2))))))).
% 2.93/1.51 thf(fact_29_process_Oset__cases, axiom, (! [A:$tType,E2:A,A2:(proces634752977rocess @ A)]: (((((member @ A) @ E2) @ ((proces1148692671rocess @ A) @ A2)) => ((! [Z2:(proces634752977rocess @ A)]: ((A2 != (((proces1525233512Action @ A) @ E2) @ Z2)))) => ((! [Z1:A,Z2:(proces634752977rocess @ A)]: (((A2 = (((proces1525233512Action @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E2) @ ((proces1148692671rocess @ A) @ Z2))))))) => ((! [Z1:(proces634752977rocess @ A)]: (((? [Z2:(proces634752977rocess @ A)]: ((A2 = (((proces1915862579Choice @ A) @ Z1) @ Z2)))) => (~ ((((member @ A) @ E2) @ ((proces1148692671rocess @ A) @ Z1))))))) => (~ ((! [Z1:(proces634752977rocess @ A),Z2:(proces634752977rocess @ A)]: (((A2 = (((proces1915862579Choice @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E2) @ ((proces1148692671rocess @ A) @ Z2)))))))))))))))).
% 2.93/1.51 thf(fact_30_process_Oset__induct, axiom, (! [A:$tType,X:A,A2:(proces634752977rocess @ A),P2:(A > ((proces634752977rocess @ A) > $o))]: (((((member @ A) @ X) @ ((proces1148692671rocess @ A) @ A2)) => ((! [Z1:A,Z2:(proces634752977rocess @ A)]: (((P2 @ Z1) @ (((proces1525233512Action @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(proces634752977rocess @ A),Xa:A]: (((((member @ A) @ Xa) @ ((proces1148692671rocess @ A) @ Z2)) => (((P2 @ Xa) @ Z2) => ((P2 @ Xa) @ (((proces1525233512Action @ A) @ Z1) @ Z2)))))) => ((! [Z1a:(proces634752977rocess @ A),Z2a:(proces634752977rocess @ A),Xb:A]: (((((member @ A) @ Xb) @ ((proces1148692671rocess @ A) @ Z1a)) => (((P2 @ Xb) @ Z1a) => ((P2 @ Xb) @ (((proces1915862579Choice @ A) @ Z1a) @ Z2a)))))) => ((! [Z1a:(proces634752977rocess @ A),Z2a:(proces634752977rocess @ A),Xc:A]: (((((member @ A) @ Xc) @ ((proces1148692671rocess @ A) @ Z2a)) => (((P2 @ Xc) @ Z2a) => ((P2 @ Xc) @ (((proces1915862579Choice @ A) @ Z1a) @ Z2a)))))) => ((P2 @ X) @ A2))))))))).
% 2.93/1.51 thf(fact_31_process_Opred__inject_I2_J, axiom, (! [A:$tType,P2:(A > $o),A2:(proces634752977rocess @ A),Aa2:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ A) @ P2) @ (((proces1915862579Choice @ A) @ A2) @ Aa2)) = ((((proces1205983068rocess @ A) @ P2) @ A2) & (((proces1205983068rocess @ A) @ P2) @ Aa2)))))).
% 2.93/1.51 thf(fact_32_process_Opred__inject_I1_J, axiom, (! [A:$tType,P2:(A > $o),A2:A,Aa2:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ A) @ P2) @ (((proces1525233512Action @ A) @ A2) @ Aa2)) = ((P2 @ A2) & (((proces1205983068rocess @ A) @ P2) @ Aa2)))))).
% 2.93/1.51 thf(fact_33_process_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = ((F2 @ X21) @ X22))))).
% 2.93/1.51 thf(fact_34_process_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X11:A,X12:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1525233512Action @ A) @ X11) @ X12)) = ((F1 @ X11) @ X12))))).
% 2.93/1.51 thf(fact_35_process_Ocollapse_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => ((((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)) = Process))))).
% 2.93/1.51 thf(fact_36_process_Ocollapse_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => ((((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process)) = Process))))).
% 2.93/1.51 thf(fact_37_process_Ocase__eq__if, axiom, (! [B:$tType,A:$tType]: ((((proces1406508781rocess @ A) @ B) = (^ [F12:(A > ((proces634752977rocess @ A) > B)),F22:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process2:(proces634752977rocess @ A)]: (((((if @ B) @ ((proces10484146Action @ A) @ Process2)) @ ((F12 @ ((proces745025900prefOf @ A) @ Process2)) @ ((proces1778668539contOf @ A) @ Process2))) @ ((F22 @ ((proces979765041_ch1Of @ A) @ Process2)) @ ((proces988026546_ch2Of @ A) @ Process2))))))))).
% 2.93/1.51 thf(fact_38_process_Opred__mono__strong, axiom, (! [A:$tType,P2:(A > $o),X:(proces634752977rocess @ A),Pa:(A > $o)]: (((((proces1205983068rocess @ A) @ P2) @ X) => ((! [Z:A]: (((((member @ A) @ Z) @ ((proces1148692671rocess @ A) @ X)) => ((P2 @ Z) => (Pa @ Z))))) => (((proces1205983068rocess @ A) @ Pa) @ X)))))).
% 2.93/1.51 thf(fact_39_process_Opred__cong, axiom, (! [A:$tType,X:(proces634752977rocess @ A),Ya:(proces634752977rocess @ A),P2:(A > $o),Pa:(A > $o)]: (((X = Ya) => ((! [Z:A]: (((((member @ A) @ Z) @ ((proces1148692671rocess @ A) @ Ya)) => ((P2 @ Z) = (Pa @ Z))))) => ((((proces1205983068rocess @ A) @ P2) @ X) = (((proces1205983068rocess @ A) @ Pa) @ Ya))))))).
% 2.93/1.51 thf(fact_40_process_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P2 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (~ ((((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) & (~ ((P2 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))))) | ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) & (~ ((P2 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))))))).
% 2.93/1.51 thf(fact_41_process_Osplit__sel, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P2 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (P2 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))) & ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) => (P2 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))).
% 2.93/1.51 thf(fact_42_process_Oexhaust__sel, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((Process != (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))).
% 2.93/1.51 thf(fact_43_process_Oexpand, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: (((((proces10484146Action @ A) @ Process) = ((proces10484146Action @ A) @ Process3)) => ((((proces10484146Action @ A) @ Process) => (((proces10484146Action @ A) @ Process3) => ((((proces745025900prefOf @ A) @ Process) = ((proces745025900prefOf @ A) @ Process3)) & (((proces1778668539contOf @ A) @ Process) = ((proces1778668539contOf @ A) @ Process3))))) => ((((proces401113213Choice @ A) @ Process) => (((proces401113213Choice @ A) @ Process3) => ((((proces979765041_ch1Of @ A) @ Process) = ((proces979765041_ch1Of @ A) @ Process3)) & (((proces988026546_ch2Of @ A) @ Process) = ((proces988026546_ch2Of @ A) @ Process3))))) => (Process = Process3))))))).
% 2.93/1.51 thf(fact_44_process_Ocoinduct, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: ((((R @ Process) @ Process3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ A)]: ((((R @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ A) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ A) @ Process5) => ((((proces745025900prefOf @ A) @ Process4) = ((proces745025900prefOf @ A) @ Process5)) & ((R @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ A) @ Process5))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ A) @ Process5) => (((R @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ A) @ Process5)) & ((R @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ A) @ Process5)))))))))) => (Process = Process3)))))).
% 2.93/1.51 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 2.93/1.51 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 2.93/1.51 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P2 @ X3) = (Q @ X3)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.93/1.51 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.93/1.51 thf(fact_49_process_Ocoinduct__strong, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: ((((R @ Process) @ Process3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ A)]: ((((R @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ A) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ A) @ Process5) => ((((proces745025900prefOf @ A) @ Process4) = ((proces745025900prefOf @ A) @ Process5)) & (((R @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ A) @ Process5)) | (((proces1778668539contOf @ A) @ Process4) = ((proces1778668539contOf @ A) @ Process5)))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ A) @ Process5) => ((((R @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ A) @ Process5)) | (((proces979765041_ch1Of @ A) @ Process4) = ((proces979765041_ch1Of @ A) @ Process5))) & (((R @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ A) @ Process5)) | (((proces988026546_ch2Of @ A) @ Process4) = ((proces988026546_ch2Of @ A) @ Process5))))))))))) => (Process = Process3)))))).
% 2.93/1.51 thf(fact_50_process_Oset__sel_I2_J, axiom, (! [A:$tType,A2:(proces634752977rocess @ A),X:A]: ((((proces10484146Action @ A) @ A2) => ((((member @ A) @ X) @ ((proces1148692671rocess @ A) @ ((proces1778668539contOf @ A) @ A2))) => (((member @ A) @ X) @ ((proces1148692671rocess @ A) @ A2))))))).
% 2.93/1.51 thf(fact_51_process_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ A2) => (((member @ A) @ ((proces745025900prefOf @ A) @ A2)) @ ((proces1148692671rocess @ A) @ A2)))))).
% 2.93/1.51 thf(fact_52_process_Oset__sel_I4_J, axiom, (! [A:$tType,A2:(proces634752977rocess @ A),Xb2:A]: ((((proces401113213Choice @ A) @ A2) => ((((member @ A) @ Xb2) @ ((proces1148692671rocess @ A) @ ((proces988026546_ch2Of @ A) @ A2))) => (((member @ A) @ Xb2) @ ((proces1148692671rocess @ A) @ A2))))))).
% 2.93/1.51 thf(fact_53_process_Oset__sel_I3_J, axiom, (! [A:$tType,A2:(proces634752977rocess @ A),Xa2:A]: ((((proces401113213Choice @ A) @ A2) => ((((member @ A) @ Xa2) @ ((proces1148692671rocess @ A) @ ((proces979765041_ch1Of @ A) @ A2))) => (((member @ A) @ Xa2) @ ((proces1148692671rocess @ A) @ A2))))))).
% 2.93/1.51 thf(fact_54_process_Oinj__map__strong, axiom, (! [B:$tType,A:$tType,X:(proces634752977rocess @ A),Xa2:(proces634752977rocess @ A),F:(A > B),Fa:(A > B)]: (((! [Z:A,Za:A]: (((((member @ A) @ Z) @ ((proces1148692671rocess @ A) @ X)) => ((((member @ A) @ Za) @ ((proces1148692671rocess @ A) @ Xa2)) => (((F @ Z) = (Fa @ Za)) => (Z = Za)))))) => ((((((proces370407749rocess @ A) @ B) @ F) @ X) = ((((proces370407749rocess @ A) @ B) @ Fa) @ Xa2)) => (X = Xa2)))))).
% 2.93/1.51 thf(fact_55_process_Omap__cong0, axiom, (! [B:$tType,A:$tType,X:(proces634752977rocess @ A),F:(A > B),G:(A > B)]: (((! [Z:A]: (((((member @ A) @ Z) @ ((proces1148692671rocess @ A) @ X)) => ((F @ Z) = (G @ Z))))) => (((((proces370407749rocess @ A) @ B) @ F) @ X) = ((((proces370407749rocess @ A) @ B) @ G) @ X)))))).
% 2.93/1.51 thf(fact_56_process_Omap__cong, axiom, (! [B:$tType,A:$tType,X:(proces634752977rocess @ A),Ya:(proces634752977rocess @ A),F:(A > B),G:(A > B)]: (((X = Ya) => ((! [Z:A]: (((((member @ A) @ Z) @ ((proces1148692671rocess @ A) @ Ya)) => ((F @ Z) = (G @ Z))))) => (((((proces370407749rocess @ A) @ B) @ F) @ X) = ((((proces370407749rocess @ A) @ B) @ G) @ Ya))))))).
% 2.93/1.51 thf(fact_57_process_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(proces634752977rocess @ A)]: ((((member @ A) @ A1) @ ((proces1148692671rocess @ A) @ (((proces1525233512Action @ A) @ A1) @ A22)))))).
% 2.93/1.51 thf(fact_58_process_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(proces634752977rocess @ A),A1:A]: (((((member @ A) @ X) @ ((proces1148692671rocess @ A) @ A22)) => (((member @ A) @ X) @ ((proces1148692671rocess @ A) @ (((proces1525233512Action @ A) @ A1) @ A22))))))).
% 2.93/1.51 thf(fact_59_process_Oset__intros_I3_J, axiom, (! [A:$tType,Xa2:A,A1a:(proces634752977rocess @ A),A2a:(proces634752977rocess @ A)]: (((((member @ A) @ Xa2) @ ((proces1148692671rocess @ A) @ A1a)) => (((member @ A) @ Xa2) @ ((proces1148692671rocess @ A) @ (((proces1915862579Choice @ A) @ A1a) @ A2a))))))).
% 2.93/1.51 thf(fact_60_process_Oset__intros_I4_J, axiom, (! [A:$tType,Xb2:A,A2a:(proces634752977rocess @ A),A1a:(proces634752977rocess @ A)]: (((((member @ A) @ Xb2) @ ((proces1148692671rocess @ A) @ A2a)) => (((member @ A) @ Xb2) @ ((proces1148692671rocess @ A) @ (((proces1915862579Choice @ A) @ A1a) @ A2a))))))).
% 2.93/1.51 thf(fact_61_process_Osel_I2_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: ((((proces1778668539contOf @ A) @ (((proces1525233512Action @ A) @ X11) @ X12)) = X12)))).
% 2.93/1.51 thf(fact_62_process_Osel_I3_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((((proces979765041_ch1Of @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = X21)))).
% 2.93/1.51 thf(fact_63_process_Osel_I4_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((((proces988026546_ch2Of @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = X22)))).
% 2.93/1.51 thf(fact_64_process_Osel_I1_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: ((((proces745025900prefOf @ A) @ (((proces1525233512Action @ A) @ X11) @ X12)) = X11)))).
% 2.93/1.51 thf(fact_65_process_Ocorec__sel_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q12:(C > $o),G11:(C > A),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((Q12 @ A2) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G121 @ A2))) & ((~ ((Q12 @ A2))) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G122 @ A2))))))))).
% 2.93/1.51 thf(fact_66_process_Ocorec__sel_I3_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q21:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((Q21 @ A2) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G211 @ A2))) & ((~ ((Q21 @ A2))) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G212 @ A2))))))))).
% 2.93/1.51 thf(fact_67_process_Ocorec__sel_I4_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q22:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((~ ((P @ A2))) => (((Q22 @ A2) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G221 @ A2))) & ((~ ((Q22 @ A2))) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G222 @ A2))))))))).
% 2.93/1.51 thf(fact_68_process_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C)]: (((P @ A2) => (((proces745025900prefOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ A2)) = (G11 @ A2)))))).
% 2.93/1.51 thf(fact_69_process_Orel__coinduct, axiom, (! [A:$tType,B:$tType,P2:((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)),X:(proces634752977rocess @ A),Y:(proces634752977rocess @ B),R:(A > (B > $o))]: ((((P2 @ X) @ Y) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ B)]: ((((P2 @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ B) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ B) @ Process5) => (((R @ ((proces745025900prefOf @ A) @ Process4)) @ ((proces745025900prefOf @ B) @ Process5)) & ((P2 @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ B) @ Process5))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ B) @ Process5) => (((P2 @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ B) @ Process5)) & ((P2 @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ B) @ Process5)))))))))) => (((((proces749077512rocess @ A) @ B) @ R) @ X) @ Y)))))).
% 2.93/1.51 thf(fact_70_process_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((proces749077512rocess @ A) @ B) = (^ [R2:(A > (B > $o)),A4:(proces634752977rocess @ A),B2:(proces634752977rocess @ B)]: (((((proces10484146Action @ A) @ A4) = ((proces10484146Action @ B) @ B2)) & ((((proces10484146Action @ A) @ A4) => (((proces10484146Action @ B) @ B2) => (((R2 @ ((proces745025900prefOf @ A) @ A4)) @ ((proces745025900prefOf @ B) @ B2)) & (((((proces749077512rocess @ A) @ B) @ R2) @ ((proces1778668539contOf @ A) @ A4)) @ ((proces1778668539contOf @ B) @ B2))))) & (((proces401113213Choice @ A) @ A4) => (((proces401113213Choice @ B) @ B2) => ((((((proces749077512rocess @ A) @ B) @ R2) @ ((proces979765041_ch1Of @ A) @ A4)) @ ((proces979765041_ch1Of @ B) @ B2)) & (((((proces749077512rocess @ A) @ B) @ R2) @ ((proces988026546_ch2Of @ A) @ A4)) @ ((proces988026546_ch2Of @ B) @ B2))))))))))))).
% 2.93/1.51 thf(fact_71_process_Osimps_I21_J, axiom, (! [A:$tType,X11:A,X12:(proces634752977rocess @ A)]: ((((proces1148692671rocess @ A) @ (((proces1525233512Action @ A) @ X11) @ X12)) = (((insert @ A) @ X11) @ ((proces1148692671rocess @ A) @ X12)))))).
% 2.93/1.51 thf(fact_72_process_Osimps_I22_J, axiom, (! [A:$tType,X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((((proces1148692671rocess @ A) @ (((proces1915862579Choice @ A) @ X21) @ X22)) = (((sup_sup @ (set @ A)) @ ((proces1148692671rocess @ A) @ X21)) @ ((proces1148692671rocess @ A) @ X22)))))).
% 2.93/1.51 thf(fact_73_process_Opred__map, axiom, (! [B:$tType,A:$tType,Q:(B > $o),F:(A > B),X:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ B) @ Q) @ ((((proces370407749rocess @ A) @ B) @ F) @ X)) = (((proces1205983068rocess @ A) @ (((((comp @ B) @ $o) @ A) @ Q) @ F)) @ X))))).
% 2.93/1.51 thf(fact_74_process_Opred__set, axiom, (! [A:$tType]: (((proces1205983068rocess @ A) = (^ [P3:(A > $o),X2:(proces634752977rocess @ A)]: ((! [Y2:A]: (((((member @ A) @ Y2) @ ((proces1148692671rocess @ A) @ X2)) => (P3 @ Y2)))))))))).
% 2.93/1.51 thf(fact_75_process_Oset__map, axiom, (! [B:$tType,A:$tType,F:(A > B),V:(proces634752977rocess @ A)]: ((((proces1148692671rocess @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ V)) = ((((image @ A) @ B) @ F) @ ((proces1148692671rocess @ A) @ V)))))).
% 2.93/1.51 thf(fact_76_process_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(proces634752977rocess @ A),B3:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ A2) @ B3) => ((! [X1:A,X23:(proces634752977rocess @ A)]: (((A2 = (((proces1525233512Action @ A) @ X1) @ X23)) => (! [Y1:B,Y23:(proces634752977rocess @ B)]: (((B3 = (((proces1525233512Action @ B) @ Y1) @ Y23)) => (((R @ X1) @ Y1) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X23) @ Y23)))))))))) => (~ ((! [X1a:(proces634752977rocess @ A),X2a:(proces634752977rocess @ A)]: (((A2 = (((proces1915862579Choice @ A) @ X1a) @ X2a)) => (! [Y1a:(proces634752977rocess @ B),Y2a:(proces634752977rocess @ B)]: (((B3 = (((proces1915862579Choice @ B) @ Y1a) @ Y2a)) => ((((((proces749077512rocess @ A) @ B) @ R) @ X1a) @ Y1a) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X2a) @ Y2a))))))))))))))))).
% 2.93/1.51 thf(fact_77_process_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,X12:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X12)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 2.93/1.51 thf(fact_78_process_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:(proces634752977rocess @ A),X22:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X21) @ X22)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22)) = ((((((proces749077512rocess @ A) @ B) @ R) @ X21) @ Y21) & (((((proces749077512rocess @ A) @ B) @ R) @ X22) @ Y22)))))).
% 2.93/1.51 thf(fact_79_process_Orel__inject_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,X12:(proces634752977rocess @ A),Y11:B,Y12:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X12)) @ (((proces1525233512Action @ B) @ Y11) @ Y12)) = (((R @ X11) @ Y11) & (((((proces749077512rocess @ A) @ B) @ R) @ X12) @ Y12)))))).
% 2.93/1.51 thf(fact_80_process_Orel__eq, axiom, (! [A:$tType]: (((((proces749077512rocess @ A) @ A) @ (^ [Y3:A,Z3:A]: ((Y3 = Z3)))) = (^ [Y3:(proces634752977rocess @ A),Z3:(proces634752977rocess @ A)]: ((Y3 = Z3))))))).
% 2.93/1.51 thf(fact_81_process_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(proces634752977rocess @ B)]: (((! [X3:B]: (((Ra @ X3) @ X3))) => (((((proces749077512rocess @ B) @ B) @ Ra) @ X) @ X))))).
% 2.93/1.51 thf(fact_82_process_Omap__o__corec, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),G:(C > $o),Ga:(C > A),Gb:(C > $o),Gc:(C > (proces634752977rocess @ A)),Gd:(C > C),Ge:(C > $o),Gf:(C > (proces634752977rocess @ A)),Gg:(C > C),Gh:(C > $o),Gi:(C > (proces634752977rocess @ A)),Gj:(C > C)]: (((((((comp @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ (((proces370407749rocess @ A) @ B) @ F)) @ (((((((((((((proces894737309rocess @ C) @ A) @ G) @ Ga) @ Gb) @ Gc) @ Gd) @ Ge) @ Gf) @ Gg) @ Gh) @ Gi) @ Gj)) = (((((((((((((proces894737309rocess @ C) @ B) @ G) @ (((((comp @ A) @ B) @ C) @ F) @ Ga)) @ Gb) @ (((((comp @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ (((proces370407749rocess @ A) @ B) @ F)) @ Gc)) @ Gd) @ Ge) @ (((((comp @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ (((proces370407749rocess @ A) @ B) @ F)) @ Gf)) @ Gg) @ Gh) @ (((((comp @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ (((proces370407749rocess @ A) @ B) @ F)) @ Gi)) @ Gj))))).
% 2.93/1.51 thf(fact_83_process_Orel__cong, axiom, (! [A:$tType,B:$tType,X:(proces634752977rocess @ A),Ya:(proces634752977rocess @ A),Y:(proces634752977rocess @ B),Xa2:(proces634752977rocess @ B),R:(A > (B > $o)),Ra:(A > (B > $o))]: (((X = Ya) => ((Y = Xa2) => ((! [Z:A,Yb:B]: (((((member @ A) @ Z) @ ((proces1148692671rocess @ A) @ Ya)) => ((((member @ B) @ Yb) @ ((proces1148692671rocess @ B) @ Xa2)) => (((R @ Z) @ Yb) = ((Ra @ Z) @ Yb)))))) => ((((((proces749077512rocess @ A) @ B) @ R) @ X) @ Y) = (((((proces749077512rocess @ A) @ B) @ Ra) @ Ya) @ Xa2)))))))).
