TPTP Problem File: PRO028^1.p
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%------------------------------------------------------------------------------
% File : PRO028^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Processes
% Problem : Process algebra 257
% Version : [Bla16] axioms : Especial.
% English :
% Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% Source : [Bla16]
% Names : process__257.p [Bla16]
% Status : Theorem
% Rating : 1.00 v7.3.0, 0.67 v7.2.0, 0.75 v7.1.0
% Syntax : Number of formulae : 319 ( 135 unt; 59 typ; 0 def)
% Number of atoms : 935 ( 388 equ; 0 cnn)
% Maximal formula atoms : 31 ( 3 avg)
% Number of connectives : 8561 ( 169 ~; 9 |; 43 &;7907 @)
% ( 0 <=>; 433 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 12 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 1299 (1299 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 56 usr; 2 con; 0-14 aty)
% Number of variables : 2042 ( 227 ^;1693 !; 23 ?;2042 :)
% ( 99 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2016-07-13 14:40:17.063
%------------------------------------------------------------------------------
%----Could-be-implicit typings (9)
thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
proces554692349s_term: $tType > $tType > $tType ).
thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
proces634752977rocess: $tType > $tType ).
thf(ty_t_Product__Type_Oprod,type,
product_prod: $tType > $tType > $tType ).
thf(ty_t_String_Ochar,type,
char: $tType ).
thf(ty_t_List_Olist,type,
list: $tType > $tType ).
thf(ty_t_Set_Oset,type,
set: $tType > $tType ).
thf(ty_t_Nat_Onat,type,
nat: $tType ).
thf(ty_t_itself,type,
itself: $tType > $tType ).
thf(ty_tf_a,type,
a: $tType ).
%----Explicit typings (50)
thf(sy_cl_Groups_Ozero,type,
zero:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_c_BNF__Def_Orel__fun,type,
bNF_rel_fun:
!>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
thf(sy_c_HOL_Oundefined,type,
undefined:
!>[A: $tType] : A ).
thf(sy_c_If,type,
if:
!>[A: $tType] : ( $o > A > A > A ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
proces1239275103le_CH1:
!>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
proces1869379930H1_rel:
!>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
proces1239275104le_CH2:
!>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
proces93903513H2_rel:
!>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
proces126235999e_CONT:
!>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
proces1004198490NT_rel:
!>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
proces1708129104e_PREF:
!>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
proces527360425EF_rel:
!>[A: $tType,B: $tType,C: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
proces1121166967uarded:
!>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
proces687458811_isACT:
!>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
proces896239806CT_rel:
!>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
proces1525233512Action:
!>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
proces1915862579Choice:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
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 ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
proces979765041_ch1Of:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
proces988026546_ch2Of:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
proces1778668539contOf:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
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 ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
proces10484146Action:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
proces401113213Choice:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
proces1205983068rocess:
!>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
proces745025900prefOf:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
proces749077512rocess:
!>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Oset__process,type,
proces1148692671rocess:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( set @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
proces1454156180ss_ACT:
!>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
proces89589571ess_CH:
!>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
proces1062592052s_PROC:
!>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
proces1627516585ss_VAR:
!>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
proces460752237s_term:
!>[Pvar: $tType,B: $tType,A: $tType] : ( ( Pvar > B ) > ( ( proces634752977rocess @ A ) > B ) > ( A > ( proces554692349s_term @ A @ Pvar ) > B ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B ) > ( proces554692349s_term @ A @ Pvar ) > B ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term,type,
proces224683037s_term:
!>[A: $tType,Aa: $tType,Pvar: $tType,Pvara: $tType] : ( ( A > Aa ) > ( Pvar > Pvara ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ Aa @ Pvara ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
proces2118920028s_term:
!>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term,type,
proces2117273769s_term:
!>[Pvar: $tType,D: $tType,A: $tType] : ( ( Pvar > D ) > ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
proces2029722208s_term:
!>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset1__process__term,type,
proces1264666542s_term:
!>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
proces1493547885s_term:
!>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
proces1652378886lution:
!>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Osys_H,type,
proces1667721le_sys:
!>[A: $tType] : ( nat > ( proces554692349s_term @ ( list @ char ) @ A ) ) ).
thf(sy_c_Product__Type_OPair,type,
product_Pair:
!>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
thf(sy_c_Product__Type_Ocurry,type,
product_curry:
!>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
thf(sy_c_Product__Type_Ointernal__case__prod,type,
produc2004651681e_prod:
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
product_rec_prod:
!>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
thf(sy_c_Pure_Otype,type,
type:
!>[A: $tType] : ( itself @ A ) ).
thf(sy_c_Set_OBall,type,
ball:
!>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
thf(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
thf(sy_c_Wellfounded_Oaccp,type,
accp:
!>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
thf(sy_c_member,type,
member:
!>[A: $tType] : ( A > ( set @ A ) > $o ) ).