% 2.93/1.51 thf(fact_84_process_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X:(proces634752977rocess @ A),Y:(proces634752977rocess @ B),Ra:(A > (B > $o))]: (((((((proces749077512rocess @ A) @ B) @ R) @ X) @ Y) => ((! [Z:A,Yb:B]: (((((member @ A) @ Z) @ ((proces1148692671rocess @ A) @ X)) => ((((member @ B) @ Yb) @ ((proces1148692671rocess @ B) @ Y)) => (((R @ Z) @ Yb) => ((Ra @ Z) @ Yb)))))) => (((((proces749077512rocess @ A) @ B) @ Ra) @ X) @ Y)))))).
% 2.93/1.51 thf(fact_85_process_Orel__refl__strong, axiom, (! [A:$tType,X:(proces634752977rocess @ A),Ra:(A > (A > $o))]: (((! [Z:A]: (((((member @ A) @ Z) @ ((proces1148692671rocess @ A) @ X)) => ((Ra @ Z) @ Z)))) => (((((proces749077512rocess @ A) @ A) @ Ra) @ X) @ X))))).
% 2.93/1.51 thf(fact_86_process_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),X22:(proces634752977rocess @ A),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ X21) @ Y21) => ((((((proces749077512rocess @ A) @ B) @ R) @ X22) @ Y22) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X21) @ X22)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 2.93/1.51 thf(fact_87_process_Orel__intros_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,Y11:B,X12:(proces634752977rocess @ A),Y12:(proces634752977rocess @ B)]: ((((R @ X11) @ Y11) => ((((((proces749077512rocess @ A) @ B) @ R) @ X12) @ Y12) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X12)) @ (((proces1525233512Action @ B) @ Y11) @ Y12))))))).
% 2.93/1.51 thf(fact_88_process_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,G:(B > C),F:(A > B),V:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ B) @ C) @ G) @ ((((proces370407749rocess @ A) @ B) @ F) @ V)) = ((((proces370407749rocess @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ V))))).
% 2.93/1.51 thf(fact_89_process_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A),X11:B,X12:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ Y21) @ Y22)) @ (((proces1525233512Action @ B) @ X11) @ X12))))))).
% 2.93/1.51 thf(fact_90_Un__insert__left, axiom, (! [A:$tType,A2:A,B4:(set @ A),C2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A2) @ B4)) @ C2) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ B4) @ C2)))))).
% 2.93/1.51 thf(fact_91_Un__insert__right, axiom, (! [A:$tType,A3:(set @ A),A2:A,B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ B4)) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ A3) @ B4)))))).
% 2.93/1.51 thf(fact_92_image__insert, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:B,B4:(set @ B)]: ((((((image @ B) @ A) @ F) @ (((insert @ B) @ A2) @ B4)) = (((insert @ A) @ (F @ A2)) @ ((((image @ B) @ A) @ F) @ B4)))))).
% 2.93/1.51 thf(fact_93_insert__image, axiom, (! [B:$tType,A:$tType,X:A,A3:(set @ A),F:(A > B)]: (((((member @ A) @ X) @ A3) => ((((insert @ B) @ (F @ X)) @ ((((image @ A) @ B) @ F) @ A3)) = ((((image @ A) @ B) @ F) @ A3)))))).
% 2.93/1.51 thf(fact_94_Ball__image__comp, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B),G:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ ((((image @ B) @ A) @ F) @ A3)) => (G @ X2)))) = (! [X2:B]: (((((member @ B) @ X2) @ A3) => ((((((comp @ A) @ $o) @ B) @ G) @ F) @ X2)))))))).
% 2.93/1.51 thf(fact_95_UnCI, axiom, (! [A:$tType,C3:A,B4:(set @ A),A3:(set @ A)]: ((((~ ((((member @ A) @ C3) @ B4))) => (((member @ A) @ C3) @ A3)) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A3) @ B4)))))).
% 2.93/1.51 thf(fact_96_image__eqI, axiom, (! [A:$tType,B:$tType,B3:A,F:(B > A),X:B,A3:(set @ B)]: (((B3 = (F @ X)) => ((((member @ B) @ X) @ A3) => (((member @ A) @ B3) @ ((((image @ B) @ A) @ F) @ A3))))))).
% 2.93/1.51 thf(fact_97_insert__absorb2, axiom, (! [A:$tType,X:A,A3:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A3)) = (((insert @ A) @ X) @ A3))))).
% 2.93/1.51 thf(fact_98_insert__iff, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A3)) = ((A2 = B3) | (((member @ A) @ A2) @ A3)))))).
% 2.93/1.51 thf(fact_99_insertCI, axiom, (! [A:$tType,A2:A,B4:(set @ A),B3:A]: ((((~ ((((member @ A) @ A2) @ B4))) => (A2 = B3)) => (((member @ A) @ A2) @ (((insert @ A) @ B3) @ B4)))))).
% 2.93/1.51 thf(fact_100_Un__iff, axiom, (! [A:$tType,C3:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A3) @ B4)) = ((((member @ A) @ C3) @ A3) | (((member @ A) @ C3) @ B4)))))).
% 2.93/1.51 thf(fact_101_rev__image__eqI, axiom, (! [B:$tType,A:$tType,X:A,A3:(set @ A),B3:B,F:(A > B)]: (((((member @ A) @ X) @ A3) => ((B3 = (F @ X)) => (((member @ B) @ B3) @ ((((image @ A) @ B) @ F) @ A3))))))).
% 2.93/1.51 thf(fact_102_ball__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B),P2:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((((image @ B) @ A) @ F) @ A3)) => (P2 @ X3)))) => (! [X4:B]: (((((member @ B) @ X4) @ A3) => (P2 @ (F @ X4))))))))).
% 2.93/1.51 thf(fact_103_image__cong, axiom, (! [B:$tType,A:$tType,M:(set @ A),N:(set @ A),F:(A > B),G:(A > B)]: (((M = N) => ((! [X3:A]: (((((member @ A) @ X3) @ N) => ((F @ X3) = (G @ X3))))) => (((((image @ A) @ B) @ F) @ M) = ((((image @ A) @ B) @ G) @ N))))))).
% 2.93/1.51 thf(fact_104_bex__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B),P2:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((((image @ B) @ A) @ F) @ A3)) & (P2 @ X4)))) => (? [X3:B]: (((((member @ B) @ X3) @ A3) & (P2 @ (F @ X3))))))))).
% 2.93/1.51 thf(fact_105_image__iff, axiom, (! [A:$tType,B:$tType,Z4:A,F:(B > A),A3:(set @ B)]: (((((member @ A) @ Z4) @ ((((image @ B) @ A) @ F) @ A3)) = (? [X2:B]: (((((member @ B) @ X2) @ A3) & (Z4 = (F @ X2))))))))).
% 2.93/1.51 thf(fact_106_imageI, axiom, (! [B:$tType,A:$tType,X:A,A3:(set @ A),F:(A > B)]: (((((member @ A) @ X) @ A3) => (((member @ B) @ (F @ X)) @ ((((image @ A) @ B) @ F) @ A3)))))).
% 2.93/1.51 thf(fact_107_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => (? [B5:(set @ A)]: (((A3 = (((insert @ A) @ A2) @ B5)) & (~ ((((member @ A) @ A2) @ B5)))))))))).
% 2.93/1.51 thf(fact_108_insert__commute, axiom, (! [A:$tType,X:A,Y:A,A3:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y) @ A3)) = (((insert @ A) @ Y) @ (((insert @ A) @ X) @ A3)))))).
% 2.93/1.51 thf(fact_109_insert__eq__iff, axiom, (! [A:$tType,A2:A,A3:(set @ A),B3:A,B4:(set @ A)]: (((~ ((((member @ A) @ A2) @ A3))) => ((~ ((((member @ A) @ B3) @ B4))) => (((((insert @ A) @ A2) @ A3) = (((insert @ A) @ B3) @ B4)) = (((A2 = B3) => (A3 = B4)) & ((A2 != B3) => (? [C4:(set @ A)]: (((A3 = (((insert @ A) @ B3) @ C4)) & ((~ ((((member @ A) @ B3) @ C4))) & ((B4 = (((insert @ A) @ A2) @ C4)) & (~ ((((member @ A) @ A2) @ C4)))))))))))))))).
% 2.93/1.51 thf(fact_110_insert__absorb, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => ((((insert @ A) @ A2) @ A3) = A3))))).
% 2.93/1.51 thf(fact_111_insert__ident, axiom, (! [A:$tType,X:A,A3:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ X) @ A3))) => ((~ ((((member @ A) @ X) @ B4))) => (((((insert @ A) @ X) @ A3) = (((insert @ A) @ X) @ B4)) = (A3 = B4))))))).
% 2.93/1.51 thf(fact_112_Set_Oset__insert, axiom, (! [A:$tType,X:A,A3:(set @ A)]: (((((member @ A) @ X) @ A3) => (~ ((! [B5:(set @ A)]: (((A3 = (((insert @ A) @ X) @ B5)) => (((member @ A) @ X) @ B5)))))))))).
% 2.93/1.51 thf(fact_113_insertI2, axiom, (! [A:$tType,A2:A,B4:(set @ A),B3:A]: (((((member @ A) @ A2) @ B4) => (((member @ A) @ A2) @ (((insert @ A) @ B3) @ B4)))))).
% 2.93/1.51 thf(fact_114_insertI1, axiom, (! [A:$tType,A2:A,B4:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B4))))).
% 2.93/1.51 thf(fact_115_insertE, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A3)) => ((A2 != B3) => (((member @ A) @ A2) @ A3)))))).
% 2.93/1.51 thf(fact_116_comp__apply__eq, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType,F:(B > A),G:(C > B),X:C,H:(D > A),K:(C > D)]: ((((F @ (G @ X)) = (H @ (K @ X))) => (((((((comp @ B) @ A) @ C) @ F) @ G) @ X) = ((((((comp @ D) @ A) @ C) @ H) @ K) @ X)))))).
% 2.93/1.51 thf(fact_117_Ball__def, axiom, (! [A:$tType]: (((ball @ A) = (^ [A5:(set @ A),P3:(A > $o)]: ((! [X2:A]: (((((member @ A) @ X2) @ A5) => (P3 @ X2)))))))))).
% 2.93/1.51 thf(fact_118_Un__left__commute, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B4) @ C2)) = (((sup_sup @ (set @ A)) @ B4) @ (((sup_sup @ (set @ A)) @ A3) @ C2)))))).
% 2.93/1.51 thf(fact_119_Un__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B4)) = (((sup_sup @ (set @ A)) @ A3) @ B4))))).
% 2.93/1.51 thf(fact_120_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: ((((sup_sup @ (set @ A)) @ B6) @ A5))))))).
% 2.93/1.51 thf(fact_121_Un__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ A3) = A3)))).
% 2.93/1.51 thf(fact_122_Un__assoc, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B4)) @ C2) = (((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B4) @ C2)))))).
% 2.93/1.51 thf(fact_123_ball__Un, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),P2:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A3) @ B4)) => (P2 @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A3) => (P2 @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B4) => (P2 @ X2))))))))).
% 2.93/1.51 thf(fact_124_bex__Un, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),P2:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A3) @ B4)) & (P2 @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A3) & (P2 @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B4) & (P2 @ X2))))))))).
% 2.93/1.51 thf(fact_125_UnI2, axiom, (! [A:$tType,C3:A,B4:(set @ A),A3:(set @ A)]: (((((member @ A) @ C3) @ B4) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A3) @ B4)))))).
% 2.93/1.51 thf(fact_126_UnI1, axiom, (! [A:$tType,C3:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C3) @ A3) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A3) @ B4)))))).
% 2.93/1.51 thf(fact_127_UnE, axiom, (! [A:$tType,C3:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A3) @ B4)) => ((~ ((((member @ A) @ C3) @ A3))) => (((member @ A) @ C3) @ B4)))))).
% 2.93/1.51 thf(fact_128_image__Un, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B),B4:(set @ B)]: ((((((image @ B) @ A) @ F) @ (((sup_sup @ (set @ B)) @ A3) @ B4)) = (((sup_sup @ (set @ A)) @ ((((image @ B) @ A) @ F) @ A3)) @ ((((image @ B) @ A) @ F) @ B4)))))).
% 2.93/1.51 thf(fact_129_not__False__in__image__Ball, axiom, (! [A:$tType,P2:(A > $o),A3:(set @ A)]: (((~ ((((member @ $o) @ $false) @ ((((image @ A) @ $o) @ P2) @ A3)))) = (! [X2:A]: (((((member @ A) @ X2) @ A3) => (P2 @ X2)))))))).
% 2.93/1.51 thf(fact_130_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F3:(B > A),G2:(C > B),X2:C]: ((F3 @ (G2 @ X2)))))))).
% 2.93/1.51 thf(fact_131_sup_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ B3) = (((sup_sup @ A) @ A2) @ B3)))))))).
% 2.93/1.51 thf(fact_132_sup__left__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.93/1.51 thf(fact_133_sup_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B3)) = (((sup_sup @ A) @ A2) @ B3)))))))).
% 2.93/1.51 thf(fact_134_sup__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F3:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F3 @ X2)) @ (G2 @ X2))))))))).
% 2.93/1.51 thf(fact_135_sup_Oidem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ A2) = A2))))))).
% 2.93/1.51 thf(fact_136_sup__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 2.93/1.51 thf(fact_137_Inf_OINF__cong, axiom, (! [A:$tType,B:$tType,A3:(set @ B),B4:(set @ B),C2:(B > A),D2:(B > A),Inf:((set @ A) > A)]: (((A3 = B4) => ((! [X3:B]: (((((member @ B) @ X3) @ B4) => ((C2 @ X3) = (D2 @ X3))))) => ((Inf @ ((((image @ B) @ A) @ C2) @ A3)) = (Inf @ ((((image @ B) @ A) @ D2) @ B4)))))))).
% 2.93/1.51 thf(fact_138_Sup_OSUP__cong, axiom, (! [A:$tType,B:$tType,A3:(set @ B),B4:(set @ B),C2:(B > A),D2:(B > A),Sup:((set @ A) > A)]: (((A3 = B4) => ((! [X3:B]: (((((member @ B) @ X3) @ B4) => ((C2 @ X3) = (D2 @ X3))))) => ((Sup @ ((((image @ B) @ A) @ C2) @ A3)) = (Sup @ ((((image @ B) @ A) @ D2) @ B4)))))))).
% 2.93/1.51 thf(fact_139_inf__sup__aci_I8_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.93/1.51 thf(fact_140_inf__sup__aci_I7_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z4:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z4)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z4))))))))).
% 2.93/1.51 thf(fact_141_inf__sup__aci_I6_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z4:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z4) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z4))))))))).
% 2.93/1.51 thf(fact_142_inf__sup__aci_I5_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X2)))))))).
% 2.93/1.51 thf(fact_143_sup__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F3:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F3 @ X2)) @ (G2 @ X2))))))))).
% 2.93/1.51 thf(fact_144_sup_Oassoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ C3) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B3) @ C3))))))))).
% 2.93/1.51 thf(fact_145_sup__assoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z4:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z4) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z4))))))))).
% 2.93/1.51 thf(fact_146_sup_Ocommute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [A4:A,B2:A]: ((((sup_sup @ A) @ B2) @ A4)))))))).
% 2.93/1.51 thf(fact_147_sup__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X2)))))))).
% 2.93/1.51 thf(fact_148_sup_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: (((((sup_sup @ A) @ B3) @ (((sup_sup @ A) @ A2) @ C3)) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B3) @ C3))))))))).
% 2.93/1.51 thf(fact_149_sup__left__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z4:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z4)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z4))))))))).
% 2.93/1.51 thf(fact_150_comp__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((comp @ B) @ C) @ A) = (^ [F3:(B > C),G2:(A > B),X2:A]: ((F3 @ (G2 @ X2)))))))).
% 2.93/1.51 thf(fact_151_comp__assoc, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F:(D > B),G:(C > D),H:(A > C)]: (((((((comp @ C) @ B) @ A) @ (((((comp @ D) @ B) @ C) @ F) @ G)) @ H) = (((((comp @ D) @ B) @ A) @ F) @ (((((comp @ C) @ D) @ A) @ G) @ H)))))).
% 2.93/1.51 thf(fact_152_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B3:(A > C),C3:(D > B),D3:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B3) = (((((comp @ D) @ B) @ A) @ C3) @ D3)) => ((A2 @ (B3 @ V)) = (C3 @ (D3 @ V))))))).
% 2.93/1.51 thf(fact_153_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B3:(A > C),C3:(D > B),D3:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A2) @ B3) = (((((comp @ D) @ B) @ A) @ C3) @ D3)) => (! [V2:A]: (((A2 @ (B3 @ V2)) = (C3 @ (D3 @ V2))))))))).
% 2.93/1.51 thf(fact_154_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B3:(A > C),C3:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B3) = C3) => ((A2 @ (B3 @ V)) = (C3 @ V)))))).
% 2.93/1.51 thf(fact_155_image__comp, axiom, (! [B:$tType,A:$tType,C:$tType,F:(B > A),G:(C > B),R3:(set @ C)]: ((((((image @ B) @ A) @ F) @ ((((image @ C) @ B) @ G) @ R3)) = ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ F) @ G)) @ R3))))).
% 2.93/1.51 thf(fact_156_image__eq__imp__comp, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,F:(B > A),A3:(set @ B),G:(C > A),B4:(set @ C),H:(A > D)]: (((((((image @ B) @ A) @ F) @ A3) = ((((image @ C) @ A) @ G) @ B4)) => (((((image @ B) @ D) @ (((((comp @ A) @ D) @ B) @ H) @ F)) @ A3) = ((((image @ C) @ D) @ (((((comp @ A) @ D) @ C) @ H) @ G)) @ B4)))))).
% 2.93/1.51 thf(fact_157_Inf_OINF__image, axiom, (! [B:$tType,A:$tType,C:$tType,Inf:((set @ A) > A),G:(B > A),F:(C > B),A3:(set @ C)]: (((Inf @ ((((image @ B) @ A) @ G) @ ((((image @ C) @ B) @ F) @ A3))) = (Inf @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ A3)))))).
% 2.93/1.51 thf(fact_158_Sup_OSUP__image, axiom, (! [B:$tType,A:$tType,C:$tType,Sup:((set @ A) > A),G:(B > A),F:(C > B),A3:(set @ C)]: (((Sup @ ((((image @ B) @ A) @ G) @ ((((image @ C) @ B) @ F) @ A3))) = (Sup @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ A3)))))).
% 2.93/1.51 thf(fact_159_ball__reg, axiom, (! [A:$tType,R:(set @ A),P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ R) => ((P2 @ X3) => (Q @ X3))))) => ((! [X3:A]: (((((member @ A) @ X3) @ R) => (P2 @ X3)))) => (! [X4:A]: (((((member @ A) @ X4) @ R) => (Q @ X4))))))))).
% 2.93/1.51 thf(fact_160_comp__cong, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,E:$tType,F:(B > A),G:(C > B),X:C,F4:(D > A),G3:(E > D),X5:E]: ((((F @ (G @ X)) = (F4 @ (G3 @ X5))) => (((((((comp @ B) @ A) @ C) @ F) @ G) @ X) = ((((((comp @ D) @ A) @ E) @ F4) @ G3) @ X5)))))).
% 2.93/1.51 thf(fact_161_fun_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,G:(B > C),F:(A > B),V:(D > A)]: (((((((comp @ B) @ C) @ D) @ G) @ (((((comp @ A) @ B) @ D) @ F) @ V)) = (((((comp @ A) @ C) @ D) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ V))))).
% 2.93/1.51 thf(fact_162_type__copy__map__cong0, axiom, (! [B:$tType,D:$tType,E:$tType,A:$tType,C:$tType,M:(B > A),G:(C > B),X:C,N:(D > A),H:(C > D),F:(A > E)]: ((((M @ (G @ X)) = (N @ (H @ X))) => (((((((comp @ B) @ E) @ C) @ (((((comp @ A) @ E) @ B) @ F) @ M)) @ G) @ X) = ((((((comp @ D) @ E) @ C) @ (((((comp @ A) @ E) @ D) @ F) @ N)) @ H) @ X)))))).
% 2.93/1.51 thf(fact_163_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E:$tType,D:$tType,A:$tType,G:(C > B),H:(A > C),R1:(D > B),R22:(A > D),F:(B > E),L:(D > E)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = (((((comp @ D) @ B) @ A) @ R1) @ R22)) => (((((((comp @ B) @ E) @ D) @ F) @ R1) = L) => ((((((comp @ C) @ E) @ A) @ (((((comp @ B) @ E) @ C) @ F) @ G)) @ H) = (((((comp @ D) @ E) @ A) @ L) @ R22))))))).
% 2.93/1.51 thf(fact_164_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E:$tType,F:(C > B),G:(A > C),L1:(D > B),L2:(A > D),H:(E > A),R3:(E > D)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E) @ L2) @ H) = R3) => ((((((comp @ C) @ B) @ E) @ F) @ (((((comp @ A) @ C) @ E) @ G) @ H)) = (((((comp @ D) @ B) @ E) @ L1) @ R3))))))).
% 2.93/1.51 thf(fact_165_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G:(C > B),H:(A > C),R3:(A > B),F:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = R3) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F) @ G)) @ H) = (((((comp @ B) @ D) @ A) @ F) @ R3)))))).
% 2.93/1.51 thf(fact_166_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F:(C > B),G:(A > C),L:(A > B),H:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = L) => ((((((comp @ C) @ B) @ D) @ F) @ (((((comp @ A) @ C) @ D) @ G) @ H)) = (((((comp @ A) @ B) @ D) @ L) @ H)))))).
% 2.93/1.51 thf(fact_167_process_Opred__rel, axiom, (! [A:$tType]: (((proces1205983068rocess @ A) = (^ [P3:(A > $o),X2:(proces634752977rocess @ A)]: ((((((proces749077512rocess @ A) @ A) @ ((bNF_eq_onp @ A) @ P3)) @ X2) @ X2))))))).
% 2.93/1.51 thf(fact_168_Sup__insert, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A2:A,A3:(set @ A)]: ((((complete_Sup_Sup @ A) @ (((insert @ A) @ A2) @ A3)) = (((sup_sup @ A) @ A2) @ ((complete_Sup_Sup @ A) @ A3))))))))).
% 2.93/1.51 thf(fact_169_SUP__image, axiom, (! [B:$tType,A:$tType,C:$tType]: ((((complete_Sup @ A) @ (type2 @ A)) => (! [G:(B > A),F:(C > B),A3:(set @ C)]: ((((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ G) @ ((((image @ C) @ B) @ F) @ A3))) = ((complete_Sup_Sup @ A) @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ A3))))))))).
% 2.93/1.51 thf(fact_170_Union__Un__distrib, axiom, (! [A:$tType,A3:(set @ (set @ A)),B4:(set @ (set @ A))]: ((((complete_Sup_Sup @ (set @ A)) @ (((sup_sup @ (set @ (set @ A))) @ A3) @ B4)) = (((sup_sup @ (set @ A)) @ ((complete_Sup_Sup @ (set @ A)) @ A3)) @ ((complete_Sup_Sup @ (set @ A)) @ B4)))))).
% 2.93/1.51 thf(fact_171_SUP__cong, axiom, (! [A:$tType,B:$tType]: ((((complete_Sup @ A) @ (type2 @ A)) => (! [A3:(set @ B),B4:(set @ B),C2:(B > A),D2:(B > A)]: (((A3 = B4) => ((! [X3:B]: (((((member @ B) @ X3) @ B4) => ((C2 @ X3) = (D2 @ X3))))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ C2) @ A3)) = ((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ D2) @ B4))))))))))).
% 2.93/1.51 thf(fact_172_process_Orel__eq__onp, axiom, (! [A:$tType,P2:(A > $o)]: (((((proces749077512rocess @ A) @ A) @ ((bNF_eq_onp @ A) @ P2)) = ((bNF_eq_onp @ (proces634752977rocess @ A)) @ ((proces1205983068rocess @ A) @ P2)))))).
% 2.93/1.51 thf(fact_173_eq__onp__eqD, axiom, (! [A:$tType,P2:(A > $o),Q:(A > (A > $o)),X:A]: (((((bNF_eq_onp @ A) @ P2) = Q) => ((P2 @ X) = ((Q @ X) @ X)))))).
% 2.93/1.51 thf(fact_174_eq__onp__mono0, axiom, (! [A:$tType,A3:(set @ A),P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ A3) => ((P2 @ X3) => (Q @ X3))))) => (! [X4:A]: (((((member @ A) @ X4) @ A3) => (! [Xa3:A]: (((((member @ A) @ Xa3) @ A3) => (((((bNF_eq_onp @ A) @ P2) @ X4) @ Xa3) => ((((bNF_eq_onp @ A) @ Q) @ X4) @ Xa3)))))))))))).
% 2.93/1.51 thf(fact_175_eq__onp__to__eq, axiom, (! [A:$tType,P2:(A > $o),X:A,Y:A]: ((((((bNF_eq_onp @ A) @ P2) @ X) @ Y) => (X = Y))))).
% 2.93/1.51 thf(fact_176_eq__onp__same__args, axiom, (! [A:$tType,P2:(A > $o),X:A]: ((((((bNF_eq_onp @ A) @ P2) @ X) @ X) = (P2 @ X))))).
% 2.93/1.51 thf(fact_177_Union__insert, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ (set @ A))]: ((((complete_Sup_Sup @ (set @ A)) @ (((insert @ (set @ A)) @ A2) @ B4)) = (((sup_sup @ (set @ A)) @ A2) @ ((complete_Sup_Sup @ (set @ A)) @ B4)))))).
% 2.93/1.51 thf(fact_178_Sup__union__distrib, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A3:(set @ A),B4:(set @ A)]: ((((complete_Sup_Sup @ A) @ (((sup_sup @ (set @ A)) @ A3) @ B4)) = (((sup_sup @ A) @ ((complete_Sup_Sup @ A) @ A3)) @ ((complete_Sup_Sup @ A) @ B4))))))))).
% 2.93/1.51 thf(fact_179_Union__image__insert, axiom, (! [A:$tType,B:$tType,F:(B > (set @ A)),A2:B,B4:(set @ B)]: ((((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ F) @ (((insert @ B) @ A2) @ B4))) = (((sup_sup @ (set @ A)) @ (F @ A2)) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ F) @ B4))))))).
% 2.93/1.51 thf(fact_180_vimage2p__comp, axiom, (! [E:$tType,D:$tType,F5:$tType,A:$tType,C:$tType,B:$tType,G4:$tType,F1:(F5 > A),F2:(D > F5),G1:(G4 > B),G22:(E > G4)]: (((((((((bNF_vimage2p @ D) @ A) @ E) @ B) @ C) @ (((((comp @ F5) @ A) @ D) @ F1) @ F2)) @ (((((comp @ G4) @ B) @ E) @ G1) @ G22)) = (((((comp @ (F5 > (G4 > C))) @ (D > (E > C))) @ (A > (B > C))) @ (((((((bNF_vimage2p @ D) @ F5) @ E) @ G4) @ C) @ F2) @ G22)) @ (((((((bNF_vimage2p @ F5) @ A) @ G4) @ B) @ C) @ F1) @ G1)))))).
% 2.93/1.51 thf(fact_181_INF__image, axiom, (! [B:$tType,A:$tType,C:$tType]: ((((complete_Inf @ A) @ (type2 @ A)) => (! [G:(B > A),F:(C > B),A3:(set @ C)]: ((((complete_Inf_Inf @ A) @ ((((image @ B) @ A) @ G) @ ((((image @ C) @ B) @ F) @ A3))) = ((complete_Inf_Inf @ A) @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ A3))))))))).
% 2.93/1.51 thf(fact_182_SUP__id__eq, axiom, (! [A:$tType]: ((((complete_Sup @ A) @ (type2 @ A)) => (! [A3:(set @ A)]: ((((complete_Sup_Sup @ A) @ ((((image @ A) @ A) @ (id @ A)) @ A3)) = ((complete_Sup_Sup @ A) @ A3)))))))).
% 2.93/1.51 thf(fact_183_UN__ball__bex__simps_I3_J, axiom, (! [D:$tType,A3:(set @ (set @ D)),P2:(D > $o)]: (((? [X2:D]: (((((member @ D) @ X2) @ ((complete_Sup_Sup @ (set @ D)) @ A3)) & (P2 @ X2)))) = (? [X2:(set @ D)]: (((((member @ (set @ D)) @ X2) @ A3) & (? [Y2:D]: (((((member @ D) @ Y2) @ X2) & (P2 @ Y2))))))))))).
% 2.93/1.51 thf(fact_184_UN__ball__bex__simps_I1_J, axiom, (! [A:$tType,A3:(set @ (set @ A)),P2:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ ((complete_Sup_Sup @ (set @ A)) @ A3)) => (P2 @ X2)))) = (! [X2:(set @ A)]: (((((member @ (set @ A)) @ X2) @ A3) => (! [Y2:A]: (((((member @ A) @ Y2) @ X2) => (P2 @ Y2))))))))))).
% 2.93/1.51 thf(fact_185_UnionI, axiom, (! [A:$tType,X6:(set @ A),C2:(set @ (set @ A)),A3:A]: (((((member @ (set @ A)) @ X6) @ C2) => ((((member @ A) @ A3) @ X6) => (((member @ A) @ A3) @ ((complete_Sup_Sup @ (set @ A)) @ C2))))))).
% 2.93/1.51 thf(fact_186_Union__iff, axiom, (! [A:$tType,A3:A,C2:(set @ (set @ A))]: (((((member @ A) @ A3) @ ((complete_Sup_Sup @ (set @ A)) @ C2)) = (? [X2:(set @ A)]: (((((member @ (set @ A)) @ X2) @ C2) & (((member @ A) @ A3) @ X2)))))))).
% 2.93/1.51 thf(fact_187_id__apply, axiom, (! [A:$tType]: (((id @ A) = (^ [X2:A]: (X2)))))).
% 2.93/1.51 thf(fact_188_image__id, axiom, (! [A:$tType]: (((((image @ A) @ A) @ (id @ A)) = (id @ (set @ A)))))).
% 2.93/1.51 thf(fact_189_ball__UN, axiom, (! [A:$tType,B:$tType,B4:(B > (set @ A)),A3:(set @ B),P2:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B4) @ A3))) => (P2 @ X2)))) = (! [X2:B]: (((((member @ B) @ X2) @ A3) => (! [Y2:A]: (((((member @ A) @ Y2) @ (B4 @ X2)) => (P2 @ Y2))))))))))).
% 2.93/1.51 thf(fact_190_bex__UN, axiom, (! [A:$tType,B:$tType,B4:(B > (set @ A)),A3:(set @ B),P2:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ B4) @ A3))) & (P2 @ X2)))) = (? [X2:B]: (((((member @ B) @ X2) @ A3) & (? [Y2:A]: (((((member @ A) @ Y2) @ (B4 @ X2)) & (P2 @ Y2))))))))))).
% 2.93/1.51 thf(fact_191_UN__ball__bex__simps_I2_J, axiom, (! [C:$tType,B:$tType,B4:(B > (set @ C)),A3:(set @ B),P2:(C > $o)]: (((! [X2:C]: (((((member @ C) @ X2) @ ((complete_Sup_Sup @ (set @ C)) @ ((((image @ B) @ (set @ C)) @ B4) @ A3))) => (P2 @ X2)))) = (! [X2:B]: (((((member @ B) @ X2) @ A3) => (! [Y2:C]: (((((member @ C) @ Y2) @ (B4 @ X2)) => (P2 @ Y2))))))))))).
% 2.93/1.51 thf(fact_192_UN__ball__bex__simps_I4_J, axiom, (! [F5:$tType,E:$tType,B4:(E > (set @ F5)),A3:(set @ E),P2:(F5 > $o)]: (((? [X2:F5]: (((((member @ F5) @ X2) @ ((complete_Sup_Sup @ (set @ F5)) @ ((((image @ E) @ (set @ F5)) @ B4) @ A3))) & (P2 @ X2)))) = (? [X2:E]: (((((member @ E) @ X2) @ A3) & (? [Y2:F5]: (((((member @ F5) @ Y2) @ (B4 @ X2)) & (P2 @ Y2))))))))))).
% 2.93/1.51 thf(fact_193_fun_Omap__id, axiom, (! [A:$tType,D:$tType,T:(D > A)]: (((((((comp @ A) @ A) @ D) @ (id @ A)) @ T) = T)))).
% 2.93/1.51 thf(fact_194_id__comp, axiom, (! [B:$tType,A:$tType,G:(A > B)]: (((((((comp @ B) @ B) @ A) @ (id @ B)) @ G) = G)))).
% 2.93/1.51 thf(fact_195_comp__id, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((((comp @ A) @ B) @ A) @ F) @ (id @ A)) = F)))).
% 2.93/1.51 thf(fact_196_INF__id__eq, axiom, (! [A:$tType]: ((((complete_Inf @ A) @ (type2 @ A)) => (! [A3:(set @ A)]: ((((complete_Inf_Inf @ A) @ ((((image @ A) @ A) @ (id @ A)) @ A3)) = ((complete_Inf_Inf @ A) @ A3)))))))).
% 2.93/1.51 thf(fact_197_UnionE, axiom, (! [A:$tType,A3:A,C2:(set @ (set @ A))]: (((((member @ A) @ A3) @ ((complete_Sup_Sup @ (set @ A)) @ C2)) => (~ ((! [X7:(set @ A)]: (((((member @ A) @ A3) @ X7) => (~ ((((member @ (set @ A)) @ X7) @ C2)))))))))))).
% 2.93/1.51 thf(fact_198_fun_Omap__id0, axiom, (! [A:$tType,D:$tType]: ((((((comp @ A) @ A) @ D) @ (id @ A)) = (id @ (D > A)))))).
% 2.93/1.51 thf(fact_199_process_Omap__id0, axiom, (! [A:$tType]: (((((proces370407749rocess @ A) @ A) @ (id @ A)) = (id @ (proces634752977rocess @ A)))))).
% 2.93/1.51 thf(fact_200_process_Omap__id, axiom, (! [A:$tType,T:(proces634752977rocess @ A)]: ((((((proces370407749rocess @ A) @ A) @ (id @ A)) @ T) = T)))).
% 2.93/1.51 thf(fact_201_Inf_OINF__id__eq, axiom, (! [A:$tType,Inf:((set @ A) > A),A3:(set @ A)]: (((Inf @ ((((image @ A) @ A) @ (id @ A)) @ A3)) = (Inf @ A3))))).
% 2.93/1.51 thf(fact_202_Sup_OSUP__id__eq, axiom, (! [A:$tType,Sup:((set @ A) > A),A3:(set @ A)]: (((Sup @ ((((image @ A) @ A) @ (id @ A)) @ A3)) = (Sup @ A3))))).
% 2.93/1.51 thf(fact_203_INF__cong, axiom, (! [A:$tType,B:$tType]: ((((complete_Inf @ A) @ (type2 @ A)) => (! [A3:(set @ B),B4:(set @ B),C2:(B > A),D2:(B > A)]: (((A3 = B4) => ((! [X3:B]: (((((member @ B) @ X3) @ B4) => ((C2 @ X3) = (D2 @ X3))))) => (((complete_Inf_Inf @ A) @ ((((image @ B) @ A) @ C2) @ A3)) = ((complete_Inf_Inf @ A) @ ((((image @ B) @ A) @ D2) @ B4))))))))))).
% 2.93/1.51 thf(fact_204_eq__id__iff, axiom, (! [A:$tType,F:(A > A)]: (((! [X2:A]: (((F @ X2) = X2))) = (F = (id @ A)))))).
% 2.93/1.51 thf(fact_205_id__def, axiom, (! [A:$tType]: (((id @ A) = (^ [X2:A]: (X2)))))).
% 2.93/1.51 thf(fact_206_comp__eq__id__dest, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B3:(A > C),C3:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B3) = (((((comp @ B) @ B) @ A) @ (id @ B)) @ C3)) => ((A2 @ (B3 @ V)) = (C3 @ V)))))).
% 2.93/1.51 thf(fact_207_pointfree__idE, axiom, (! [B:$tType,A:$tType,F:(B > A),G:(A > B),X:A]: ((((((((comp @ B) @ A) @ A) @ F) @ G) = (id @ A)) => ((F @ (G @ X)) = X))))).
% 2.93/1.51 thf(fact_208_member__bind, axiom, (! [A:$tType,B:$tType,X:A,P2:(set @ B),F:(B > (set @ A))]: (((((member @ A) @ X) @ ((((bind @ B) @ A) @ P2) @ F)) = (((member @ A) @ X) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ F) @ P2))))))).
% 2.93/1.51 thf(fact_209_Sup__SUP__eq, axiom, (! [A:$tType]: (((complete_Sup_Sup @ (A > $o)) = (^ [S:(set @ (A > $o)),X2:A]: ((((member @ A) @ X2) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ (A > $o)) @ (set @ A)) @ (collect @ A)) @ S))))))))).
% 2.93/1.51 thf(fact_210_Union__image__empty, axiom, (! [B:$tType,A:$tType,A3:(set @ A),F:(B > (set @ A))]: (((((sup_sup @ (set @ A)) @ A3) @ ((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ F) @ (bot_bot @ (set @ B))))) = A3)))).
% 2.93/1.51 thf(fact_211_empty__iff, axiom, (! [A:$tType,C3:A]: ((~ ((((member @ A) @ C3) @ (bot_bot @ (set @ A)))))))).
% 2.93/1.51 thf(fact_212_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X2:A]: ((~ ((((member @ A) @ X2) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 2.93/1.51 thf(fact_213_Collect__empty__eq, axiom, (! [A:$tType,P2:(A > $o)]: (((((collect @ A) @ P2) = (bot_bot @ (set @ A))) = (! [X2:A]: ((~ ((P2 @ X2))))))))).
% 2.93/1.51 thf(fact_214_empty__Collect__eq, axiom, (! [A:$tType,P2:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P2)) = (! [X2:A]: ((~ ((P2 @ X2))))))))).
% 2.93/1.51 thf(fact_215_Sup1__I, axiom, (! [A:$tType,P2:(A > $o),A3:(set @ (A > $o)),A2:A]: (((((member @ (A > $o)) @ P2) @ A3) => ((P2 @ A2) => (((complete_Sup_Sup @ (A > $o)) @ A3) @ A2)))))).
% 2.93/1.51 thf(fact_216_image__empty, axiom, (! [B:$tType,A:$tType,F:(B > A)]: ((((((image @ B) @ A) @ F) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 2.93/1.51 thf(fact_217_empty__is__image, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B)]: ((((bot_bot @ (set @ A)) = ((((image @ B) @ A) @ F) @ A3)) = (A3 = (bot_bot @ (set @ B))))))).
% 2.93/1.51 thf(fact_218_image__is__empty, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B)]: (((((((image @ B) @ A) @ F) @ A3) = (bot_bot @ (set @ A))) = (A3 = (bot_bot @ (set @ B))))))).
% 2.93/1.51 thf(fact_219_sup__bot_Oright__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ (bot_bot @ A)) = A2))))))).
% 2.93/1.51 thf(fact_220_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A2) = A2))))))).
% 2.93/1.51 thf(fact_221_sup__eq__bot__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((sup_sup @ A) @ X) @ Y) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.93/1.51 thf(fact_222_bot__eq__sup__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.93/1.51 thf(fact_223_Sup__bot__conv_I2_J, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A3:(set @ A)]: ((((bot_bot @ A) = ((complete_Sup_Sup @ A) @ A3)) = (! [X2:A]: (((((member @ A) @ X2) @ A3) => (X2 = (bot_bot @ A)))))))))))).
% 2.93/1.51 thf(fact_224_Sup__bot__conv_I1_J, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [A3:(set @ A)]: (((((complete_Sup_Sup @ A) @ A3) = (bot_bot @ A)) = (! [X2:A]: (((((member @ A) @ X2) @ A3) => (X2 = (bot_bot @ A)))))))))))).
% 2.93/1.51 thf(fact_225_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.93/1.51 thf(fact_226_ball__empty, axiom, (! [A:$tType,P2:(A > $o),X4:A]: (((((member @ A) @ X4) @ (bot_bot @ (set @ A))) => (P2 @ X4))))).
% 2.93/1.51 thf(fact_227_Un__empty, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A3) @ B4) = (bot_bot @ (set @ A))) = ((A3 = (bot_bot @ (set @ A))) & (B4 = (bot_bot @ (set @ A)))))))).
% 2.93/1.51 thf(fact_228_empty__bind, axiom, (! [B:$tType,A:$tType,F:(B > (set @ A))]: ((((((bind @ B) @ A) @ (bot_bot @ (set @ B))) @ F) = (bot_bot @ (set @ A)))))).
% 2.93/1.51 thf(fact_229_Sup__empty, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (((complete_Sup_Sup @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ A)))))).
% 2.93/1.51 thf(fact_230_Sup1__E, axiom, (! [A:$tType,A3:(set @ (A > $o)),A2:A]: (((((complete_Sup_Sup @ (A > $o)) @ A3) @ A2) => (~ ((! [P4:(A > $o)]: (((((member @ (A > $o)) @ P4) @ A3) => (~ ((P4 @ A2)))))))))))).
% 2.93/1.51 thf(fact_231_Union__empty, axiom, (! [A:$tType]: ((((complete_Sup_Sup @ (set @ A)) @ (bot_bot @ (set @ (set @ A)))) = (bot_bot @ (set @ A)))))).
% 2.93/1.51 thf(fact_232_Union__empty__conv, axiom, (! [A:$tType,A3:(set @ (set @ A))]: (((((complete_Sup_Sup @ (set @ A)) @ A3) = (bot_bot @ (set @ A))) = (! [X2:(set @ A)]: (((((member @ (set @ A)) @ X2) @ A3) => (X2 = (bot_bot @ (set @ A)))))))))).
% 2.93/1.51 thf(fact_233_empty__Union__conv, axiom, (! [A:$tType,A3:(set @ (set @ A))]: ((((bot_bot @ (set @ A)) = ((complete_Sup_Sup @ (set @ A)) @ A3)) = (! [X2:(set @ A)]: (((((member @ (set @ A)) @ X2) @ A3) => (X2 = (bot_bot @ (set @ A)))))))))).
% 2.93/1.51 thf(fact_234_sup__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 2.93/1.51 thf(fact_235_sup__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 2.93/1.51 thf(fact_236_Un__empty__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = A3)))).
% 2.93/1.51 thf(fact_237_Un__empty__left, axiom, (! [A:$tType,B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B4) = B4)))).
% 2.93/1.51 thf(fact_238_image__bind, axiom, (! [A:$tType,B:$tType,C:$tType,F:(B > A),A3:(set @ C),G:(C > (set @ B))]: ((((((image @ B) @ A) @ F) @ ((((bind @ C) @ B) @ A3) @ G)) = ((((bind @ C) @ A) @ A3) @ (((((comp @ (set @ B)) @ (set @ A)) @ C) @ (((image @ B) @ A) @ F)) @ G)))))).
% 2.93/1.51 thf(fact_239_bind__image, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > B),A3:(set @ C),G:(B > (set @ A))]: ((((((bind @ B) @ A) @ ((((image @ C) @ B) @ F) @ A3)) @ G) = ((((bind @ C) @ A) @ A3) @ (((((comp @ B) @ (set @ A)) @ C) @ G) @ F)))))).
% 2.93/1.51 thf(fact_240_singletonD, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B3 = A2))))).
% 2.93/1.51 thf(fact_241_singleton__iff, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B3 = A2))))).
% 2.93/1.51 thf(fact_242_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B3:A,C3:A,D3:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C3) @ (((insert @ A) @ D3) @ (bot_bot @ (set @ A))))) = (((A2 = C3) & (B3 = D3)) | ((A2 = D3) & (B3 = C3))))))).
% 2.93/1.51 thf(fact_243_insert__not__empty, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((insert @ A) @ A2) @ A3) != (bot_bot @ (set @ A)))))).