%----Relevant facts (255)
thf(fact_0_process__term_Oinject_I1_J,axiom,
! [A: $tType,Pvar: $tType,X1: Pvar,Y1: Pvar] :
( ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
= ( proces1627516585ss_VAR @ Pvar @ A @ Y1 ) )
= ( X1 = Y1 ) ) ).
% process_term.inject(1)
thf(fact_1_guarded__def,axiom,
! [C: $tType,B: $tType,A: $tType] :
( ( proces1121166967uarded @ A @ B @ C )
= ( ^ [Sys: A > ( proces554692349s_term @ B @ C )] :
! [X: A,Y: C] :
( ( Sys @ X )
!= ( proces1627516585ss_VAR @ C @ B @ Y ) ) ) ) ).
% guarded_def
thf(fact_2_process__term_Opred__inject_I1_J,axiom,
! [A: $tType,Pvar: $tType,P1: A > $o,P2: Pvar > $o,A2: Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
= ( P2 @ A2 ) ) ).
% process_term.pred_inject(1)
thf(fact_3_process__term_Osimps_I21_J,axiom,
! [A: $tType,D: $tType,Pvar: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X1: Pvar] :
( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
= ( F1 @ X1 ) ) ).
% process_term.simps(21)
thf(fact_4_process__term_Osimps_I17_J,axiom,
! [A: $tType,B: $tType,Pvar: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X1: Pvar] :
( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
= ( F1 @ X1 ) ) ).
% process_term.simps(17)
thf(fact_5_process__term_Oset__intros_I6_J,axiom,
! [A: $tType,Pvar: $tType,Ab: Pvar] : ( member @ Pvar @ Ab @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab ) ) ) ).
% process_term.set_intros(6)
thf(fact_6_process__term_Osimps_I25_J,axiom,
! [A: $tType,B: $tType,C: $tType,Pvar: $tType,F1: A > B,F2: Pvar > C,X1: Pvar] :
( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
= ( proces1627516585ss_VAR @ C @ B @ ( F2 @ X1 ) ) ) ).
% process_term.simps(25)
thf(fact_7_process__term_Odistinct_I3_J,axiom,
! [Pvar: $tType,A: $tType,X1: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
!= ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% process_term.distinct(3)
thf(fact_8_process__term_Odistinct_I5_J,axiom,
! [Pvar: $tType,A: $tType,X1: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
!= ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% process_term.distinct(5)
thf(fact_9_process__term_Odistinct_I1_J,axiom,
! [Pvar: $tType,A: $tType,X1: Pvar,X2: proces634752977rocess @ A] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
!= ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% process_term.distinct(1)
thf(fact_10_process__term_Orel__inject_I1_J,axiom,
! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R2: Pvar > C > $o,X1: Pvar,Y1: C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) )
= ( R2 @ X1 @ Y1 ) ) ).
% process_term.rel_inject(1)
thf(fact_11_process__term_Orel__intros_I1_J,axiom,
! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R2: Pvar > C > $o,X1: Pvar,Y1: C,R1: A > B > $o] :
( ( R2 @ X1 @ Y1 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) ) ) ).
% process_term.rel_intros(1)
thf(fact_12_isACT__VAR,axiom,
! [C: $tType,B: $tType,A: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces1121166967uarded @ A @ B @ A @ Sys2 )
=> ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys2 @ ( proces1627516585ss_VAR @ A @ C @ X3 ) )
= ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ ( Sys2 @ X3 ) ) ) ) ).
% isACT_VAR
thf(fact_13_process__term_Oinject_I2_J,axiom,
! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
= ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
= ( X2 = Y2 ) ) ).
% process_term.inject(2)
thf(fact_14_process__term_Oinject_I3_J,axiom,
! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
= ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
= ( ( X31 = Y31 )
& ( X32 = Y32 ) ) ) ).
% process_term.inject(3)
thf(fact_15_process__term_Oinject_I4_J,axiom,
! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
= ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
= ( ( X41 = Y41 )
& ( X42 = Y42 ) ) ) ).
% process_term.inject(4)
thf(fact_16_process__term_Opred__inject_I3_J,axiom,
! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
= ( ( P1 @ A2 )
& ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% process_term.pred_inject(3)
thf(fact_17_process__term_Opred__inject_I4_J,axiom,
! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
= ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ A2 )
& ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% process_term.pred_inject(4)
thf(fact_18_isACT_Osimps_I4_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,Sys2: A > ( proces554692349s_term @ B @ C ),T1: proces554692349s_term @ D @ A,T2: proces554692349s_term @ D @ A] :
~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T1 @ T2 ) ) ).
% isACT.simps(4)
thf(fact_19_isACT_Osimps_I3_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,Sys2: A > ( proces554692349s_term @ B @ C ),A2: D,T3: proces554692349s_term @ D @ A] : ( proces687458811_isACT @ A @ B @ C @ D @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A2 @ T3 ) ) ).
% isACT.simps(3)
thf(fact_20_process__term_Osimps_I51_J,axiom,
! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
= ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% process_term.simps(51)
thf(fact_21_process__term_Osimps_I28_J,axiom,
! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
= ( proces89589571ess_CH @ B @ C @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X41 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X42 ) ) ) ).
% process_term.simps(28)
thf(fact_22_process__term_Osimps_I27_J,axiom,
! [C: $tType,B: $tType,Pvar: $tType,A: $tType,F1: A > B,F2: Pvar > C,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
= ( proces1454156180ss_ACT @ B @ C @ ( F1 @ X31 ) @ ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ X32 ) ) ) ).
% process_term.simps(27)
thf(fact_23_process__term_Osimps_I24_J,axiom,
! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
= ( F4 @ X41 @ X42 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X41 ) @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X42 ) ) ) ).
% process_term.simps(24)
thf(fact_24_process__term_Osimps_I23_J,axiom,
! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
= ( F3 @ X31 @ X32 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X32 ) ) ) ).
% process_term.simps(23)
thf(fact_25_process__term_Osimps_I22_J,axiom,
! [Pvar: $tType,D: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X2: proces634752977rocess @ A] :
( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
= ( F2 @ X2 ) ) ).
% process_term.simps(22)
thf(fact_26_process__term_Osimps_I20_J,axiom,
! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
= ( F4 @ X41 @ X42 ) ) ).
% process_term.simps(20)
thf(fact_27_process__term_Osimps_I19_J,axiom,
! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
= ( F3 @ X31 @ X32 ) ) ).
% process_term.simps(19)
thf(fact_28_process__term_Osimps_I18_J,axiom,
! [Pvar: $tType,B: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X2: proces634752977rocess @ A] :
( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
= ( F2 @ X2 ) ) ).
% process_term.simps(18)
thf(fact_29_process__term_Odistinct_I11_J,axiom,
! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
!= ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% process_term.distinct(11)
thf(fact_30_process__term_Odistinct_I9_J,axiom,
! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
!= ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% process_term.distinct(9)
thf(fact_31_process__term_Odistinct_I7_J,axiom,
! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
!= ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% process_term.distinct(7)
thf(fact_32_process__term_Oset__cases_I2_J,axiom,
! [Pvar: $tType,A: $tType,E: Pvar,A2: proces554692349s_term @ A @ Pvar] :
( ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
=> ( ( A2
!= ( proces1627516585ss_VAR @ Pvar @ A @ E ) )
=> ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
=> ( ! [Z1: proces554692349s_term @ A @ Pvar] :
( ? [Z2: proces554692349s_term @ A @ Pvar] :
( A2
= ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
=> ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ Pvar @ E @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% process_term.set_cases(2)
thf(fact_33_process__term_Orel__inject_I4_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
= ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X41 @ Y41 )
& ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X42 @ Y42 ) ) ) ).
% process_term.rel_inject(4)
thf(fact_34_process__term_Orel__inject_I3_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
= ( ( R1 @ X31 @ Y31 )
& ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X32 @ Y32 ) ) ) ).