% 2.93/1.51 thf(fact_244_singleton__inject, axiom, (! [A:$tType,A2:A,B3:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A2 = B3))))).
% 2.93/1.51 thf(fact_245_Inf__INT__eq, axiom, (! [A:$tType]: (((complete_Inf_Inf @ (A > $o)) = (^ [S:(set @ (A > $o)),X2:A]: ((((member @ A) @ X2) @ ((complete_Inf_Inf @ (set @ A)) @ ((((image @ (A > $o)) @ (set @ A)) @ (collect @ A)) @ S))))))))).
% 2.93/1.51 thf(fact_246_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.93/1.51 thf(fact_247_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 2.93/1.51 thf(fact_248_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y4:A]: ((~ ((((member @ A) @ Y4) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 2.93/1.51 thf(fact_249_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X2:A]: ((((member @ A) @ X2) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 2.93/1.51 thf(fact_250_SUP__eq__const, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [I:(set @ B),F:(B > A),X:A]: (((I != (bot_bot @ (set @ B))) => ((! [I2:B]: (((((member @ B) @ I2) @ I) => ((F @ I2) = X)))) => (((complete_Sup_Sup @ A) @ ((((image @ B) @ A) @ F) @ I)) = X))))))))).
% 2.93/1.51 thf(fact_251_INF__eq__const, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [I:(set @ B),F:(B > A),X:A]: (((I != (bot_bot @ (set @ B))) => ((! [I2:B]: (((((member @ B) @ I2) @ I) => ((F @ I2) = X)))) => (((complete_Inf_Inf @ A) @ ((((image @ B) @ A) @ F) @ I)) = X))))))))).
% 2.93/1.51 thf(fact_252_singleton__Un__iff, axiom, (! [A:$tType,X:A,A3:(set @ A),B4:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A3) @ B4)) = (((A3 = (bot_bot @ (set @ A))) & (B4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B4 = (bot_bot @ (set @ A)))) | ((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.93/1.51 thf(fact_253_Un__singleton__iff, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A3) @ B4) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A3 = (bot_bot @ (set @ A))) & (B4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B4 = (bot_bot @ (set @ A)))) | ((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B4 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.93/1.51 thf(fact_254_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A4:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A)))))))))).
% 2.93/1.51 thf(fact_255_bind__UNION, axiom, (! [A:$tType,B:$tType]: ((((bind @ B) @ A) = (^ [A5:(set @ B),F3:(B > (set @ A))]: (((complete_Sup_Sup @ (set @ A)) @ ((((image @ B) @ (set @ A)) @ F3) @ A5)))))))).
% 2.93/1.51 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.93/1.51 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A6:$tType]: (((bounded_lattice @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.93/1.51 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A6:$tType,A7:$tType]: ((((bounded_lattice @ A7) @ (type2 @ A7)) => ((bounded_lattice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.93/1.51 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A6:$tType,A7:$tType]: ((((bounded_lattice @ A7) @ (type2 @ A7)) => ((bounde1808546759up_bot @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.93/1.51 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice, axiom, (! [A6:$tType,A7:$tType]: ((((comple187826305attice @ A7) @ (type2 @ A7)) => ((comple187826305attice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.93/1.51 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A6:$tType,A7:$tType]: ((((bounded_lattice @ A7) @ (type2 @ A7)) => ((bounded_lattice_bot @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.93/1.51 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A6:$tType,A7:$tType]: ((((semilattice_sup @ A7) @ (type2 @ A7)) => ((semilattice_sup @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.93/1.51 thf(tcon_fun___Complete__Lattices_OSup, axiom, (! [A6:$tType,A7:$tType]: ((((complete_Sup @ A7) @ (type2 @ A7)) => ((complete_Sup @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.93/1.51 thf(tcon_fun___Complete__Lattices_OInf, axiom, (! [A6:$tType,A7:$tType]: ((((complete_Inf @ A7) @ (type2 @ A7)) => ((complete_Inf @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.93/1.51 thf(tcon_fun___Lattices_Olattice, axiom, (! [A6:$tType,A7:$tType]: ((((lattice @ A7) @ (type2 @ A7)) => ((lattice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.93/1.51 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3, axiom, (! [A6:$tType]: (((bounde1808546759up_bot @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.93/1.51 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_4, axiom, (! [A6:$tType]: (((comple187826305attice @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.93/1.51 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_5, axiom, (! [A6:$tType]: (((bounded_lattice_bot @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.93/1.51 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_6, axiom, (! [A6:$tType]: (((semilattice_sup @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.93/1.51 thf(tcon_Set_Oset___Complete__Lattices_OSup_7, axiom, (! [A6:$tType]: (((complete_Sup @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.93/1.51 thf(tcon_Set_Oset___Complete__Lattices_OInf_8, axiom, (! [A6:$tType]: (((complete_Inf @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.93/1.51 thf(tcon_Set_Oset___Lattices_Olattice_9, axiom, (! [A6:$tType]: (((lattice @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.93/1.51 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_10, axiom, ((bounde1808546759up_bot @ $o) @ (type2 @ $o))).
% 2.93/1.51 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_11, axiom, ((comple187826305attice @ $o) @ (type2 @ $o))).
% 2.93/1.51 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12, axiom, ((bounded_lattice_bot @ $o) @ (type2 @ $o))).
% 2.93/1.51 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_13, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 2.93/1.51 thf(tcon_HOL_Obool___Complete__Lattices_OSup_14, axiom, ((complete_Sup @ $o) @ (type2 @ $o))).
% 2.93/1.51 thf(tcon_HOL_Obool___Complete__Lattices_OInf_15, axiom, ((complete_Inf @ $o) @ (type2 @ $o))).
% 2.93/1.51 thf(tcon_HOL_Obool___Lattices_Olattice_16, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 2.93/1.51 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 2.93/1.51 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.93/1.51 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.93/1.51 thf(conj_0, conjecture, (((proces10484146Action @ a) @ p) | ((proces401113213Choice @ a) @ p))).
% 2.93/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.lJEBhRXwsb/DTF2DTF10395.p
% 2.93/1.51 ------------------------
% 2.93/1.54 ---- Cleaned THF ---
% 2.93/1.54 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 2.93/1.54 proces634752977rocess: $tType > $tType ).
% 2.93/1.54
% 2.93/1.54 thf(ty_t_Set_Oset,type,
% 2.93/1.54 set: $tType > $tType ).
% 2.93/1.54
% 2.93/1.54 thf(ty_t_itself,type,
% 2.93/1.54 itself: $tType > $tType ).
% 2.93/1.54
% 2.93/1.54 thf(ty_tf_a,type,
% 2.93/1.54 a: $tType ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.93/1.54 bounded_lattice:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_HOL_Otype,type,
% 2.93/1.54 type:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_Lattices_Olattice,type,
% 2.93/1.54 lattice:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_Complete__Lattices_OInf,type,
% 2.93/1.54 complete_Inf:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_Complete__Lattices_OSup,type,
% 2.93/1.54 complete_Sup:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.93/1.54 semilattice_sup:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 2.93/1.54 bounded_lattice_bot:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 2.93/1.54 comple187826305attice:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 2.93/1.54 bounde1808546759up_bot:
% 2.93/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_BNF__Def_Oeq__onp,type,
% 2.93/1.54 bNF_eq_onp:
% 2.93/1.54 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_BNF__Def_Ovimage2p,type,
% 2.93/1.54 bNF_vimage2p:
% 2.93/1.54 !>[A: $tType,D: $tType,B: $tType,E: $tType,C: $tType] : ( ( A > D ) > ( B > E ) > ( D > E > C ) > A > B > C ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Complete__Lattices_OInf__class_OInf,type,
% 2.93/1.54 complete_Inf_Inf:
% 2.93/1.54 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Complete__Lattices_OSup__class_OSup,type,
% 2.93/1.54 complete_Sup_Sup:
% 2.93/1.54 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Fun_Ocomp,type,
% 2.93/1.54 comp:
% 2.93/1.54 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Fun_Oid,type,
% 2.93/1.54 id:
% 2.93/1.54 !>[A: $tType] : ( A > A ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_If,type,
% 2.93/1.54 if:
% 2.93/1.54 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.93/1.54 sup_sup:
% 2.93/1.54 !>[A: $tType] : ( A > A > A ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.93/1.54 bot_bot:
% 2.93/1.54 !>[A: $tType] : A ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 2.93/1.54 proces1525233512Action:
% 2.93/1.54 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 2.93/1.54 proces1915862579Choice:
% 2.93/1.54 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 2.93/1.54 proces1406508781rocess:
% 2.93/1.54 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 2.93/1.54 proces979765041_ch1Of:
% 2.93/1.54 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 2.93/1.54 proces988026546_ch2Of:
% 2.93/1.54 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 2.93/1.54 proces1778668539contOf:
% 2.93/1.54 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 2.93/1.54 proces894737309rocess:
% 2.93/1.54 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 2.93/1.54 proces10484146Action:
% 2.93/1.54 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 2.93/1.54 proces401113213Choice:
% 2.93/1.54 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
% 2.93/1.54 proces370407749rocess:
% 2.93/1.54 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
% 2.93/1.54 proces1205983068rocess:
% 2.93/1.54 !>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 2.93/1.54 proces745025900prefOf:
% 2.93/1.54 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 2.93/1.54 proces749077512rocess:
% 2.93/1.54 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Oset__process,type,
% 2.93/1.54 proces1148692671rocess:
% 2.93/1.54 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( set @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Pure_Otype,type,
% 2.93/1.54 type2:
% 2.93/1.54 !>[A: $tType] : ( itself @ A ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Set_OBall,type,
% 2.93/1.54 ball:
% 2.93/1.54 !>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Set_OCollect,type,
% 2.93/1.54 collect:
% 2.93/1.54 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Set_Obind,type,
% 2.93/1.54 bind:
% 2.93/1.54 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > ( set @ B ) ) > ( set @ B ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Set_Oimage,type,
% 2.93/1.54 image:
% 2.93/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_Set_Oinsert,type,
% 2.93/1.54 insert:
% 2.93/1.54 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_c_member,type,
% 2.93/1.54 member:
% 2.93/1.54 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(sy_v_p,type,
% 2.93/1.54 p: proces634752977rocess @ a ).
% 2.93/1.54
% 2.93/1.54 thf(fact_0_process_Odistinct__disc_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces401113213Choice @ A @ Process )
% 2.93/1.54 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_1_process_Odistinct__disc_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces10484146Action @ A @ Process )
% 2.93/1.54 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_2_process_Oexhaust__disc,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.93/1.54 ( ~ ( proces10484146Action @ A @ Process )
% 2.93/1.54 => ( proces401113213Choice @ A @ Process ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_3_process_Ocorec__disc__iff_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
% 2.93/1.54 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( ~ ( P @ A2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_4_process_Ocorec__disc__iff_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
% 2.93/1.54 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( P @ A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_5_process_Omap__disc__iff_I2_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 2.93/1.54 = ( proces401113213Choice @ A @ A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_6_process_Omap__disc__iff_I1_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 2.93/1.54 = ( proces10484146Action @ A @ A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_7_process_Ocorec__disc_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 2.93/1.54 ( ~ ( P @ A2 )
% 2.93/1.54 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_8_process_Ocorec__disc_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 2.93/1.54 ( ( P @ A2 )
% 2.93/1.54 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_9_process_Odisc_I4_J,axiom,
% 2.93/1.54 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_10_process_Odisc_I3_J,axiom,
% 2.93/1.54 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 2.93/1.54 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_11_process_OdiscI_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 2.93/1.54 ( ( Process
% 2.93/1.54 = ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 2.93/1.54 => ( proces401113213Choice @ A @ Process ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_12_isChoice__def,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( proces401113213Choice @ A )
% 2.93/1.54 = ( ^ [Process2: proces634752977rocess @ A] :
% 2.93/1.54 ? [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 2.93/1.54 ( Process2
% 2.93/1.54 = ( proces1915862579Choice @ A @ X212 @ X222 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_13_process_Odisc_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 2.93/1.54 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_14_process_Odisc_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_15_process_Oinject_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 2.93/1.54 ( ( ( proces1915862579Choice @ A @ X21 @ X22 )
% 2.93/1.54 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 2.93/1.54 = ( ( X21 = Y21 )
% 2.93/1.54 & ( X22 = Y22 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_16_process_Oinject_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,X11: A,X12: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 2.93/1.54 ( ( ( proces1525233512Action @ A @ X11 @ X12 )
% 2.93/1.54 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 2.93/1.54 = ( ( X11 = Y11 )
% 2.93/1.54 & ( X12 = Y12 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_17_process_Ocorec_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 2.93/1.54 ( ~ ( P @ A2 )
% 2.93/1.54 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 2.93/1.54 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A2 ) @ ( G211 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A2 ) @ ( G221 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_18_process_Ocorec_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 2.93/1.54 ( ( P @ A2 )
% 2.93/1.54 => ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
% 2.93/1.54 = ( proces1525233512Action @ A @ ( G11 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A2 ) @ ( G121 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_19_process_Osimps_I16_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: A > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces370407749rocess @ A @ B @ F @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 2.93/1.54 = ( proces1915862579Choice @ B @ ( proces370407749rocess @ A @ B @ F @ X21 ) @ ( proces370407749rocess @ A @ B @ F @ X22 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_20_process_Osimps_I15_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: A > B,X11: A,X12: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces370407749rocess @ A @ B @ F @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 2.93/1.54 = ( proces1525233512Action @ B @ ( F @ X11 ) @ ( proces370407749rocess @ A @ B @ F @ X12 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_21_process_Odistinct_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,X11: A,X12: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1525233512Action @ A @ X11 @ X12 )
% 2.93/1.54 != ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_22_process_Oexhaust,axiom,
% 2.93/1.54 ! [A: $tType,Y: proces634752977rocess @ A] :
% 2.93/1.54 ( ! [X112: A,X122: proces634752977rocess @ A] :
% 2.93/1.54 ( Y
% 2.93/1.54 != ( proces1525233512Action @ A @ X112 @ X122 ) )
% 2.93/1.54 => ~ ! [X213: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 2.93/1.54 ( Y
% 2.93/1.54 != ( proces1915862579Choice @ A @ X213 @ X223 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_23_isAction__def,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( proces10484146Action @ A )
% 2.93/1.54 = ( ^ [Process2: proces634752977rocess @ A] :
% 2.93/1.54 ? [X113: A,X123: proces634752977rocess @ A] :
% 2.93/1.54 ( Process2
% 2.93/1.54 = ( proces1525233512Action @ A @ X113 @ X123 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_24_process_OdiscI_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A,X11: A,X12: proces634752977rocess @ A] :
% 2.93/1.54 ( ( Process
% 2.93/1.54 = ( proces1525233512Action @ A @ X11 @ X12 ) )
% 2.93/1.54 => ( proces10484146Action @ A @ Process ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_25_process_Omap__sel_I1_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 2.93/1.54 ( ( proces10484146Action @ A @ A2 )
% 2.93/1.54 => ( ( proces745025900prefOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 2.93/1.54 = ( F @ ( proces745025900prefOf @ A @ A2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_26_process_Omap__sel_I3_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 2.93/1.54 ( ( proces401113213Choice @ A @ A2 )
% 2.93/1.54 => ( ( proces979765041_ch1Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 2.93/1.54 = ( proces370407749rocess @ A @ B @ F @ ( proces979765041_ch1Of @ A @ A2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_27_process_Omap__sel_I4_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 2.93/1.54 ( ( proces401113213Choice @ A @ A2 )
% 2.93/1.54 => ( ( proces988026546_ch2Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 2.93/1.54 = ( proces370407749rocess @ A @ B @ F @ ( proces988026546_ch2Of @ A @ A2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_28_process_Omap__sel_I2_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
% 2.93/1.54 ( ( proces10484146Action @ A @ A2 )
% 2.93/1.54 => ( ( proces1778668539contOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 2.93/1.54 = ( proces370407749rocess @ A @ B @ F @ ( proces1778668539contOf @ A @ A2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_29_process_Oset__cases,axiom,
% 2.93/1.54 ! [A: $tType,E2: A,A2: proces634752977rocess @ A] :
% 2.93/1.54 ( ( member @ A @ E2 @ ( proces1148692671rocess @ A @ A2 ) )
% 2.93/1.54 => ( ! [Z2: proces634752977rocess @ A] :
% 2.93/1.54 ( A2
% 2.93/1.54 != ( proces1525233512Action @ A @ E2 @ Z2 ) )
% 2.93/1.54 => ( ! [Z1: A,Z2: proces634752977rocess @ A] :
% 2.93/1.54 ( ( A2
% 2.93/1.54 = ( proces1525233512Action @ A @ Z1 @ Z2 ) )
% 2.93/1.54 => ~ ( member @ A @ E2 @ ( proces1148692671rocess @ A @ Z2 ) ) )
% 2.93/1.54 => ( ! [Z1: proces634752977rocess @ A] :
% 2.93/1.54 ( ? [Z2: proces634752977rocess @ A] :
% 2.93/1.54 ( A2
% 2.93/1.54 = ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
% 2.93/1.54 => ~ ( member @ A @ E2 @ ( proces1148692671rocess @ A @ Z1 ) ) )
% 2.93/1.54 => ~ ! [Z1: proces634752977rocess @ A,Z2: proces634752977rocess @ A] :
% 2.93/1.54 ( ( A2
% 2.93/1.54 = ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
% 2.93/1.54 => ~ ( member @ A @ E2 @ ( proces1148692671rocess @ A @ Z2 ) ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_30_process_Oset__induct,axiom,
% 2.93/1.54 ! [A: $tType,X: A,A2: proces634752977rocess @ A,P2: A > ( proces634752977rocess @ A ) > $o] :
% 2.93/1.54 ( ( member @ A @ X @ ( proces1148692671rocess @ A @ A2 ) )
% 2.93/1.54 => ( ! [Z1: A,Z2: proces634752977rocess @ A] : ( P2 @ Z1 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) )
% 2.93/1.54 => ( ! [Z1: A,Z2: proces634752977rocess @ A,Xa: A] :
% 2.93/1.54 ( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ Z2 ) )
% 2.93/1.54 => ( ( P2 @ Xa @ Z2 )
% 2.93/1.54 => ( P2 @ Xa @ ( proces1525233512Action @ A @ Z1 @ Z2 ) ) ) )
% 2.93/1.54 => ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xb: A] :
% 2.93/1.54 ( ( member @ A @ Xb @ ( proces1148692671rocess @ A @ Z1a ) )
% 2.93/1.54 => ( ( P2 @ Xb @ Z1a )
% 2.93/1.54 => ( P2 @ Xb @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
% 2.93/1.54 => ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xc: A] :
% 2.93/1.54 ( ( member @ A @ Xc @ ( proces1148692671rocess @ A @ Z2a ) )
% 2.93/1.54 => ( ( P2 @ Xc @ Z2a )
% 2.93/1.54 => ( P2 @ Xc @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
% 2.93/1.54 => ( P2 @ X @ A2 ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_31_process_Opred__inject_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1205983068rocess @ A @ P2 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
% 2.93/1.54 = ( ( proces1205983068rocess @ A @ P2 @ A2 )
% 2.93/1.54 & ( proces1205983068rocess @ A @ P2 @ Aa2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_32_process_Opred__inject_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1205983068rocess @ A @ P2 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
% 2.93/1.54 = ( ( P2 @ A2 )
% 2.93/1.54 & ( proces1205983068rocess @ A @ P2 @ Aa2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_33_process_Osimps_I6_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 2.93/1.54 = ( F2 @ X21 @ X22 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_34_process_Osimps_I5_J,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X12: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 2.93/1.54 = ( F1 @ X11 @ X12 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_35_process_Ocollapse_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces10484146Action @ A @ Process )
% 2.93/1.54 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 2.93/1.54 = Process ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_36_process_Ocollapse_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces401113213Choice @ A @ Process )
% 2.93/1.54 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 2.93/1.54 = Process ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_37_process_Ocase__eq__if,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType] :
% 2.93/1.54 ( ( proces1406508781rocess @ A @ B )
% 2.93/1.54 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process2: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process2 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process2 ) @ ( proces1778668539contOf @ A @ Process2 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process2 ) @ ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_38_process_Opred__mono__strong,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,X: proces634752977rocess @ A,Pa: A > $o] :
% 2.93/1.54 ( ( proces1205983068rocess @ A @ P2 @ X )
% 2.93/1.54 => ( ! [Z: A] :
% 2.93/1.54 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 2.93/1.54 => ( ( P2 @ Z )
% 2.93/1.54 => ( Pa @ Z ) ) )
% 2.93/1.54 => ( proces1205983068rocess @ A @ Pa @ X ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_39_process_Opred__cong,axiom,
% 2.93/1.54 ! [A: $tType,X: proces634752977rocess @ A,Ya: proces634752977rocess @ A,P2: A > $o,Pa: A > $o] :
% 2.93/1.54 ( ( X = Ya )
% 2.93/1.54 => ( ! [Z: A] :
% 2.93/1.54 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ Ya ) )
% 2.93/1.54 => ( ( P2 @ Z )
% 2.93/1.54 = ( Pa @ Z ) ) )
% 2.93/1.54 => ( ( proces1205983068rocess @ A @ P2 @ X )