% process_term.rel_inject(3)
thf(fact_35_process__term_Orel__intros_I4_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,X42: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ B @ C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X41 @ Y41 )
=> ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X42 @ Y42 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% process_term.rel_intros(4)
thf(fact_36_process__term_Orel__intros_I3_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X31: A,Y31: B,R2: Pvar > C > $o,X32: proces554692349s_term @ A @ Pvar,Y32: proces554692349s_term @ B @ C] :
( ( R1 @ X31 @ Y31 )
=> ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X32 @ Y32 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% process_term.rel_intros(3)
thf(fact_37_process__term_Oset__intros_I9_J,axiom,
! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
=> ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% process_term.set_intros(9)
thf(fact_38_process__term_Oset__intros_I8_J,axiom,
! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
=> ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% process_term.set_intros(8)
thf(fact_39_process__term_Oset__intros_I7_J,axiom,
! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
=> ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% process_term.set_intros(7)
thf(fact_40_process__term_Orel__distinct_I12_J,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X31: C,X32: proces554692349s_term @ C @ D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% process_term.rel_distinct(12)
thf(fact_41_process__term_Orel__distinct_I11_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% process_term.rel_distinct(11)
thf(fact_42_process__term_Orel__distinct_I10_J,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% process_term.rel_distinct(10)
thf(fact_43_process__term_Orel__distinct_I9_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X2: proces634752977rocess @ A,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% process_term.rel_distinct(9)
thf(fact_44_process__term_Orel__distinct_I8_J,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% process_term.rel_distinct(8)
thf(fact_45_mem__Collect__eq,axiom,
! [A: $tType,A2: A,P: A > $o] :
( ( member @ A @ A2 @ ( collect @ A @ P ) )
= ( P @ A2 ) ) ).
% mem_Collect_eq
thf(fact_46_Collect__mem__eq,axiom,
! [A: $tType,A3: set @ A] :
( ( collect @ A
@ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_47_Collect__cong,axiom,
! [A: $tType,P: A > $o,Q: A > $o] :
( ! [X5: A] :
( ( P @ X5 )
= ( Q @ X5 ) )
=> ( ( collect @ A @ P )
= ( collect @ A @ Q ) ) ) ).
% Collect_cong
thf(fact_48_ext,axiom,
! [B: $tType,A: $tType,F: A > B,G: A > B] :
( ! [X5: A] :
( ( F @ X5 )
= ( G @ X5 ) )
=> ( F = G ) ) ).
% ext
thf(fact_49_process__term_Orel__distinct_I7_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X2: proces634752977rocess @ A,Y31: B,Y32: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% process_term.rel_distinct(7)
thf(fact_50_CH2_Oinduct,axiom,
! [A: $tType,B: $tType,P: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X6: A] : ( P @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P3: proces634752977rocess @ B] : ( P @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : ( P @ Sys3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T22 ) )
=> ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( P @ A0 @ A1 ) ) ) ) ) ).
% CH2.induct
thf(fact_51_CONT_Oinduct,axiom,
! [A: $tType,B: $tType,P: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X6: A] : ( P @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P3: proces634752977rocess @ B] : ( P @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] : ( P @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( P @ A0 @ A1 ) ) ) ) ) ).
% CONT.induct
thf(fact_52_PREF_Oinduct,axiom,
! [C: $tType,A: $tType,B: $tType,P: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ B @ A] :
( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X6: A] : ( P @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P3: proces634752977rocess @ B] : ( P @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] : ( P @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( P @ A0 @ A1 ) ) ) ) ) ).
% PREF.induct
thf(fact_53_isACT_Oinduct,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,P: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ D @ A] :
( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X6: A] : ( P @ Sys3 @ ( proces1627516585ss_VAR @ A @ D @ X6 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P3: proces634752977rocess @ D] : ( P @ Sys3 @ ( proces1062592052s_PROC @ D @ A @ P3 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] : ( P @ Sys3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] : ( P @ Sys3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T22 ) )
=> ( P @ A0 @ A1 ) ) ) ) ) ).
% isACT.induct
thf(fact_54_process__term_Oinduct,axiom,
! [Pvar: $tType,A: $tType,P: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
( ! [X5: Pvar] : ( P @ ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
=> ( ! [X5: proces634752977rocess @ A] : ( P @ ( proces1062592052s_PROC @ A @ Pvar @ X5 ) )
=> ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
( ( P @ X2a )
=> ( P @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
=> ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
( ( P @ X1a )
=> ( ( P @ X2a )
=> ( P @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
=> ( P @ Process_term ) ) ) ) ) ).
% process_term.induct
thf(fact_55_process__term_Oexhaust,axiom,
! [Pvar: $tType,A: $tType,Y3: proces554692349s_term @ A @ Pvar] :
( ! [X12: Pvar] :
( Y3
!= ( proces1627516585ss_VAR @ Pvar @ A @ X12 ) )
=> ( ! [X22: proces634752977rocess @ A] :
( Y3
!= ( proces1062592052s_PROC @ A @ Pvar @ X22 ) )
=> ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
( Y3
!= ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
=> ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
( Y3
!= ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% process_term.exhaust
thf(fact_56_process__term_Orel__eq,axiom,
! [B: $tType,A: $tType] :
( ( proces2029722208s_term @ A @ A @ B @ B
@ ^ [Y4: A,Z: A] : Y4 = Z
@ ^ [Y4: B,Z: B] : Y4 = Z )
= ( ^ [Y4: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : Y4 = Z ) ) ).
% process_term.rel_eq
thf(fact_57_process__term_Orel__refl,axiom,
! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X7: proces554692349s_term @ C @ D] :
( ! [X5: C] : ( R1a @ X5 @ X5 )
=> ( ! [X5: D] : ( R2a @ X5 @ X5 )
=> ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X7 @ X7 ) ) ) ).
% process_term.rel_refl
thf(fact_58_process__term_Orel__distinct_I1_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X1: Pvar,Y2: proces634752977rocess @ B] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% process_term.rel_distinct(1)
thf(fact_59_process__term_Orel__distinct_I2_J,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,Y2: proces634752977rocess @ A,X1: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% process_term.rel_distinct(2)
thf(fact_60_process__term_Orel__distinct_I5_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X1: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% process_term.rel_distinct(5)
thf(fact_61_process__term_Orel__distinct_I6_J,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X1: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% process_term.rel_distinct(6)
thf(fact_62_process__term_Orel__distinct_I3_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X1: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% process_term.rel_distinct(3)
thf(fact_63_process__term_Orel__distinct_I4_J,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R2: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X1: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% process_term.rel_distinct(4)
thf(fact_64_process__term_Orel__cases,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,A2: proces554692349s_term @ A @ Pvar,B2: proces554692349s_term @ B @ C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ A2 @ B2 )
=> ( ! [X5: Pvar] :
( ( A2
= ( proces1627516585ss_VAR @ Pvar @ A @ X5 ) )
=> ! [Y5: C] :
( ( B2
= ( proces1627516585ss_VAR @ C @ B @ Y5 ) )
=> ~ ( R2 @ X5 @ Y5 ) ) )
=> ( ! [Xa: proces634752977rocess @ A] :
( ( A2
= ( proces1062592052s_PROC @ A @ Pvar @ Xa ) )
=> ! [Ya: proces634752977rocess @ B] :
( ( B2
= ( proces1062592052s_PROC @ B @ C @ Ya ) )
=> ~ ( proces749077512rocess @ A @ B @ R1 @ Xa @ Ya ) ) )
=> ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
=> ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
( ( B2
= ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
=> ( ( R1 @ X1a @ Y1a )
=> ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X2a @ Y2a ) ) ) )
=> ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
=> ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
( ( B2
= ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
=> ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X1b @ Y1b )
=> ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% process_term.rel_cases
thf(fact_65_process__term_Orel__induct,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X7: proces554692349s_term @ A @ Pvar,Y3: proces554692349s_term @ B @ C,Q: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ X7 @ Y3 )
=> ( ! [A12: Pvar,B1: C] :
( ( R2 @ A12 @ B1 )
=> ( Q @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
=> ( ! [A22: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R1 @ A22 @ B22 )
=> ( Q @ ( proces1062592052s_PROC @ A @ Pvar @ A22 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
=> ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
( ( R1 @ A31 @ B31 )
=> ( ( Q @ A32 @ B32 )
=> ( Q @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
=> ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
( ( Q @ A41 @ B41 )
=> ( ( Q @ A42 @ B42 )
=> ( Q @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
=> ( Q @ X7 @ Y3 ) ) ) ) ) ) ).