% 2.93/1.54 = ( proces1205983068rocess @ A @ Pa @ Ya ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_40_process_Osplit__sel__asm,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,P2: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 2.93/1.54 ( ( P2 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 2.93/1.54 = ( ~ ( ( ( Process
% 2.93/1.54 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 2.93/1.54 & ~ ( P2 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 2.93/1.54 | ( ( Process
% 2.93/1.54 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 2.93/1.54 & ~ ( P2 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_41_process_Osplit__sel,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,P2: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 2.93/1.54 ( ( P2 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 2.93/1.54 = ( ( ( Process
% 2.93/1.54 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 2.93/1.54 => ( P2 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 2.93/1.54 & ( ( Process
% 2.93/1.54 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 2.93/1.54 => ( P2 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_42_process_Oexhaust__sel,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A] :
% 2.93/1.54 ( ( Process
% 2.93/1.54 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 2.93/1.54 => ( Process
% 2.93/1.54 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_43_process_Oexpand,axiom,
% 2.93/1.54 ! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 2.93/1.54 ( ( ( proces10484146Action @ A @ Process )
% 2.93/1.54 = ( proces10484146Action @ A @ Process3 ) )
% 2.93/1.54 => ( ( ( proces10484146Action @ A @ Process )
% 2.93/1.54 => ( ( proces10484146Action @ A @ Process3 )
% 2.93/1.54 => ( ( ( proces745025900prefOf @ A @ Process )
% 2.93/1.54 = ( proces745025900prefOf @ A @ Process3 ) )
% 2.93/1.54 & ( ( proces1778668539contOf @ A @ Process )
% 2.93/1.54 = ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
% 2.93/1.54 => ( ( ( proces401113213Choice @ A @ Process )
% 2.93/1.54 => ( ( proces401113213Choice @ A @ Process3 )
% 2.93/1.54 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 2.93/1.54 = ( proces979765041_ch1Of @ A @ Process3 ) )
% 2.93/1.54 & ( ( proces988026546_ch2Of @ A @ Process )
% 2.93/1.54 = ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
% 2.93/1.54 => ( Process = Process3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_44_process_Ocoinduct,axiom,
% 2.93/1.54 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 2.93/1.54 ( ( R @ Process @ Process3 )
% 2.93/1.54 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 2.93/1.54 ( ( R @ Process4 @ Process5 )
% 2.93/1.54 => ( ( ( proces10484146Action @ A @ Process4 )
% 2.93/1.54 = ( proces10484146Action @ A @ Process5 ) )
% 2.93/1.54 & ( ( proces10484146Action @ A @ Process4 )
% 2.93/1.54 => ( ( proces10484146Action @ A @ Process5 )
% 2.93/1.54 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 2.93/1.54 = ( proces745025900prefOf @ A @ Process5 ) )
% 2.93/1.54 & ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
% 2.93/1.54 & ( ( proces401113213Choice @ A @ Process4 )
% 2.93/1.54 => ( ( proces401113213Choice @ A @ Process5 )
% 2.93/1.54 => ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 2.93/1.54 & ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
% 2.93/1.54 => ( Process = Process3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_45_mem__Collect__eq,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,P2: A > $o] :
% 2.93/1.54 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 2.93/1.54 = ( P2 @ A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_46_Collect__mem__eq,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A] :
% 2.93/1.54 ( ( collect @ A
% 2.93/1.54 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 2.93/1.54 = A3 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_47_Collect__cong,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.93/1.54 ( ! [X3: A] :
% 2.93/1.54 ( ( P2 @ X3 )
% 2.93/1.54 = ( Q @ X3 ) )
% 2.93/1.54 => ( ( collect @ A @ P2 )
% 2.93/1.54 = ( collect @ A @ Q ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_48_ext,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.93/1.54 ( ! [X3: A] :
% 2.93/1.54 ( ( F @ X3 )
% 2.93/1.54 = ( G @ X3 ) )
% 2.93/1.54 => ( F = G ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_49_process_Ocoinduct__strong,axiom,
% 2.93/1.54 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 2.93/1.54 ( ( R @ Process @ Process3 )
% 2.93/1.54 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 2.93/1.54 ( ( R @ Process4 @ Process5 )
% 2.93/1.54 => ( ( ( proces10484146Action @ A @ Process4 )
% 2.93/1.54 = ( proces10484146Action @ A @ Process5 ) )
% 2.93/1.54 & ( ( proces10484146Action @ A @ Process4 )
% 2.93/1.54 => ( ( proces10484146Action @ A @ Process5 )
% 2.93/1.54 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 2.93/1.54 = ( proces745025900prefOf @ A @ Process5 ) )
% 2.93/1.54 & ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
% 2.93/1.54 | ( ( proces1778668539contOf @ A @ Process4 )
% 2.93/1.54 = ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
% 2.93/1.54 & ( ( proces401113213Choice @ A @ Process4 )
% 2.93/1.54 => ( ( proces401113213Choice @ A @ Process5 )
% 2.93/1.54 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 2.93/1.54 | ( ( proces979765041_ch1Of @ A @ Process4 )
% 2.93/1.54 = ( proces979765041_ch1Of @ A @ Process5 ) ) )
% 2.93/1.54 & ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
% 2.93/1.54 | ( ( proces988026546_ch2Of @ A @ Process4 )
% 2.93/1.54 = ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
% 2.93/1.54 => ( Process = Process3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_50_process_Oset__sel_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,A2: proces634752977rocess @ A,X: A] :
% 2.93/1.54 ( ( proces10484146Action @ A @ A2 )
% 2.93/1.54 => ( ( member @ A @ X @ ( proces1148692671rocess @ A @ ( proces1778668539contOf @ A @ A2 ) ) )
% 2.93/1.54 => ( member @ A @ X @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_51_process_Oset__sel_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,A2: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces10484146Action @ A @ A2 )
% 2.93/1.54 => ( member @ A @ ( proces745025900prefOf @ A @ A2 ) @ ( proces1148692671rocess @ A @ A2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_52_process_Oset__sel_I4_J,axiom,
% 2.93/1.54 ! [A: $tType,A2: proces634752977rocess @ A,Xb2: A] :
% 2.93/1.54 ( ( proces401113213Choice @ A @ A2 )
% 2.93/1.54 => ( ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ ( proces988026546_ch2Of @ A @ A2 ) ) )
% 2.93/1.54 => ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_53_process_Oset__sel_I3_J,axiom,
% 2.93/1.54 ! [A: $tType,A2: proces634752977rocess @ A,Xa2: A] :
% 2.93/1.54 ( ( proces401113213Choice @ A @ A2 )
% 2.93/1.54 => ( ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ ( proces979765041_ch1Of @ A @ A2 ) ) )
% 2.93/1.54 => ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_54_process_Oinj__map__strong,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,X: proces634752977rocess @ A,Xa2: proces634752977rocess @ A,F: A > B,Fa: A > B] :
% 2.93/1.54 ( ! [Z: A,Za: A] :
% 2.93/1.54 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 2.93/1.54 => ( ( member @ A @ Za @ ( proces1148692671rocess @ A @ Xa2 ) )
% 2.93/1.54 => ( ( ( F @ Z )
% 2.93/1.54 = ( Fa @ Za ) )
% 2.93/1.54 => ( Z = Za ) ) ) )
% 2.93/1.54 => ( ( ( proces370407749rocess @ A @ B @ F @ X )
% 2.93/1.54 = ( proces370407749rocess @ A @ B @ Fa @ Xa2 ) )
% 2.93/1.54 => ( X = Xa2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_55_process_Omap__cong0,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,X: proces634752977rocess @ A,F: A > B,G: A > B] :
% 2.93/1.54 ( ! [Z: A] :
% 2.93/1.54 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 2.93/1.54 => ( ( F @ Z )
% 2.93/1.54 = ( G @ Z ) ) )
% 2.93/1.54 => ( ( proces370407749rocess @ A @ B @ F @ X )
% 2.93/1.54 = ( proces370407749rocess @ A @ B @ G @ X ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_56_process_Omap__cong,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,X: proces634752977rocess @ A,Ya: proces634752977rocess @ A,F: A > B,G: A > B] :
% 2.93/1.54 ( ( X = Ya )
% 2.93/1.54 => ( ! [Z: A] :
% 2.93/1.54 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ Ya ) )
% 2.93/1.54 => ( ( F @ Z )
% 2.93/1.54 = ( G @ Z ) ) )
% 2.93/1.54 => ( ( proces370407749rocess @ A @ B @ F @ X )
% 2.93/1.54 = ( proces370407749rocess @ A @ B @ G @ Ya ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_57_process_Oset__intros_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,A1: A,A22: proces634752977rocess @ A] : ( member @ A @ A1 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_58_process_Oset__intros_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,X: A,A22: proces634752977rocess @ A,A1: A] :
% 2.93/1.54 ( ( member @ A @ X @ ( proces1148692671rocess @ A @ A22 ) )
% 2.93/1.54 => ( member @ A @ X @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_59_process_Oset__intros_I3_J,axiom,
% 2.93/1.54 ! [A: $tType,Xa2: A,A1a: proces634752977rocess @ A,A2a: proces634752977rocess @ A] :
% 2.93/1.54 ( ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ A1a ) )
% 2.93/1.54 => ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_60_process_Oset__intros_I4_J,axiom,
% 2.93/1.54 ! [A: $tType,Xb2: A,A2a: proces634752977rocess @ A,A1a: proces634752977rocess @ A] :
% 2.93/1.54 ( ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ A2a ) )
% 2.93/1.54 => ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_61_process_Osel_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 2.93/1.54 = X12 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_62_process_Osel_I3_J,axiom,
% 2.93/1.54 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 2.93/1.54 = X21 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_63_process_Osel_I4_J,axiom,
% 2.93/1.54 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 2.93/1.54 = X22 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_64_process_Osel_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 2.93/1.54 = X11 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_65_process_Ocorec__sel_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q12: C > $o,G11: C > A,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 2.93/1.54 ( ( P @ A2 )
% 2.93/1.54 => ( ( ( Q12 @ A2 )
% 2.93/1.54 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( G121 @ A2 ) ) )
% 2.93/1.54 & ( ~ ( Q12 @ A2 )
% 2.93/1.54 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_66_process_Ocorec__sel_I3_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q21: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 2.93/1.54 ( ~ ( P @ A2 )
% 2.93/1.54 => ( ( ( Q21 @ A2 )
% 2.93/1.54 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( G211 @ A2 ) ) )
% 2.93/1.54 & ( ~ ( Q21 @ A2 )
% 2.93/1.54 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_67_process_Ocorec__sel_I4_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q22: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 2.93/1.54 ( ~ ( P @ A2 )
% 2.93/1.54 => ( ( ( Q22 @ A2 )
% 2.93/1.54 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( G221 @ A2 ) ) )
% 2.93/1.54 & ( ~ ( Q22 @ A2 )
% 2.93/1.54 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_68_process_Ocorec__sel_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
% 2.93/1.54 ( ( P @ A2 )
% 2.93/1.54 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
% 2.93/1.54 = ( G11 @ A2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_69_process_Orel__coinduct,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,P2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X: proces634752977rocess @ A,Y: proces634752977rocess @ B,R: A > B > $o] :
% 2.93/1.54 ( ( P2 @ X @ Y )
% 2.93/1.54 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
% 2.93/1.54 ( ( P2 @ Process4 @ Process5 )
% 2.93/1.54 => ( ( ( proces10484146Action @ A @ Process4 )
% 2.93/1.54 = ( proces10484146Action @ B @ Process5 ) )
% 2.93/1.54 & ( ( proces10484146Action @ A @ Process4 )
% 2.93/1.54 => ( ( proces10484146Action @ B @ Process5 )
% 2.93/1.54 => ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
% 2.93/1.54 & ( P2 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
% 2.93/1.54 & ( ( proces401113213Choice @ A @ Process4 )
% 2.93/1.54 => ( ( proces401113213Choice @ B @ Process5 )
% 2.93/1.54 => ( ( P2 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
% 2.93/1.54 & ( P2 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
% 2.93/1.54 => ( proces749077512rocess @ A @ B @ R @ X @ Y ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_70_process_Orel__sel,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType] :
% 2.93/1.54 ( ( proces749077512rocess @ A @ B )
% 2.93/1.54 = ( ^ [R2: A > B > $o,A4: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 2.93/1.54 ( ( ( proces10484146Action @ A @ A4 )
% 2.93/1.54 = ( proces10484146Action @ B @ B2 ) )
% 2.93/1.54 & ( ( proces10484146Action @ A @ A4 )
% 2.93/1.54 => ( ( proces10484146Action @ B @ B2 )
% 2.93/1.54 => ( ( R2 @ ( proces745025900prefOf @ A @ A4 ) @ ( proces745025900prefOf @ B @ B2 ) )
% 2.93/1.54 & ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A4 ) @ ( proces1778668539contOf @ B @ B2 ) ) ) ) )
% 2.93/1.54 & ( ( proces401113213Choice @ A @ A4 )
% 2.93/1.54 => ( ( proces401113213Choice @ B @ B2 )
% 2.93/1.54 => ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A4 ) @ ( proces979765041_ch1Of @ B @ B2 ) )
% 2.93/1.54 & ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A4 ) @ ( proces988026546_ch2Of @ B @ B2 ) ) ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_71_process_Osimps_I21_J,axiom,
% 2.93/1.54 ! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
% 2.93/1.54 = ( insert @ A @ X11 @ ( proces1148692671rocess @ A @ X12 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_72_process_Osimps_I22_J,axiom,
% 2.93/1.54 ! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ ( proces1148692671rocess @ A @ X21 ) @ ( proces1148692671rocess @ A @ X22 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_73_process_Opred__map,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,Q: B > $o,F: A > B,X: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1205983068rocess @ B @ Q @ ( proces370407749rocess @ A @ B @ F @ X ) )
% 2.93/1.54 = ( proces1205983068rocess @ A @ ( comp @ B @ $o @ A @ Q @ F ) @ X ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_74_process_Opred__set,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( proces1205983068rocess @ A )
% 2.93/1.54 = ( ^ [P3: A > $o,X2: proces634752977rocess @ A] :
% 2.93/1.54 ! [Y2: A] :
% 2.93/1.54 ( ( member @ A @ Y2 @ ( proces1148692671rocess @ A @ X2 ) )
% 2.93/1.54 => ( P3 @ Y2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_75_process_Oset__map,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: A > B,V: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces1148692671rocess @ B @ ( proces370407749rocess @ A @ B @ F @ V ) )
% 2.93/1.54 = ( image @ A @ B @ F @ ( proces1148692671rocess @ A @ V ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_76_process_Orel__cases,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B3: proces634752977rocess @ B] :
% 2.93/1.54 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B3 )
% 2.93/1.54 => ( ! [X1: A,X23: proces634752977rocess @ A] :
% 2.93/1.54 ( ( A2
% 2.93/1.54 = ( proces1525233512Action @ A @ X1 @ X23 ) )
% 2.93/1.54 => ! [Y1: B,Y23: proces634752977rocess @ B] :
% 2.93/1.54 ( ( B3
% 2.93/1.54 = ( proces1525233512Action @ B @ Y1 @ Y23 ) )
% 2.93/1.54 => ( ( R @ X1 @ Y1 )
% 2.93/1.54 => ~ ( proces749077512rocess @ A @ B @ R @ X23 @ Y23 ) ) ) )
% 2.93/1.54 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 2.93/1.54 ( ( A2
% 2.93/1.54 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 2.93/1.54 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 2.93/1.54 ( ( B3
% 2.93/1.54 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 2.93/1.54 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 2.93/1.54 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_77_process_Orel__distinct_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 2.93/1.54 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_78_process_Orel__inject_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 2.93/1.54 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 2.93/1.54 = ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 2.93/1.54 & ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_79_process_Orel__inject_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 2.93/1.54 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 2.93/1.54 = ( ( R @ X11 @ Y11 )
% 2.93/1.54 & ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_80_process_Orel__eq,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( proces749077512rocess @ A @ A
% 2.93/1.54 @ ^ [Y3: A,Z3: A] : ( Y3 = Z3 ) )
% 2.93/1.54 = ( ^ [Y3: proces634752977rocess @ A,Z3: proces634752977rocess @ A] : ( Y3 = Z3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_81_process_Orel__refl,axiom,
% 2.93/1.54 ! [B: $tType,Ra: B > B > $o,X: proces634752977rocess @ B] :
% 2.93/1.54 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 2.93/1.54 => ( proces749077512rocess @ B @ B @ Ra @ X @ X ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_82_process_Omap__o__corec,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: C > $o,Ga: C > A,Gb: C > $o,Gc: C > ( proces634752977rocess @ A ),Gd: C > C,Ge: C > $o,Gf: C > ( proces634752977rocess @ A ),Gg: C > C,Gh: C > $o,Gi: C > ( proces634752977rocess @ A ),Gj: C > C] :
% 2.93/1.54 ( ( comp @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ ( proces370407749rocess @ A @ B @ F ) @ ( proces894737309rocess @ C @ A @ G @ Ga @ Gb @ Gc @ Gd @ Ge @ Gf @ Gg @ Gh @ Gi @ Gj ) )
% 2.93/1.54 = ( proces894737309rocess @ C @ B @ G @ ( comp @ A @ B @ C @ F @ Ga ) @ Gb @ ( comp @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ ( proces370407749rocess @ A @ B @ F ) @ Gc ) @ Gd @ Ge @ ( comp @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ ( proces370407749rocess @ A @ B @ F ) @ Gf ) @ Gg @ Gh @ ( comp @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ ( proces370407749rocess @ A @ B @ F ) @ Gi ) @ Gj ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_83_process_Orel__cong,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,X: proces634752977rocess @ A,Ya: proces634752977rocess @ A,Y: proces634752977rocess @ B,Xa2: proces634752977rocess @ B,R: A > B > $o,Ra: A > B > $o] :
% 2.93/1.54 ( ( X = Ya )
% 2.93/1.54 => ( ( Y = Xa2 )
% 2.93/1.54 => ( ! [Z: A,Yb: B] :
% 2.93/1.54 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ Ya ) )
% 2.93/1.54 => ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Xa2 ) )
% 2.93/1.54 => ( ( R @ Z @ Yb )
% 2.93/1.54 = ( Ra @ Z @ Yb ) ) ) )
% 2.93/1.54 => ( ( proces749077512rocess @ A @ B @ R @ X @ Y )
% 2.93/1.54 = ( proces749077512rocess @ A @ B @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_84_process_Orel__mono__strong,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,R: A > B > $o,X: proces634752977rocess @ A,Y: proces634752977rocess @ B,Ra: A > B > $o] :
% 2.93/1.54 ( ( proces749077512rocess @ A @ B @ R @ X @ Y )
% 2.93/1.54 => ( ! [Z: A,Yb: B] :
% 2.93/1.54 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 2.93/1.54 => ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Y ) )
% 2.93/1.54 => ( ( R @ Z @ Yb )
% 2.93/1.54 => ( Ra @ Z @ Yb ) ) ) )
% 2.93/1.54 => ( proces749077512rocess @ A @ B @ Ra @ X @ Y ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_85_process_Orel__refl__strong,axiom,
% 2.93/1.54 ! [A: $tType,X: proces634752977rocess @ A,Ra: A > A > $o] :
% 2.93/1.54 ( ! [Z: A] :
% 2.93/1.54 ( ( member @ A @ Z @ ( proces1148692671rocess @ A @ X ) )
% 2.93/1.54 => ( Ra @ Z @ Z ) )
% 2.93/1.54 => ( proces749077512rocess @ A @ A @ Ra @ X @ X ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_86_process_Orel__intros_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X22: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 2.93/1.54 ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
% 2.93/1.54 => ( ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 )
% 2.93/1.54 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_87_process_Orel__intros_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X12: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 2.93/1.54 ( ( R @ X11 @ Y11 )
% 2.93/1.54 => ( ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 )
% 2.93/1.54 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_88_process_Omap__comp,axiom,
% 2.93/1.54 ! [B: $tType,C: $tType,A: $tType,G: B > C,F: A > B,V: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces370407749rocess @ B @ C @ G @ ( proces370407749rocess @ A @ B @ F @ V ) )
% 2.93/1.54 = ( proces370407749rocess @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_89_process_Orel__distinct_I2_J,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X12: proces634752977rocess @ B] :
% 2.93/1.54 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X12 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_90_Un__insert__left,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,B4: set @ A,C2: set @ A] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B4 ) @ C2 )
% 2.93/1.54 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B4 @ C2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_91_Un__insert__right,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,A2: A,B4: set @ A] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B4 ) )
% 2.93/1.54 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_92_image__insert,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,F: B > A,A2: B,B4: set @ B] :
% 2.93/1.54 ( ( image @ B @ A @ F @ ( insert @ B @ A2 @ B4 ) )
% 2.93/1.54 = ( insert @ A @ ( F @ A2 ) @ ( image @ B @ A @ F @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_93_insert__image,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,X: A,A3: set @ A,F: A > B] :
% 2.93/1.54 ( ( member @ A @ X @ A3 )
% 2.93/1.54 => ( ( insert @ B @ ( F @ X ) @ ( image @ A @ B @ F @ A3 ) )
% 2.93/1.54 = ( image @ A @ B @ F @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_94_Ball__image__comp,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,G: A > $o] :
% 2.93/1.54 ( ( ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ ( image @ B @ A @ F @ A3 ) )
% 2.93/1.54 => ( G @ X2 ) ) )
% 2.93/1.54 = ( ! [X2: B] :
% 2.93/1.54 ( ( member @ B @ X2 @ A3 )
% 2.93/1.54 => ( comp @ A @ $o @ B @ G @ F @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_95_UnCI,axiom,
% 2.93/1.54 ! [A: $tType,C3: A,B4: set @ A,A3: set @ A] :
% 2.93/1.54 ( ( ~ ( member @ A @ C3 @ B4 )
% 2.93/1.54 => ( member @ A @ C3 @ A3 ) )
% 2.93/1.54 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_96_image__eqI,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,B3: A,F: B > A,X: B,A3: set @ B] :
% 2.93/1.54 ( ( B3
% 2.93/1.54 = ( F @ X ) )
% 2.93/1.54 => ( ( member @ B @ X @ A3 )
% 2.93/1.54 => ( member @ A @ B3 @ ( image @ B @ A @ F @ A3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_97_insert__absorb2,axiom,
% 2.93/1.54 ! [A: $tType,X: A,A3: set @ A] :
% 2.93/1.54 ( ( insert @ A @ X @ ( insert @ A @ X @ A3 ) )
% 2.93/1.54 = ( insert @ A @ X @ A3 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_98_insert__iff,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 2.93/1.54 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 2.93/1.54 = ( ( A2 = B3 )
% 2.93/1.54 | ( member @ A @ A2 @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_99_insertCI,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 2.93/1.54 ( ( ~ ( member @ A @ A2 @ B4 )
% 2.93/1.54 => ( A2 = B3 ) )
% 2.93/1.54 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_100_Un__iff,axiom,
% 2.93/1.54 ! [A: $tType,C3: A,A3: set @ A,B4: set @ A] :
% 2.93/1.54 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 2.93/1.54 = ( ( member @ A @ C3 @ A3 )
% 2.93/1.54 | ( member @ A @ C3 @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_101_rev__image__eqI,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,X: A,A3: set @ A,B3: B,F: A > B] :
% 2.93/1.54 ( ( member @ A @ X @ A3 )
% 2.93/1.54 => ( ( B3