% process_term.rel_induct
thf(fact_66_CH2_Ocases,axiom,
! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X6: A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P3: proces634752977rocess @ B] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P3 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T22 ) ) )
=> ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% CH2.cases
thf(fact_67_CONT_Ocases,axiom,
! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X6: A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P3: proces634752977rocess @ B] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P3 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
=> ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% CONT.cases
thf(fact_68_PREF_Ocases,axiom,
! [C: $tType,A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X6: A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P3: proces634752977rocess @ B] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P3 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) )
=> ~ ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% PREF.cases
thf(fact_69_isACT_Ocases,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X6: A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ D @ X6 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P3: proces634752977rocess @ D] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1062592052s_PROC @ D @ A @ P3 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) )
=> ~ ! [Sys3: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T22 ) ) ) ) ) ) ).
% isACT.cases
thf(fact_70_process__term_Opred__inject_I2_J,axiom,
! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces634752977rocess @ A] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1062592052s_PROC @ A @ Pvar @ A2 ) )
= ( proces1205983068rocess @ A @ P1 @ A2 ) ) ).
% process_term.pred_inject(2)
thf(fact_71_solution__VAR,axiom,
! [B: $tType,A: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces1121166967uarded @ A @ B @ A @ Sys2 )
=> ( ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces1652378886lution @ A @ B @ Sys2 @ ( Sys2 @ X3 ) ) ) ) ).
% solution_VAR
thf(fact_72_process__term_Opred__cong,axiom,
! [B: $tType,A: $tType,X7: proces554692349s_term @ A @ B,Ya2: proces554692349s_term @ A @ B,P1: A > $o,P1a: A > $o,P2: B > $o,P2a: B > $o] :
( ( X7 = Ya2 )
=> ( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya2 ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya2 ) )
=> ( ( P2 @ Z2 )
= ( P2a @ Z2 ) ) )
=> ( ( proces2118920028s_term @ A @ B @ P1 @ P2 @ X7 )
= ( proces2118920028s_term @ A @ B @ P1a @ P2a @ Ya2 ) ) ) ) ) ).
% process_term.pred_cong
thf(fact_73_process__term_Opred__mono__strong,axiom,
! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,X7: proces554692349s_term @ A @ B,P1a: A > $o,P2a: B > $o] :
( ( proces2118920028s_term @ A @ B @ P1 @ P2 @ X7 )
=> ( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X7 ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X7 ) )
=> ( ( P2 @ Z2 )
=> ( P2a @ Z2 ) ) )
=> ( proces2118920028s_term @ A @ B @ P1a @ P2a @ X7 ) ) ) ) ).
% process_term.pred_mono_strong
thf(fact_74_process__term_Omap__cong,axiom,
! [D: $tType,C: $tType,B: $tType,A: $tType,X7: proces554692349s_term @ A @ B,Ya2: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
( ( X7 = Ya2 )
=> ( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya2 ) )
=> ( ( F1 @ Z1 )
= ( G1 @ Z1 ) ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya2 ) )
=> ( ( F2 @ Z2 )
= ( G2 @ Z2 ) ) )
=> ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X7 )
= ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ Ya2 ) ) ) ) ) ).
% process_term.map_cong
thf(fact_75_solution__PROC,axiom,
! [B: $tType,A: $tType,Sys2: B > ( proces554692349s_term @ A @ B ),P4: proces634752977rocess @ A] :
( ( proces1652378886lution @ B @ A @ Sys2 @ ( proces1062592052s_PROC @ A @ B @ P4 ) )
= P4 ) ).
% solution_PROC
thf(fact_76_process_Orel__refl,axiom,
! [B: $tType,Ra: B > B > $o,X7: proces634752977rocess @ B] :
( ! [X5: B] : ( Ra @ X5 @ X5 )
=> ( proces749077512rocess @ B @ B @ Ra @ X7 @ X7 ) ) ).
% process.rel_refl
thf(fact_77_process_Orel__eq,axiom,
! [A: $tType] :
( ( proces749077512rocess @ A @ A
@ ^ [Y4: A,Z: A] : Y4 = Z )
= ( ^ [Y4: proces634752977rocess @ A,Z: proces634752977rocess @ A] : Y4 = Z ) ) ).