% 2.93/1.54 = ( F @ X ) )
% 2.93/1.54 => ( member @ B @ B3 @ ( image @ A @ B @ F @ A3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_102_ball__imageD,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P2: A > $o] :
% 2.93/1.54 ( ! [X3: A] :
% 2.93/1.54 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A3 ) )
% 2.93/1.54 => ( P2 @ X3 ) )
% 2.93/1.54 => ! [X4: B] :
% 2.93/1.54 ( ( member @ B @ X4 @ A3 )
% 2.93/1.54 => ( P2 @ ( F @ X4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_103_image__cong,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,M: set @ A,N: set @ A,F: A > B,G: A > B] :
% 2.93/1.54 ( ( M = N )
% 2.93/1.54 => ( ! [X3: A] :
% 2.93/1.54 ( ( member @ A @ X3 @ N )
% 2.93/1.54 => ( ( F @ X3 )
% 2.93/1.54 = ( G @ X3 ) ) )
% 2.93/1.54 => ( ( image @ A @ B @ F @ M )
% 2.93/1.54 = ( image @ A @ B @ G @ N ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_104_bex__imageD,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P2: A > $o] :
% 2.93/1.54 ( ? [X4: A] :
% 2.93/1.54 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A3 ) )
% 2.93/1.54 & ( P2 @ X4 ) )
% 2.93/1.54 => ? [X3: B] :
% 2.93/1.54 ( ( member @ B @ X3 @ A3 )
% 2.93/1.54 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_105_image__iff,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,Z4: A,F: B > A,A3: set @ B] :
% 2.93/1.54 ( ( member @ A @ Z4 @ ( image @ B @ A @ F @ A3 ) )
% 2.93/1.54 = ( ? [X2: B] :
% 2.93/1.54 ( ( member @ B @ X2 @ A3 )
% 2.93/1.54 & ( Z4
% 2.93/1.54 = ( F @ X2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_106_imageI,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,X: A,A3: set @ A,F: A > B] :
% 2.93/1.54 ( ( member @ A @ X @ A3 )
% 2.93/1.54 => ( member @ B @ ( F @ X ) @ ( image @ A @ B @ F @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_107_mk__disjoint__insert,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,A3: set @ A] :
% 2.93/1.54 ( ( member @ A @ A2 @ A3 )
% 2.93/1.54 => ? [B5: set @ A] :
% 2.93/1.54 ( ( A3
% 2.93/1.54 = ( insert @ A @ A2 @ B5 ) )
% 2.93/1.54 & ~ ( member @ A @ A2 @ B5 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_108_insert__commute,axiom,
% 2.93/1.54 ! [A: $tType,X: A,Y: A,A3: set @ A] :
% 2.93/1.54 ( ( insert @ A @ X @ ( insert @ A @ Y @ A3 ) )
% 2.93/1.54 = ( insert @ A @ Y @ ( insert @ A @ X @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_109_insert__eq__iff,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,A3: set @ A,B3: A,B4: set @ A] :
% 2.93/1.54 ( ~ ( member @ A @ A2 @ A3 )
% 2.93/1.54 => ( ~ ( member @ A @ B3 @ B4 )
% 2.93/1.54 => ( ( ( insert @ A @ A2 @ A3 )
% 2.93/1.54 = ( insert @ A @ B3 @ B4 ) )
% 2.93/1.54 = ( ( ( A2 = B3 )
% 2.93/1.54 => ( A3 = B4 ) )
% 2.93/1.54 & ( ( A2 != B3 )
% 2.93/1.54 => ? [C4: set @ A] :
% 2.93/1.54 ( ( A3
% 2.93/1.54 = ( insert @ A @ B3 @ C4 ) )
% 2.93/1.54 & ~ ( member @ A @ B3 @ C4 )
% 2.93/1.54 & ( B4
% 2.93/1.54 = ( insert @ A @ A2 @ C4 ) )
% 2.93/1.54 & ~ ( member @ A @ A2 @ C4 ) ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_110_insert__absorb,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,A3: set @ A] :
% 2.93/1.54 ( ( member @ A @ A2 @ A3 )
% 2.93/1.54 => ( ( insert @ A @ A2 @ A3 )
% 2.93/1.54 = A3 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_111_insert__ident,axiom,
% 2.93/1.54 ! [A: $tType,X: A,A3: set @ A,B4: set @ A] :
% 2.93/1.54 ( ~ ( member @ A @ X @ A3 )
% 2.93/1.54 => ( ~ ( member @ A @ X @ B4 )
% 2.93/1.54 => ( ( ( insert @ A @ X @ A3 )
% 2.93/1.54 = ( insert @ A @ X @ B4 ) )
% 2.93/1.54 = ( A3 = B4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_112_Set_Oset__insert,axiom,
% 2.93/1.54 ! [A: $tType,X: A,A3: set @ A] :
% 2.93/1.54 ( ( member @ A @ X @ A3 )
% 2.93/1.54 => ~ ! [B5: set @ A] :
% 2.93/1.54 ( ( A3
% 2.93/1.54 = ( insert @ A @ X @ B5 ) )
% 2.93/1.54 => ( member @ A @ X @ B5 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_113_insertI2,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,B4: set @ A,B3: A] :
% 2.93/1.54 ( ( member @ A @ A2 @ B4 )
% 2.93/1.54 => ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_114_insertI1,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,B4: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B4 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_115_insertE,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 2.93/1.54 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 2.93/1.54 => ( ( A2 != B3 )
% 2.93/1.54 => ( member @ A @ A2 @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_116_comp__apply__eq,axiom,
% 2.93/1.54 ! [B: $tType,D: $tType,A: $tType,C: $tType,F: B > A,G: C > B,X: C,H: D > A,K: C > D] :
% 2.93/1.54 ( ( ( F @ ( G @ X ) )
% 2.93/1.54 = ( H @ ( K @ X ) ) )
% 2.93/1.54 => ( ( comp @ B @ A @ C @ F @ G @ X )
% 2.93/1.54 = ( comp @ D @ A @ C @ H @ K @ X ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_117_Ball__def,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( ball @ A )
% 2.93/1.54 = ( ^ [A5: set @ A,P3: A > $o] :
% 2.93/1.54 ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ A5 )
% 2.93/1.54 => ( P3 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_118_Un__left__commute,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,B4: set @ A,C2: set @ A] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B4 @ C2 ) )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A3 @ C2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_119_Un__left__absorb,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_120_Un__commute,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) )
% 2.93/1.54 = ( ^ [A5: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A5 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_121_Un__absorb,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 2.93/1.54 = A3 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_122_Un__assoc,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,B4: set @ A,C2: set @ A] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) @ C2 )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B4 @ C2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_123_ball__Un,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,B4: set @ A,P2: A > $o] :
% 2.93/1.54 ( ( ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 2.93/1.54 => ( P2 @ X2 ) ) )
% 2.93/1.54 = ( ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ A3 )
% 2.93/1.54 => ( P2 @ X2 ) )
% 2.93/1.54 & ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ B4 )
% 2.93/1.54 => ( P2 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_124_bex__Un,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,B4: set @ A,P2: A > $o] :
% 2.93/1.54 ( ( ? [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 2.93/1.54 & ( P2 @ X2 ) ) )
% 2.93/1.54 = ( ? [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ A3 )
% 2.93/1.54 & ( P2 @ X2 ) )
% 2.93/1.54 | ? [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ B4 )
% 2.93/1.54 & ( P2 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_125_UnI2,axiom,
% 2.93/1.54 ! [A: $tType,C3: A,B4: set @ A,A3: set @ A] :
% 2.93/1.54 ( ( member @ A @ C3 @ B4 )
% 2.93/1.54 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_126_UnI1,axiom,
% 2.93/1.54 ! [A: $tType,C3: A,A3: set @ A,B4: set @ A] :
% 2.93/1.54 ( ( member @ A @ C3 @ A3 )
% 2.93/1.54 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_127_UnE,axiom,
% 2.93/1.54 ! [A: $tType,C3: A,A3: set @ A,B4: set @ A] :
% 2.93/1.54 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 2.93/1.54 => ( ~ ( member @ A @ C3 @ A3 )
% 2.93/1.54 => ( member @ A @ C3 @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_128_image__Un,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,B4: set @ B] :
% 2.93/1.54 ( ( image @ B @ A @ F @ ( sup_sup @ ( set @ B ) @ A3 @ B4 ) )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ ( image @ B @ A @ F @ A3 ) @ ( image @ B @ A @ F @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_129_not__False__in__image__Ball,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,A3: set @ A] :
% 2.93/1.54 ( ( ~ ( member @ $o @ $false @ ( image @ A @ $o @ P2 @ A3 ) ) )
% 2.93/1.54 = ( ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ A3 )
% 2.93/1.54 => ( P2 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_130_comp__apply,axiom,
% 2.93/1.54 ! [C: $tType,A: $tType,B: $tType] :
% 2.93/1.54 ( ( comp @ B @ A @ C )
% 2.93/1.54 = ( ^ [F3: B > A,G2: C > B,X2: C] : ( F3 @ ( G2 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_131_sup_Oright__idem,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A2: A,B3: A] :
% 2.93/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ B3 )
% 2.93/1.54 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_132_sup__left__idem,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A,Y: A] :
% 2.93/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.93/1.54 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_133_sup_Oleft__idem,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A2: A,B3: A] :
% 2.93/1.54 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) )
% 2.93/1.54 = ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_134_sup__apply,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.93/1.54 => ( ( sup_sup @ ( A > B ) )
% 2.93/1.54 = ( ^ [F3: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F3 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_135_sup_Oidem,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A2: A] :
% 2.93/1.54 ( ( sup_sup @ A @ A2 @ A2 )
% 2.93/1.54 = A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_136_sup__idem,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A] :
% 2.93/1.54 ( ( sup_sup @ A @ X @ X )
% 2.93/1.54 = X ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_137_Inf_OINF__cong,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,A3: set @ B,B4: set @ B,C2: B > A,D2: B > A,Inf: ( set @ A ) > A] :
% 2.93/1.54 ( ( A3 = B4 )
% 2.93/1.54 => ( ! [X3: B] :
% 2.93/1.54 ( ( member @ B @ X3 @ B4 )
% 2.93/1.54 => ( ( C2 @ X3 )
% 2.93/1.54 = ( D2 @ X3 ) ) )
% 2.93/1.54 => ( ( Inf @ ( image @ B @ A @ C2 @ A3 ) )
% 2.93/1.54 = ( Inf @ ( image @ B @ A @ D2 @ B4 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_138_Sup_OSUP__cong,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,A3: set @ B,B4: set @ B,C2: B > A,D2: B > A,Sup: ( set @ A ) > A] :
% 2.93/1.54 ( ( A3 = B4 )
% 2.93/1.54 => ( ! [X3: B] :
% 2.93/1.54 ( ( member @ B @ X3 @ B4 )
% 2.93/1.54 => ( ( C2 @ X3 )
% 2.93/1.54 = ( D2 @ X3 ) ) )
% 2.93/1.54 => ( ( Sup @ ( image @ B @ A @ C2 @ A3 ) )
% 2.93/1.54 = ( Sup @ ( image @ B @ A @ D2 @ B4 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_139_inf__sup__aci_I8_J,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A,Y: A] :
% 2.93/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.93/1.54 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_140_inf__sup__aci_I7_J,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A,Y: A,Z4: A] :
% 2.93/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z4 ) )
% 2.93/1.54 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_141_inf__sup__aci_I6_J,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A,Y: A,Z4: A] :
% 2.93/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z4 )
% 2.93/1.54 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_142_inf__sup__aci_I5_J,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ( ( sup_sup @ A )
% 2.93/1.54 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_143_sup__fun__def,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.93/1.54 => ( ( sup_sup @ ( A > B ) )
% 2.93/1.54 = ( ^ [F3: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F3 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_144_sup_Oassoc,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A2: A,B3: A,C3: A] :
% 2.93/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B3 ) @ C3 )
% 2.93/1.54 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_145_sup__assoc,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A,Y: A,Z4: A] :
% 2.93/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z4 )
% 2.93/1.54 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_146_sup_Ocommute,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ( ( sup_sup @ A )
% 2.93/1.54 = ( ^ [A4: A,B2: A] : ( sup_sup @ A @ B2 @ A4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_147_sup__commute,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ( ( sup_sup @ A )
% 2.93/1.54 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_148_sup_Oleft__commute,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [B3: A,A2: A,C3: A] :
% 2.93/1.54 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A2 @ C3 ) )
% 2.93/1.54 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B3 @ C3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_149_sup__left__commute,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A,Y: A,Z4: A] :
% 2.93/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z4 ) )
% 2.93/1.54 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_150_comp__def,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,B: $tType] :
% 2.93/1.54 ( ( comp @ B @ C @ A )
% 2.93/1.54 = ( ^ [F3: B > C,G2: A > B,X2: A] : ( F3 @ ( G2 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_151_comp__assoc,axiom,
% 2.93/1.54 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H: A > C] :
% 2.93/1.54 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H )
% 2.93/1.54 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_152_comp__eq__dest,axiom,
% 2.93/1.54 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B3: A > C,C3: D > B,D3: A > D,V: A] :
% 2.93/1.54 ( ( ( comp @ C @ B @ A @ A2 @ B3 )
% 2.93/1.54 = ( comp @ D @ B @ A @ C3 @ D3 ) )
% 2.93/1.54 => ( ( A2 @ ( B3 @ V ) )
% 2.93/1.54 = ( C3 @ ( D3 @ V ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_153_comp__eq__elim,axiom,
% 2.93/1.54 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B3: A > C,C3: D > B,D3: A > D] :
% 2.93/1.54 ( ( ( comp @ C @ B @ A @ A2 @ B3 )
% 2.93/1.54 = ( comp @ D @ B @ A @ C3 @ D3 ) )
% 2.93/1.54 => ! [V2: A] :
% 2.93/1.54 ( ( A2 @ ( B3 @ V2 ) )
% 2.93/1.54 = ( C3 @ ( D3 @ V2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_154_comp__eq__dest__lhs,axiom,
% 2.93/1.54 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B3: A > C,C3: A > B,V: A] :
% 2.93/1.54 ( ( ( comp @ C @ B @ A @ A2 @ B3 )
% 2.93/1.54 = C3 )
% 2.93/1.54 => ( ( A2 @ ( B3 @ V ) )
% 2.93/1.54 = ( C3 @ V ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_155_image__comp,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,C: $tType,F: B > A,G: C > B,R3: set @ C] :
% 2.93/1.54 ( ( image @ B @ A @ F @ ( image @ C @ B @ G @ R3 ) )
% 2.93/1.54 = ( image @ C @ A @ ( comp @ B @ A @ C @ F @ G ) @ R3 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_156_image__eq__imp__comp,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: B > A,A3: set @ B,G: C > A,B4: set @ C,H: A > D] :
% 2.93/1.54 ( ( ( image @ B @ A @ F @ A3 )
% 2.93/1.54 = ( image @ C @ A @ G @ B4 ) )
% 2.93/1.54 => ( ( image @ B @ D @ ( comp @ A @ D @ B @ H @ F ) @ A3 )
% 2.93/1.54 = ( image @ C @ D @ ( comp @ A @ D @ C @ H @ G ) @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_157_Inf_OINF__image,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,C: $tType,Inf: ( set @ A ) > A,G: B > A,F: C > B,A3: set @ C] :
% 2.93/1.54 ( ( Inf @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A3 ) ) )
% 2.93/1.54 = ( Inf @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_158_Sup_OSUP__image,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,C: $tType,Sup: ( set @ A ) > A,G: B > A,F: C > B,A3: set @ C] :
% 2.93/1.54 ( ( Sup @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A3 ) ) )
% 2.93/1.54 = ( Sup @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_159_ball__reg,axiom,
% 2.93/1.54 ! [A: $tType,R: set @ A,P2: A > $o,Q: A > $o] :
% 2.93/1.54 ( ! [X3: A] :
% 2.93/1.54 ( ( member @ A @ X3 @ R )
% 2.93/1.54 => ( ( P2 @ X3 )
% 2.93/1.54 => ( Q @ X3 ) ) )
% 2.93/1.54 => ( ! [X3: A] :
% 2.93/1.54 ( ( member @ A @ X3 @ R )
% 2.93/1.54 => ( P2 @ X3 ) )
% 2.93/1.54 => ! [X4: A] :
% 2.93/1.54 ( ( member @ A @ X4 @ R )
% 2.93/1.54 => ( Q @ X4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_160_comp__cong,axiom,
% 2.93/1.54 ! [C: $tType,B: $tType,D: $tType,A: $tType,E: $tType,F: B > A,G: C > B,X: C,F4: D > A,G3: E > D,X5: E] :
% 2.93/1.54 ( ( ( F @ ( G @ X ) )
% 2.93/1.54 = ( F4 @ ( G3 @ X5 ) ) )
% 2.93/1.54 => ( ( comp @ B @ A @ C @ F @ G @ X )
% 2.93/1.54 = ( comp @ D @ A @ E @ F4 @ G3 @ X5 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_161_fun_Omap__comp,axiom,
% 2.93/1.54 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 2.93/1.54 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 2.93/1.54 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_162_type__copy__map__cong0,axiom,
% 2.93/1.54 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X: C,N: D > A,H: C > D,F: A > E] :
% 2.93/1.54 ( ( ( M @ ( G @ X ) )
% 2.93/1.54 = ( N @ ( H @ X ) ) )
% 2.93/1.54 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F @ M ) @ G @ X )
% 2.93/1.54 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F @ N ) @ H @ X ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_163_rewriteR__comp__comp2,axiom,
% 2.93/1.54 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R1: D > B,R22: A > D,F: B > E,L: D > E] :
% 2.93/1.54 ( ( ( comp @ C @ B @ A @ G @ H )
% 2.93/1.54 = ( comp @ D @ B @ A @ R1 @ R22 ) )
% 2.93/1.54 => ( ( ( comp @ B @ E @ D @ F @ R1 )
% 2.93/1.54 = L )
% 2.93/1.54 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H )
% 2.93/1.54 = ( comp @ D @ E @ A @ L @ R22 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_164_rewriteL__comp__comp2,axiom,
% 2.93/1.54 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H: E > A,R3: E > D] :
% 2.93/1.54 ( ( ( comp @ C @ B @ A @ F @ G )
% 2.93/1.54 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 2.93/1.54 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 2.93/1.54 = R3 )
% 2.93/1.54 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H ) )
% 2.93/1.54 = ( comp @ D @ B @ E @ L1 @ R3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_165_rewriteR__comp__comp,axiom,
% 2.93/1.54 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R3: A > B,F: B > D] :
% 2.93/1.54 ( ( ( comp @ C @ B @ A @ G @ H )
% 2.93/1.54 = R3 )
% 2.93/1.54 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H )
% 2.93/1.54 = ( comp @ B @ D @ A @ F @ R3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_166_rewriteL__comp__comp,axiom,
% 2.93/1.54 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H: D > A] :
% 2.93/1.54 ( ( ( comp @ C @ B @ A @ F @ G )
% 2.93/1.54 = L )
% 2.93/1.54 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H ) )
% 2.93/1.54 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_167_process_Opred__rel,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( proces1205983068rocess @ A )
% 2.93/1.54 = ( ^ [P3: A > $o,X2: proces634752977rocess @ A] : ( proces749077512rocess @ A @ A @ ( bNF_eq_onp @ A @ P3 ) @ X2 @ X2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_168_Sup__insert,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A2: A,A3: set @ A] :
% 2.93/1.54 ( ( complete_Sup_Sup @ A @ ( insert @ A @ A2 @ A3 ) )
% 2.93/1.54 = ( sup_sup @ A @ A2 @ ( complete_Sup_Sup @ A @ A3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_169_SUP__image,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,C: $tType] :
% 2.93/1.54 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [G: B > A,F: C > B,A3: set @ C] :
% 2.93/1.54 ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A3 ) ) )
% 2.93/1.54 = ( complete_Sup_Sup @ A @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_170_Union__Un__distrib,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ ( set @ A ),B4: set @ ( set @ A )] :
% 2.93/1.54 ( ( complete_Sup_Sup @ ( set @ A ) @ ( sup_sup @ ( set @ ( set @ A ) ) @ A3 @ B4 ) )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ ( complete_Sup_Sup @ ( set @ A ) @ A3 ) @ ( complete_Sup_Sup @ ( set @ A ) @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_171_SUP__cong,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType] :
% 2.93/1.54 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A3: set @ B,B4: set @ B,C2: B > A,D2: B > A] :
% 2.93/1.54 ( ( A3 = B4 )
% 2.93/1.54 => ( ! [X3: B] :
% 2.93/1.54 ( ( member @ B @ X3 @ B4 )
% 2.93/1.54 => ( ( C2 @ X3 )
% 2.93/1.54 = ( D2 @ X3 ) ) )
% 2.93/1.54 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ C2 @ A3 ) )
% 2.93/1.54 = ( complete_Sup_Sup @ A @ ( image @ B @ A @ D2 @ B4 ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_172_process_Orel__eq__onp,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o] :
% 2.93/1.54 ( ( proces749077512rocess @ A @ A @ ( bNF_eq_onp @ A @ P2 ) )
% 2.93/1.54 = ( bNF_eq_onp @ ( proces634752977rocess @ A ) @ ( proces1205983068rocess @ A @ P2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_173_eq__onp__eqD,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,Q: A > A > $o,X: A] :
% 2.93/1.54 ( ( ( bNF_eq_onp @ A @ P2 )
% 2.93/1.54 = Q )
% 2.93/1.54 => ( ( P2 @ X )
% 2.93/1.54 = ( Q @ X @ X ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_174_eq__onp__mono0,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,P2: A > $o,Q: A > $o] :
% 2.93/1.54 ( ! [X3: A] :
% 2.93/1.54 ( ( member @ A @ X3 @ A3 )
% 2.93/1.54 => ( ( P2 @ X3 )
% 2.93/1.54 => ( Q @ X3 ) ) )
% 2.93/1.54 => ! [X4: A] :
% 2.93/1.54 ( ( member @ A @ X4 @ A3 )
% 2.93/1.54 => ! [Xa3: A] :
% 2.93/1.54 ( ( member @ A @ Xa3 @ A3 )
% 2.93/1.54 => ( ( bNF_eq_onp @ A @ P2 @ X4 @ Xa3 )
% 2.93/1.54 => ( bNF_eq_onp @ A @ Q @ X4 @ Xa3 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_175_eq__onp__to__eq,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,X: A,Y: A] :
% 2.93/1.54 ( ( bNF_eq_onp @ A @ P2 @ X @ Y )
% 2.93/1.54 => ( X = Y ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_176_eq__onp__same__args,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,X: A] :
% 2.93/1.54 ( ( bNF_eq_onp @ A @ P2 @ X @ X )
% 2.93/1.54 = ( P2 @ X ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_177_Union__insert,axiom,
% 2.93/1.54 ! [A: $tType,A2: set @ A,B4: set @ ( set @ A )] :
% 2.93/1.54 ( ( complete_Sup_Sup @ ( set @ A ) @ ( insert @ ( set @ A ) @ A2 @ B4 ) )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ A2 @ ( complete_Sup_Sup @ ( set @ A ) @ B4 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_178_Sup__union__distrib,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A3: set @ A,B4: set @ A] :
% 2.93/1.54 ( ( complete_Sup_Sup @ A @ ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 2.93/1.54 = ( sup_sup @ A @ ( complete_Sup_Sup @ A @ A3 ) @ ( complete_Sup_Sup @ A @ B4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_179_Union__image__insert,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,F: B > ( set @ A ),A2: B,B4: set @ B] :
% 2.93/1.54 ( ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ ( insert @ B @ A2 @ B4 ) ) )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ ( F @ A2 ) @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ B4 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_180_vimage2p__comp,axiom,
% 2.93/1.54 ! [E: $tType,D: $tType,F5: $tType,A: $tType,C: $tType,B: $tType,G4: $tType,F1: F5 > A,F2: D > F5,G1: G4 > B,G22: E > G4] :
% 2.93/1.54 ( ( bNF_vimage2p @ D @ A @ E @ B @ C @ ( comp @ F5 @ A @ D @ F1 @ F2 ) @ ( comp @ G4 @ B @ E @ G1 @ G22 ) )
% 2.93/1.54 = ( comp @ ( F5 > G4 > C ) @ ( D > E > C ) @ ( A > B > C ) @ ( bNF_vimage2p @ D @ F5 @ E @ G4 @ C @ F2 @ G22 ) @ ( bNF_vimage2p @ F5 @ A @ G4 @ B @ C @ F1 @ G1 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_181_INF__image,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,C: $tType] :
% 2.93/1.54 ( ( complete_Inf @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [G: B > A,F: C > B,A3: set @ C] :
% 2.93/1.54 ( ( complete_Inf_Inf @ A @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A3 ) ) )
% 2.93/1.54 = ( complete_Inf_Inf @ A @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_182_SUP__id__eq,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( complete_Sup @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A3: set @ A] :
% 2.93/1.54 ( ( complete_Sup_Sup @ A @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 2.93/1.54 = ( complete_Sup_Sup @ A @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_183_UN__ball__bex__simps_I3_J,axiom,
% 2.93/1.54 ! [D: $tType,A3: set @ ( set @ D ),P2: D > $o] :
% 2.93/1.54 ( ( ? [X2: D] :
% 2.93/1.54 ( ( member @ D @ X2 @ ( complete_Sup_Sup @ ( set @ D ) @ A3 ) )
% 2.93/1.54 & ( P2 @ X2 ) ) )
% 2.93/1.54 = ( ? [X2: set @ D] :
% 2.93/1.54 ( ( member @ ( set @ D ) @ X2 @ A3 )
% 2.93/1.54 & ? [Y2: D] :
% 2.93/1.54 ( ( member @ D @ Y2 @ X2 )
% 2.93/1.54 & ( P2 @ Y2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_184_UN__ball__bex__simps_I1_J,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ ( set @ A ),P2: A > $o] :
% 2.93/1.54 ( ( ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ ( complete_Sup_Sup @ ( set @ A ) @ A3 ) )
% 2.93/1.54 => ( P2 @ X2 ) ) )
% 2.93/1.54 = ( ! [X2: set @ A] :
% 2.93/1.54 ( ( member @ ( set @ A ) @ X2 @ A3 )
% 2.93/1.54 => ! [Y2: A] :
% 2.93/1.54 ( ( member @ A @ Y2 @ X2 )
% 2.93/1.54 => ( P2 @ Y2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_185_UnionI,axiom,
% 2.93/1.54 ! [A: $tType,X6: set @ A,C2: set @ ( set @ A ),A3: A] :
% 2.93/1.54 ( ( member @ ( set @ A ) @ X6 @ C2 )
% 2.93/1.54 => ( ( member @ A @ A3 @ X6 )
% 2.93/1.54 => ( member @ A @ A3 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_186_Union__iff,axiom,
% 2.93/1.54 ! [A: $tType,A3: A,C2: set @ ( set @ A )] :
% 2.93/1.54 ( ( member @ A @ A3 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) )
% 2.93/1.54 = ( ? [X2: set @ A] :
% 2.93/1.54 ( ( member @ ( set @ A ) @ X2 @ C2 )
% 2.93/1.54 & ( member @ A @ A3 @ X2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_187_id__apply,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( id @ A )
% 2.93/1.54 = ( ^ [X2: A] : X2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_188_image__id,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( image @ A @ A @ ( id @ A ) )
% 2.93/1.54 = ( id @ ( set @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_189_ball__UN,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,B4: B > ( set @ A ),A3: set @ B,P2: A > $o] :
% 2.93/1.54 ( ( ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B4 @ A3 ) ) )
% 2.93/1.54 => ( P2 @ X2 ) ) )
% 2.93/1.54 = ( ! [X2: B] :
% 2.93/1.54 ( ( member @ B @ X2 @ A3 )
% 2.93/1.54 => ! [Y2: A] :
% 2.93/1.54 ( ( member @ A @ Y2 @ ( B4 @ X2 ) )
% 2.93/1.54 => ( P2 @ Y2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_190_bex__UN,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,B4: B > ( set @ A ),A3: set @ B,P2: A > $o] :
% 2.93/1.54 ( ( ? [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ B4 @ A3 ) ) )
% 2.93/1.54 & ( P2 @ X2 ) ) )
% 2.93/1.54 = ( ? [X2: B] :
% 2.93/1.54 ( ( member @ B @ X2 @ A3 )
% 2.93/1.54 & ? [Y2: A] :
% 2.93/1.54 ( ( member @ A @ Y2 @ ( B4 @ X2 ) )
% 2.93/1.54 & ( P2 @ Y2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_191_UN__ball__bex__simps_I2_J,axiom,
% 2.93/1.54 ! [C: $tType,B: $tType,B4: B > ( set @ C ),A3: set @ B,P2: C > $o] :
% 2.93/1.54 ( ( ! [X2: C] :
% 2.93/1.54 ( ( member @ C @ X2 @ ( complete_Sup_Sup @ ( set @ C ) @ ( image @ B @ ( set @ C ) @ B4 @ A3 ) ) )
% 2.93/1.54 => ( P2 @ X2 ) ) )
% 2.93/1.54 = ( ! [X2: B] :
% 2.93/1.54 ( ( member @ B @ X2 @ A3 )
% 2.93/1.54 => ! [Y2: C] :
% 2.93/1.54 ( ( member @ C @ Y2 @ ( B4 @ X2 ) )
% 2.93/1.54 => ( P2 @ Y2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_192_UN__ball__bex__simps_I4_J,axiom,
% 2.93/1.54 ! [F5: $tType,E: $tType,B4: E > ( set @ F5 ),A3: set @ E,P2: F5 > $o] :
% 2.93/1.54 ( ( ? [X2: F5] :
% 2.93/1.54 ( ( member @ F5 @ X2 @ ( complete_Sup_Sup @ ( set @ F5 ) @ ( image @ E @ ( set @ F5 ) @ B4 @ A3 ) ) )
% 2.93/1.54 & ( P2 @ X2 ) ) )
% 2.93/1.54 = ( ? [X2: E] :
% 2.93/1.54 ( ( member @ E @ X2 @ A3 )
% 2.93/1.54 & ? [Y2: F5] :
% 2.93/1.54 ( ( member @ F5 @ Y2 @ ( B4 @ X2 ) )
% 2.93/1.54 & ( P2 @ Y2 ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_193_fun_Omap__id,axiom,
% 2.93/1.54 ! [A: $tType,D: $tType,T: D > A] :
% 2.93/1.54 ( ( comp @ A @ A @ D @ ( id @ A ) @ T )
% 2.93/1.54 = T ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_194_id__comp,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,G: A > B] :
% 2.93/1.54 ( ( comp @ B @ B @ A @ ( id @ B ) @ G )
% 2.93/1.54 = G ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_195_comp__id,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: A > B] :
% 2.93/1.54 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 2.93/1.54 = F ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_196_INF__id__eq,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( complete_Inf @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A3: set @ A] :
% 2.93/1.54 ( ( complete_Inf_Inf @ A @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 2.93/1.54 = ( complete_Inf_Inf @ A @ A3 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_197_UnionE,axiom,
% 2.93/1.54 ! [A: $tType,A3: A,C2: set @ ( set @ A )] :
% 2.93/1.54 ( ( member @ A @ A3 @ ( complete_Sup_Sup @ ( set @ A ) @ C2 ) )
% 2.93/1.54 => ~ ! [X7: set @ A] :
% 2.93/1.54 ( ( member @ A @ A3 @ X7 )
% 2.93/1.54 => ~ ( member @ ( set @ A ) @ X7 @ C2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_198_fun_Omap__id0,axiom,
% 2.93/1.54 ! [A: $tType,D: $tType] :
% 2.93/1.54 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 2.93/1.54 = ( id @ ( D > A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_199_process_Omap__id0,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( proces370407749rocess @ A @ A @ ( id @ A ) )
% 2.93/1.54 = ( id @ ( proces634752977rocess @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_200_process_Omap__id,axiom,
% 2.93/1.54 ! [A: $tType,T: proces634752977rocess @ A] :
% 2.93/1.54 ( ( proces370407749rocess @ A @ A @ ( id @ A ) @ T )
% 2.93/1.54 = T ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_201_Inf_OINF__id__eq,axiom,
% 2.93/1.54 ! [A: $tType,Inf: ( set @ A ) > A,A3: set @ A] :
% 2.93/1.54 ( ( Inf @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 2.93/1.54 = ( Inf @ A3 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_202_Sup_OSUP__id__eq,axiom,
% 2.93/1.54 ! [A: $tType,Sup: ( set @ A ) > A,A3: set @ A] :
% 2.93/1.54 ( ( Sup @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 2.93/1.54 = ( Sup @ A3 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_203_INF__cong,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType] :
% 2.93/1.54 ( ( complete_Inf @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A3: set @ B,B4: set @ B,C2: B > A,D2: B > A] :
% 2.93/1.54 ( ( A3 = B4 )
% 2.93/1.54 => ( ! [X3: B] :
% 2.93/1.54 ( ( member @ B @ X3 @ B4 )
% 2.93/1.54 => ( ( C2 @ X3 )
% 2.93/1.54 = ( D2 @ X3 ) ) )
% 2.93/1.54 => ( ( complete_Inf_Inf @ A @ ( image @ B @ A @ C2 @ A3 ) )
% 2.93/1.54 = ( complete_Inf_Inf @ A @ ( image @ B @ A @ D2 @ B4 ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_204_eq__id__iff,axiom,
% 2.93/1.54 ! [A: $tType,F: A > A] :
% 2.93/1.54 ( ( ! [X2: A] :
% 2.93/1.54 ( ( F @ X2 )
% 2.93/1.54 = X2 ) )
% 2.93/1.54 = ( F
% 2.93/1.54 = ( id @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_205_id__def,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( id @ A )
% 2.93/1.54 = ( ^ [X2: A] : X2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_206_comp__eq__id__dest,axiom,
% 2.93/1.54 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B3: A > C,C3: A > B,V: A] :
% 2.93/1.54 ( ( ( comp @ C @ B @ A @ A2 @ B3 )
% 2.93/1.54 = ( comp @ B @ B @ A @ ( id @ B ) @ C3 ) )
% 2.93/1.54 => ( ( A2 @ ( B3 @ V ) )
% 2.93/1.54 = ( C3 @ V ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_207_pointfree__idE,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: B > A,G: A > B,X: A] :
% 2.93/1.54 ( ( ( comp @ B @ A @ A @ F @ G )
% 2.93/1.54 = ( id @ A ) )
% 2.93/1.54 => ( ( F @ ( G @ X ) )
% 2.93/1.54 = X ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_208_member__bind,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,X: A,P2: set @ B,F: B > ( set @ A )] :
% 2.93/1.54 ( ( member @ A @ X @ ( bind @ B @ A @ P2 @ F ) )
% 2.93/1.54 = ( member @ A @ X @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ P2 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_209_Sup__SUP__eq,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( complete_Sup_Sup @ ( A > $o ) )
% 2.93/1.54 = ( ^ [S: set @ ( A > $o ),X2: A] : ( member @ A @ X2 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ ( A > $o ) @ ( set @ A ) @ ( collect @ A ) @ S ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_210_Union__image__empty,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,A3: set @ A,F: B > ( set @ A )] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ A3 @ ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F @ ( bot_bot @ ( set @ B ) ) ) ) )
% 2.93/1.54 = A3 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_211_empty__iff,axiom,
% 2.93/1.54 ! [A: $tType,C3: A] :
% 2.93/1.54 ~ ( member @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_212_all__not__in__conv,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A] :
% 2.93/1.54 ( ( ! [X2: A] :
% 2.93/1.54 ~ ( member @ A @ X2 @ A3 ) )
% 2.93/1.54 = ( A3
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_213_Collect__empty__eq,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o] :
% 2.93/1.54 ( ( ( collect @ A @ P2 )
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 = ( ! [X2: A] :
% 2.93/1.54 ~ ( P2 @ X2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_214_empty__Collect__eq,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o] :
% 2.93/1.54 ( ( ( bot_bot @ ( set @ A ) )
% 2.93/1.54 = ( collect @ A @ P2 ) )
% 2.93/1.54 = ( ! [X2: A] :
% 2.93/1.54 ~ ( P2 @ X2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_215_Sup1__I,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,A3: set @ ( A > $o ),A2: A] :
% 2.93/1.54 ( ( member @ ( A > $o ) @ P2 @ A3 )
% 2.93/1.54 => ( ( P2 @ A2 )
% 2.93/1.54 => ( complete_Sup_Sup @ ( A > $o ) @ A3 @ A2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_216_image__empty,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: B > A] :
% 2.93/1.54 ( ( image @ B @ A @ F @ ( bot_bot @ ( set @ B ) ) )
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_217_empty__is__image,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,F: B > A,A3: set @ B] :
% 2.93/1.54 ( ( ( bot_bot @ ( set @ A ) )
% 2.93/1.54 = ( image @ B @ A @ F @ A3 ) )
% 2.93/1.54 = ( A3
% 2.93/1.54 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_218_image__is__empty,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,F: B > A,A3: set @ B] :
% 2.93/1.54 ( ( ( image @ B @ A @ F @ A3 )
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 = ( A3
% 2.93/1.54 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_219_sup__bot_Oright__neutral,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A2: A] :
% 2.93/1.54 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 2.93/1.54 = A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_220_sup__bot_Oleft__neutral,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A2: A] :
% 2.93/1.54 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 2.93/1.54 = A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_221_sup__eq__bot__iff,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A,Y: A] :
% 2.93/1.54 ( ( ( sup_sup @ A @ X @ Y )
% 2.93/1.54 = ( bot_bot @ A ) )
% 2.93/1.54 = ( ( X
% 2.93/1.54 = ( bot_bot @ A ) )
% 2.93/1.54 & ( Y
% 2.93/1.54 = ( bot_bot @ A ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_222_bot__eq__sup__iff,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A,Y: A] :
% 2.93/1.54 ( ( ( bot_bot @ A )
% 2.93/1.54 = ( sup_sup @ A @ X @ Y ) )
% 2.93/1.54 = ( ( X
% 2.93/1.54 = ( bot_bot @ A ) )
% 2.93/1.54 & ( Y
% 2.93/1.54 = ( bot_bot @ A ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_223_Sup__bot__conv_I2_J,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A3: set @ A] :
% 2.93/1.54 ( ( ( bot_bot @ A )
% 2.93/1.54 = ( complete_Sup_Sup @ A @ A3 ) )
% 2.93/1.54 = ( ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ A3 )
% 2.93/1.54 => ( X2
% 2.93/1.54 = ( bot_bot @ A ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_224_Sup__bot__conv_I1_J,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [A3: set @ A] :
% 2.93/1.54 ( ( ( complete_Sup_Sup @ A @ A3 )
% 2.93/1.54 = ( bot_bot @ A ) )
% 2.93/1.54 = ( ! [X2: A] :
% 2.93/1.54 ( ( member @ A @ X2 @ A3 )
% 2.93/1.54 => ( X2
% 2.93/1.54 = ( bot_bot @ A ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_225_singletonI,axiom,
% 2.93/1.54 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_226_ball__empty,axiom,
% 2.93/1.54 ! [A: $tType,P2: A > $o,X4: A] :
% 2.93/1.54 ( ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 => ( P2 @ X4 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_227_Un__empty,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.93/1.54 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B4 )
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 = ( ( A3
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 & ( B4
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_228_empty__bind,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType,F: B > ( set @ A )] :
% 2.93/1.54 ( ( bind @ B @ A @ ( bot_bot @ ( set @ B ) ) @ F )
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_229_Sup__empty,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ( ( complete_Sup_Sup @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 = ( bot_bot @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_230_Sup1__E,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ ( A > $o ),A2: A] :
% 2.93/1.54 ( ( complete_Sup_Sup @ ( A > $o ) @ A3 @ A2 )
% 2.93/1.54 => ~ ! [P4: A > $o] :
% 2.93/1.54 ( ( member @ ( A > $o ) @ P4 @ A3 )
% 2.93/1.54 => ~ ( P4 @ A2 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_231_Union__empty,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( complete_Sup_Sup @ ( set @ A ) @ ( bot_bot @ ( set @ ( set @ A ) ) ) )
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_232_Union__empty__conv,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ ( set @ A )] :
% 2.93/1.54 ( ( ( complete_Sup_Sup @ ( set @ A ) @ A3 )
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 = ( ! [X2: set @ A] :
% 2.93/1.54 ( ( member @ ( set @ A ) @ X2 @ A3 )
% 2.93/1.54 => ( X2
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_233_empty__Union__conv,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ ( set @ A )] :
% 2.93/1.54 ( ( ( bot_bot @ ( set @ A ) )
% 2.93/1.54 = ( complete_Sup_Sup @ ( set @ A ) @ A3 ) )
% 2.93/1.54 = ( ! [X2: set @ A] :
% 2.93/1.54 ( ( member @ ( set @ A ) @ X2 @ A3 )
% 2.93/1.54 => ( X2
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_234_sup__bot__right,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A] :
% 2.93/1.54 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 2.93/1.54 = X ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_235_sup__bot__left,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [X: A] :
% 2.93/1.54 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 2.93/1.54 = X ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_236_Un__empty__right,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 = A3 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_237_Un__empty__left,axiom,
% 2.93/1.54 ! [A: $tType,B4: set @ A] :
% 2.93/1.54 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 2.93/1.54 = B4 ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_238_image__bind,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,C: $tType,F: B > A,A3: set @ C,G: C > ( set @ B )] :
% 2.93/1.54 ( ( image @ B @ A @ F @ ( bind @ C @ B @ A3 @ G ) )
% 2.93/1.54 = ( bind @ C @ A @ A3 @ ( comp @ ( set @ B ) @ ( set @ A ) @ C @ ( image @ B @ A @ F ) @ G ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_239_bind__image,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType,C: $tType,F: C > B,A3: set @ C,G: B > ( set @ A )] :
% 2.93/1.54 ( ( bind @ B @ A @ ( image @ C @ B @ F @ A3 ) @ G )
% 2.93/1.54 = ( bind @ C @ A @ A3 @ ( comp @ B @ ( set @ A ) @ C @ G @ F ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_240_singletonD,axiom,
% 2.93/1.54 ! [A: $tType,B3: A,A2: A] :
% 2.93/1.54 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 => ( B3 = A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_241_singleton__iff,axiom,
% 2.93/1.54 ! [A: $tType,B3: A,A2: A] :
% 2.93/1.54 ( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 = ( B3 = A2 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_242_doubleton__eq__iff,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,B3: A,C3: A,D3: A] :
% 2.93/1.54 ( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 = ( insert @ A @ C3 @ ( insert @ A @ D3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.93/1.54 = ( ( ( A2 = C3 )
% 2.93/1.54 & ( B3 = D3 ) )
% 2.93/1.54 | ( ( A2 = D3 )
% 2.93/1.54 & ( B3 = C3 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_243_insert__not__empty,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,A3: set @ A] :
% 2.93/1.54 ( ( insert @ A @ A2 @ A3 )
% 2.93/1.54 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_244_singleton__inject,axiom,
% 2.93/1.54 ! [A: $tType,A2: A,B3: A] :
% 2.93/1.54 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 => ( A2 = B3 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_245_Inf__INT__eq,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( complete_Inf_Inf @ ( A > $o ) )
% 2.93/1.54 = ( ^ [S: set @ ( A > $o ),X2: A] : ( member @ A @ X2 @ ( complete_Inf_Inf @ ( set @ A ) @ ( image @ ( A > $o ) @ ( set @ A ) @ ( collect @ A ) @ S ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_246_emptyE,axiom,
% 2.93/1.54 ! [A: $tType,A2: A] :
% 2.93/1.54 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_247_equals0D,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,A2: A] :
% 2.93/1.54 ( ( A3
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_248_equals0I,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A] :
% 2.93/1.54 ( ! [Y4: A] :
% 2.93/1.54 ~ ( member @ A @ Y4 @ A3 )
% 2.93/1.54 => ( A3
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_249_ex__in__conv,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A] :
% 2.93/1.54 ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 2.93/1.54 = ( A3
% 2.93/1.54 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_250_SUP__eq__const,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType] :
% 2.93/1.54 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [I: set @ B,F: B > A,X: A] :
% 2.93/1.54 ( ( I
% 2.93/1.54 != ( bot_bot @ ( set @ B ) ) )
% 2.93/1.54 => ( ! [I2: B] :
% 2.93/1.54 ( ( member @ B @ I2 @ I )
% 2.93/1.54 => ( ( F @ I2 )
% 2.93/1.54 = X ) )
% 2.93/1.54 => ( ( complete_Sup_Sup @ A @ ( image @ B @ A @ F @ I ) )
% 2.93/1.54 = X ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_251_INF__eq__const,axiom,
% 2.93/1.54 ! [B: $tType,A: $tType] :
% 2.93/1.54 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.93/1.54 => ! [I: set @ B,F: B > A,X: A] :
% 2.93/1.54 ( ( I
% 2.93/1.54 != ( bot_bot @ ( set @ B ) ) )
% 2.93/1.54 => ( ! [I2: B] :
% 2.93/1.54 ( ( member @ B @ I2 @ I )
% 2.93/1.54 => ( ( F @ I2 )
% 2.93/1.54 = X ) )
% 2.93/1.54 => ( ( complete_Inf_Inf @ A @ ( image @ B @ A @ F @ I ) )
% 2.93/1.54 = X ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_252_singleton__Un__iff,axiom,
% 2.93/1.54 ! [A: $tType,X: A,A3: set @ A,B4: set @ A] :
% 2.93/1.54 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 = ( sup_sup @ ( set @ A ) @ A3 @ B4 ) )
% 2.93/1.54 = ( ( ( A3
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 & ( B4
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.93/1.54 | ( ( A3
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 & ( B4
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 | ( ( A3
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 & ( B4
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_253_Un__singleton__iff,axiom,
% 2.93/1.54 ! [A: $tType,A3: set @ A,B4: set @ A,X: A] :
% 2.93/1.54 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B4 )
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 = ( ( ( A3
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) )
% 2.93/1.54 & ( B4
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.93/1.54 | ( ( A3
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 & ( B4
% 2.93/1.54 = ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 | ( ( A3
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.93/1.54 & ( B4
% 2.93/1.54 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_254_insert__is__Un,axiom,
% 2.93/1.54 ! [A: $tType] :
% 2.93/1.54 ( ( insert @ A )
% 2.93/1.54 = ( ^ [A4: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(fact_255_bind__UNION,axiom,
% 2.93/1.54 ! [A: $tType,B: $tType] :
% 2.93/1.54 ( ( bind @ B @ A )
% 2.93/1.54 = ( ^ [A5: set @ B,F3: B > ( set @ A )] : ( complete_Sup_Sup @ ( set @ A ) @ ( image @ B @ ( set @ A ) @ F3 @ A5 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.93/1.54 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.93/1.54 ! [A6: $tType] : ( bounded_lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.93/1.54 ! [A6: $tType,A7: $tType] :
% 2.93/1.54 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 2.93/1.54 => ( bounded_lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 2.93/1.54 ! [A6: $tType,A7: $tType] :
% 2.93/1.54 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 2.93/1.54 => ( bounde1808546759up_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 2.93/1.54 ! [A6: $tType,A7: $tType] :
% 2.93/1.54 ( ( comple187826305attice @ A7 @ ( type2 @ A7 ) )
% 2.93/1.54 => ( comple187826305attice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 2.93/1.54 ! [A6: $tType,A7: $tType] :
% 2.93/1.54 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 2.93/1.54 => ( bounded_lattice_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.93/1.54 ! [A6: $tType,A7: $tType] :
% 2.93/1.54 ( ( semilattice_sup @ A7 @ ( type2 @ A7 ) )
% 2.93/1.54 => ( semilattice_sup @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_fun___Complete__Lattices_OSup,axiom,
% 2.93/1.54 ! [A6: $tType,A7: $tType] :
% 2.93/1.54 ( ( complete_Sup @ A7 @ ( type2 @ A7 ) )
% 2.93/1.54 => ( complete_Sup @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_fun___Complete__Lattices_OInf,axiom,
% 2.93/1.54 ! [A6: $tType,A7: $tType] :
% 2.93/1.54 ( ( complete_Inf @ A7 @ ( type2 @ A7 ) )
% 2.93/1.54 => ( complete_Inf @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.93/1.54 ! [A6: $tType,A7: $tType] :
% 2.93/1.54 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 2.93/1.54 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 2.93/1.54 ! [A6: $tType] : ( bounde1808546759up_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_4,axiom,
% 2.93/1.54 ! [A6: $tType] : ( comple187826305attice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_5,axiom,
% 2.93/1.54 ! [A6: $tType] : ( bounded_lattice_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_6,axiom,
% 2.93/1.54 ! [A6: $tType] : ( semilattice_sup @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_Set_Oset___Complete__Lattices_OSup_7,axiom,
% 2.93/1.54 ! [A6: $tType] : ( complete_Sup @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_Set_Oset___Complete__Lattices_OInf_8,axiom,
% 2.93/1.54 ! [A6: $tType] : ( complete_Inf @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_Set_Oset___Lattices_Olattice_9,axiom,
% 2.93/1.54 ! [A6: $tType] : ( lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_10,axiom,
% 2.93/1.54 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_11,axiom,
% 2.93/1.54 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12,axiom,
% 2.93/1.54 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_13,axiom,
% 2.93/1.54 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_HOL_Obool___Complete__Lattices_OSup_14,axiom,
% 2.93/1.54 complete_Sup @ $o @ ( type2 @ $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_HOL_Obool___Complete__Lattices_OInf_15,axiom,
% 2.93/1.54 complete_Inf @ $o @ ( type2 @ $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(tcon_HOL_Obool___Lattices_Olattice_16,axiom,
% 2.93/1.54 lattice @ $o @ ( type2 @ $o ) ).
% 2.93/1.54
% 2.93/1.54 thf(help_If_3_1_T,axiom,
% 2.93/1.54 ! [P2: $o] :
% 2.93/1.54 ( ( P2 = $true )
% 2.93/1.54 | ( P2 = $false ) ) ).
% 2.93/1.54
% 2.93/1.54 thf(help_If_2_1_T,axiom,
% 2.93/1.54 ! [A: $tType,X: A,Y: A] :
% 2.93/1.54 ( ( if @ A @ $false @ X @ Y )
% 2.93/1.54 = Y ) ).
% 2.93/1.54
% 2.93/1.54 thf(help_If_1_1_T,axiom,
% 2.93/1.54 ! [A: $tType,X: A,Y: A] :
% 2.93/1.54 ( ( if @ A @ $true @ X @ Y )
% 2.93/1.54 = X ) ).
% 2.93/1.54
% 2.93/1.54 thf(conj_0,conjecture,
% 2.93/1.54 ( ( proces10484146Action @ a @ p )
% 2.93/1.54 | ( proces401113213Choice @ a @ p ) ) ).
% 2.93/1.54 ------------------------
% 2.93/1.57 % (10589)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10395 for (2999ds/183Mi)
% 2.93/1.57 % (10590)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_10395 for (2999ds/4Mi)
% 2.93/1.57 % (10593)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_10395 for (2999ds/2Mi)
% 2.93/1.57 % (10590)Instruction limit reached!
% 2.93/1.57 % (10590)------------------------------
% 2.93/1.57 % (10590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.57 % (10590)Termination reason: Unknown
% 2.93/1.57 % (10590)Termination phase: shuffling
% 2.93/1.57
% 2.93/1.57 % (10590)Memory used [KB]: 1535
% 2.93/1.57 % (10590)Time elapsed: 0.004 s
% 2.93/1.57 % (10590)Instructions burned: 7 (million)
% 2.93/1.57 % (10590)------------------------------
% 2.93/1.57 % (10590)------------------------------
% 2.93/1.57 % (10593)Instruction limit reached!
% 2.93/1.57 % (10593)------------------------------
% 2.93/1.57 % (10593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.57 % (10593)Termination reason: Unknown
% 2.93/1.57 % (10593)Termination phase: shuffling
% 2.93/1.57
% 2.93/1.57 % (10593)Memory used [KB]: 1407
% 2.93/1.57 % (10593)Time elapsed: 0.002 s
% 2.93/1.57 % (10593)Instructions burned: 3 (million)
% 2.93/1.57 % (10593)------------------------------
% 2.93/1.57 % (10593)------------------------------
% 2.93/1.57 % (10595)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10395 for (2999ds/18Mi)
% 2.93/1.58 % (10596)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10395 for (2999ds/3Mi)
% 2.93/1.58 % (10592)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10395 for (2999ds/2Mi)
% 2.93/1.58 % (10595)Instruction limit reached!
% 2.93/1.58 % (10595)------------------------------
% 2.93/1.58 % (10595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.58 % (10595)Termination reason: Unknown
% 2.93/1.58 % (10595)Termination phase: shuffling
% 2.93/1.58
% 2.93/1.58 % (10595)Memory used [KB]: 1791
% 2.93/1.58 % (10595)Time elapsed: 0.009 s
% 2.93/1.58 % (10595)Instructions burned: 18 (million)
% 2.93/1.58 % (10595)------------------------------
% 2.93/1.58 % (10595)------------------------------
% 2.93/1.58 % (10594)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_10395 for (2999ds/275Mi)
% 2.93/1.58 % (10592)Instruction limit reached!
% 2.93/1.58 % (10592)------------------------------
% 2.93/1.58 % (10592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.58 % (10592)Termination reason: Unknown
% 2.93/1.58 % (10592)Termination phase: shuffling
% 2.93/1.58
% 2.93/1.58 % (10592)Memory used [KB]: 1407
% 2.93/1.58 % (10592)Time elapsed: 0.003 s
% 2.93/1.58 % (10592)Instructions burned: 2 (million)
% 2.93/1.58 % (10592)------------------------------
% 2.93/1.58 % (10592)------------------------------
% 2.93/1.58 % (10596)Instruction limit reached!
% 2.93/1.58 % (10596)------------------------------
% 2.93/1.58 % (10596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.58 % (10596)Termination reason: Unknown
% 2.93/1.58 % (10596)Termination phase: shuffling
% 2.93/1.58
% 2.93/1.58 % (10596)Memory used [KB]: 1407
% 2.93/1.58 % (10596)Time elapsed: 0.003 s
% 2.93/1.58 % (10596)Instructions burned: 5 (million)
% 2.93/1.58 % (10596)------------------------------
% 2.93/1.58 % (10596)------------------------------
% 2.93/1.58 % (10597)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_10395 for (2999ds/37Mi)
% 2.93/1.58 % (10591)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_10395 for (2999ds/27Mi)
% 2.93/1.59 % (10600)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_10395 for (2999ds/1041Mi)
% 2.93/1.59 % (10598)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_10395 for (2999ds/15Mi)
% 2.93/1.59 % (10599)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_10395 for (2999ds/3Mi)
% 2.93/1.59 % (10599)Instruction limit reached!
% 2.93/1.59 % (10599)------------------------------
% 2.93/1.59 % (10599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.59 % (10599)Termination reason: Unknown
% 2.93/1.59 % (10599)Termination phase: shuffling
% 2.93/1.59
% 2.93/1.59 % (10599)Memory used [KB]: 1407
% 2.93/1.59 % (10599)Time elapsed: 0.003 s
% 2.93/1.59 % (10599)Instructions burned: 3 (million)
% 2.93/1.59 % (10599)------------------------------
% 2.93/1.59 % (10599)------------------------------
% 3.00/1.60 % (10598)Instruction limit reached!
% 3.00/1.60 % (10598)------------------------------
% 3.00/1.60 % (10598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (10598)Termination reason: Unknown
% 3.00/1.60 % (10598)Termination phase: shuffling
% 3.00/1.60
% 3.00/1.60 % (10598)Memory used [KB]: 1663
% 3.00/1.60 % (10598)Time elapsed: 0.008 s
% 3.00/1.60 % (10598)Instructions burned: 17 (million)
% 3.00/1.60 % (10598)------------------------------
% 3.00/1.60 % (10598)------------------------------
% 3.00/1.60 % (10591)Instruction limit reached!
% 3.00/1.60 % (10591)------------------------------
% 3.00/1.60 % (10591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (10591)Termination reason: Unknown
% 3.00/1.60 % (10591)Termination phase: shuffling
% 3.00/1.60
% 3.00/1.60 % (10591)Memory used [KB]: 1918
% 3.00/1.60 % (10591)Time elapsed: 0.015 s
% 3.00/1.60 % (10591)Instructions burned: 27 (million)
% 3.00/1.60 % (10591)------------------------------
% 3.00/1.60 % (10591)------------------------------
% 3.00/1.60 % (10597)Instruction limit reached!
% 3.00/1.60 % (10597)------------------------------
% 3.00/1.60 % (10597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (10597)Termination reason: Unknown
% 3.00/1.60 % (10597)Termination phase: shuffling
% 3.00/1.60
% 3.00/1.60 % (10597)Memory used [KB]: 2174
% 3.00/1.60 % (10597)Time elapsed: 0.018 s
% 3.00/1.60 % (10597)Instructions burned: 38 (million)
% 3.00/1.60 % (10597)------------------------------
% 3.00/1.60 % (10597)------------------------------
% 3.00/1.60 % (10594)First to succeed.
% 3.00/1.60 % (10601)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10395 for (2999ds/7Mi)
% 3.00/1.60 % (10594)Refutation found. Thanks to Tanya!
% 3.00/1.60 % SZS status Theorem for DTF2THF_10395
% 3.00/1.60 % SZS output start Proof for DTF2THF_10395
% 3.00/1.60 thf(type_def_5, type, itself: ($tType) > $tType).
% 3.00/1.60 thf(type_def_7, type, set: ($tType) > $tType).
% 3.00/1.60 thf(type_def_8, type, proces634752977rocess: ($tType) > $tType).
% 3.00/1.60 thf(type_def_9, type, a: $tType).
% 3.00/1.60 thf(func_def_0, type, proces634752977rocess: ($tType) > $tType).
% 3.00/1.60 thf(func_def_1, type, set: ($tType) > $tType).
% 3.00/1.60 thf(func_def_2, type, itself: ($tType) > $tType).
% 3.00/1.60 thf(func_def_3, type, a: $tType).
% 3.00/1.60 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_6, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_7, type, complete_Inf: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_8, type, complete_Sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_9, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_10, type, bounded_lattice_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_11, type, comple187826305attice: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_12, type, bounde1808546759up_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.00/1.60 thf(func_def_13, type, bNF_eq_onp: !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 3.00/1.60 thf(func_def_14, type, bNF_vimage2p: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((X0 > X1) > (X2 > X3) > (X1 > X3 > X4) > X0 > X2 > X4)).
% 3.00/1.60 thf(func_def_15, type, complete_Inf_Inf: !>[X0: $tType]:(set @ X0 > X0)).
% 3.00/1.60 thf(func_def_16, type, complete_Sup_Sup: !>[X0: $tType]:(set @ X0 > X0)).
% 3.00/1.60 thf(func_def_17, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 3.00/1.60 thf(func_def_18, type, id: !>[X0: $tType]:(X0 > X0)).
% 3.00/1.60 thf(func_def_19, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.00/1.60 thf(func_def_20, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.00/1.60 thf(func_def_21, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.00/1.60 thf(func_def_22, type, proces1525233512Action: !>[X0: $tType]:(X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.00/1.60 thf(func_def_23, type, proces1915862579Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.00/1.60 thf(func_def_24, type, proces1406508781rocess: !>[X0: $tType, X1: $tType]:((X0 > proces634752977rocess @ X0 > X1) > (proces634752977rocess @ X0 > proces634752977rocess @ X0 > X1) > proces634752977rocess @ X0 > X1)).
% 3.00/1.60 thf(func_def_25, type, proces979765041_ch1Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.00/1.60 thf(func_def_26, type, proces988026546_ch2Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.00/1.60 thf(func_def_27, type, proces1778668539contOf: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.00/1.60 thf(func_def_28, type, proces894737309rocess: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > X0 > proces634752977rocess @ X1)).
% 3.00/1.60 thf(func_def_29, type, proces10484146Action: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 3.00/1.60 thf(func_def_30, type, proces401113213Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 3.00/1.60 thf(func_def_31, type, proces370407749rocess: !>[X0: $tType, X1: $tType]:((X0 > X1) > proces634752977rocess @ X0 > proces634752977rocess @ X1)).
% 3.00/1.60 thf(func_def_32, type, proces1205983068rocess: !>[X0: $tType]:((X0 > $o) > proces634752977rocess @ X0 > $o)).
% 3.00/1.60 thf(func_def_33, type, proces745025900prefOf: !>[X0: $tType]:(proces634752977rocess @ X0 > X0)).
% 3.00/1.60 thf(func_def_34, type, proces749077512rocess: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X1 > $o)).
% 3.00/1.60 thf(func_def_35, type, proces1148692671rocess: !>[X0: $tType]:(proces634752977rocess @ X0 > set @ X0)).
% 3.00/1.60 thf(func_def_36, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.00/1.60 thf(func_def_37, type, ball: !>[X0: $tType]:(set @ X0 > (X0 > $o) > $o)).
% 3.00/1.60 thf(func_def_38, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.00/1.60 thf(func_def_39, type, bind: !>[X0: $tType, X1: $tType]:(set @ X0 > (X0 > set @ X1) > set @ X1)).
% 3.00/1.60 thf(func_def_40, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 3.00/1.60 thf(func_def_41, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 3.00/1.60 thf(func_def_42, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.00/1.60 thf(func_def_43, type, p: proces634752977rocess @ a).
% 3.00/1.60 thf(func_def_56, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.00/1.60 thf(func_def_57, type, sK1: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.00/1.60 thf(func_def_58, type, sK2: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.00/1.60 thf(func_def_59, type, sK3: !>[X0: $tType]:(proces634752977rocess @ X0 > X0)).
% 3.00/1.60 thf(func_def_60, type, sK4: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 3.00/1.60 thf(f757,plain,(
% 3.00/1.60 $false),
% 3.00/1.60 inference(subsumption_resolution,[status(thm)],[f756,f737])).
% 3.00/1.60 thf(f737,plain,(
% 3.00/1.60 ((proces10484146Action @ a @ p) != $true)),
% 3.00/1.60 inference(cnf_transformation,[status(thm)],[f712])).
% 3.00/1.60 thf(f712,plain,(
% 3.00/1.60 ((proces401113213Choice @ a @ p) != $true) & ((proces10484146Action @ a @ p) != $true)),
% 3.00/1.60 inference(ennf_transformation,[status(thm)],[f302])).
% 3.00/1.60 thf(f302,plain,(
% 3.00/1.60 ~(((proces10484146Action @ a @ p) = $true) | ((proces401113213Choice @ a @ p) = $true))),
% 3.00/1.60 inference(fool_elimination,[status(thm)],[f301])).
% 3.00/1.60 thf(f301,plain,(
% 3.00/1.60 ~((proces10484146Action @ a @ p) | (proces401113213Choice @ a @ p))),
% 3.00/1.60 inference(rectify,[status(thm)],[f285])).
% 3.00/1.60 thf(f285,negated_conjecture,(
% 3.00/1.60 ~((proces10484146Action @ a @ p) | (proces401113213Choice @ a @ p))),
% 3.00/1.60 inference(negated_conjecture,[status(cth)],[f284])).
% 3.00/1.60 thf(f284,conjecture,(
% 3.00/1.60 (proces10484146Action @ a @ p) | (proces401113213Choice @ a @ p)),
% 3.00/1.60 file('/export/starexec/sandbox/tmp/tmp.lJEBhRXwsb/DTF2THF_10395.p',conj_0)).
% 3.00/1.60 thf(f756,plain,(
% 3.00/1.60 ((proces10484146Action @ a @ p) = $true)),
% 3.00/1.60 inference(trivial_inequality_removal,[status(thm)],[f755])).
% 3.00/1.60 thf(f755,plain,(
% 3.00/1.60 ((proces10484146Action @ a @ p) = $true) | ($true != $true)),
% 3.00/1.60 inference(superposition,[status(thm)],[f738,f740])).
% 3.00/1.60 thf(f740,plain,(
% 3.00/1.60 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true = (proces401113213Choice @ X0 @ X1)) | ($true = (proces10484146Action @ X0 @ X1))) )),
% 3.00/1.60 inference(cnf_transformation,[status(thm)],[f710])).
% 3.00/1.60 thf(f710,plain,(
% 3.00/1.60 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true = (proces401113213Choice @ X0 @ X1)) | ($true = (proces10484146Action @ X0 @ X1)))),
% 3.00/1.60 inference(ennf_transformation,[status(thm)],[f700])).
% 3.00/1.60 thf(f700,plain,(
% 3.00/1.60 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true != (proces10484146Action @ X0 @ X1)) => ($true = (proces401113213Choice @ X0 @ X1)))),
% 3.00/1.60 inference(flattening,[status(thm)],[f578])).
% 3.00/1.60 thf(f578,plain,(
% 3.00/1.60 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (~($true = (proces10484146Action @ X0 @ X1)) => ($true = (proces401113213Choice @ X0 @ X1)))),
% 3.00/1.60 inference(fool_elimination,[status(thm)],[f577])).
% 3.00/1.60 thf(f577,plain,(
% 3.00/1.60 ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (~(proces10484146Action @ X0 @ X1) => (proces401113213Choice @ X0 @ X1))),
% 3.00/1.60 inference(rectify,[status(thm)],[f3])).
% 3.00/1.60 thf(f3,axiom,(
% 3.00/1.60 ! [X0 : $tType,X6 : proces634752977rocess @ X0] : (~(proces10484146Action @ X0 @ X6) => (proces401113213Choice @ X0 @ X6))),
% 3.00/1.60 file('/export/starexec/sandbox/tmp/tmp.lJEBhRXwsb/DTF2THF_10395.p',fact_2_process_Oexhaust__disc)).
% 3.00/1.60 thf(f738,plain,(
% 3.00/1.60 ((proces401113213Choice @ a @ p) != $true)),
% 3.00/1.60 inference(cnf_transformation,[status(thm)],[f712])).
% 3.00/1.60 % SZS output end Proof for DTF2THF_10395
% 3.00/1.60 % (10594)------------------------------
% 3.00/1.60 % (10594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.60 % (10594)Termination reason: Refutation
% 3.00/1.60
% 3.00/1.60 % (10594)Memory used [KB]: 6524
% 3.00/1.60 % (10594)Time elapsed: 0.022 s
% 3.00/1.60 % (10594)Instructions burned: 55 (million)
% 3.00/1.60 % (10594)------------------------------
% 3.00/1.60 % (10594)------------------------------
% 3.00/1.60 % (10588)Success in time 0.045 s
%------------------------------------------------------------------------------