% process.rel_eq
thf(fact_78_process__term_Oset__intros_I2_J,axiom,
! [Pvar: $tType,A: $tType,A1: A,A23: proces554692349s_term @ A @ Pvar] : ( member @ A @ A1 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1 @ A23 ) ) ) ).
% process_term.set_intros(2)
thf(fact_79_process__term_Oset__intros_I3_J,axiom,
! [Pvar: $tType,A: $tType,Xa2: A,A23: proces554692349s_term @ A @ Pvar,A1: A] :
( ( member @ A @ Xa2 @ ( proces1264666542s_term @ A @ Pvar @ A23 ) )
=> ( member @ A @ Xa2 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1 @ A23 ) ) ) ) ).
% process_term.set_intros(3)
thf(fact_80_process__term_Oset__intros_I4_J,axiom,
! [Pvar: $tType,A: $tType,Xc: A,A1a: proces554692349s_term @ A @ Pvar,A2a: proces554692349s_term @ A @ Pvar] :
( ( member @ A @ Xc @ ( proces1264666542s_term @ A @ Pvar @ A1a ) )
=> ( member @ A @ Xc @ ( proces1264666542s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1a @ A2a ) ) ) ) ).
% process_term.set_intros(4)
thf(fact_81_process__term_Oset__intros_I5_J,axiom,
! [Pvar: $tType,A: $tType,Xe: A,A2a: proces554692349s_term @ A @ Pvar,A1a: proces554692349s_term @ A @ Pvar] :
( ( member @ A @ Xe @ ( proces1264666542s_term @ A @ Pvar @ A2a ) )
=> ( member @ A @ Xe @ ( proces1264666542s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1a @ A2a ) ) ) ) ).
% process_term.set_intros(5)
thf(fact_82_process__term_Orel__intros_I2_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R2: Pvar > C > $o] :
( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% process_term.rel_intros(2)
thf(fact_83_process__term_Orel__inject_I2_J,axiom,
! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
= ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% process_term.rel_inject(2)
thf(fact_84_process__term_Orel__refl__strong,axiom,
! [B: $tType,A: $tType,X7: proces554692349s_term @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X7 ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X7 ) )
=> ( R2a @ Z2 @ Z2 ) )
=> ( proces2029722208s_term @ A @ A @ B @ B @ R1a @ R2a @ X7 @ X7 ) ) ) ).
% process_term.rel_refl_strong
thf(fact_85_process__term_Orel__mono__strong,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X7: proces554692349s_term @ A @ B,Y3: proces554692349s_term @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
( ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 @ X7 @ Y3 )
=> ( ! [Z1: A,Y12: C] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X7 ) )
=> ( ( member @ C @ Y12 @ ( proces1264666542s_term @ C @ D @ Y3 ) )
=> ( ( R1 @ Z1 @ Y12 )
=> ( R1a @ Z1 @ Y12 ) ) ) )
=> ( ! [Z2: B,Y22: D] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X7 ) )
=> ( ( member @ D @ Y22 @ ( proces1493547885s_term @ C @ D @ Y3 ) )
=> ( ( R2 @ Z2 @ Y22 )
=> ( R2a @ Z2 @ Y22 ) ) ) )
=> ( proces2029722208s_term @ A @ C @ B @ D @ R1a @ R2a @ X7 @ Y3 ) ) ) ) ).
% process_term.rel_mono_strong
thf(fact_86_process__term_Orel__cong,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,X7: proces554692349s_term @ A @ B,Ya2: proces554692349s_term @ A @ B,Y3: proces554692349s_term @ C @ D,Xa2: proces554692349s_term @ C @ D,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
( ( X7 = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z1: A,Y12: C] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya2 ) )
=> ( ( member @ C @ Y12 @ ( proces1264666542s_term @ C @ D @ Xa2 ) )
=> ( ( R1 @ Z1 @ Y12 )
= ( R1a @ Z1 @ Y12 ) ) ) )
=> ( ! [Z2: B,Y22: D] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya2 ) )
=> ( ( member @ D @ Y22 @ ( proces1493547885s_term @ C @ D @ Xa2 ) )
=> ( ( R2 @ Z2 @ Y22 )
= ( R2a @ Z2 @ Y22 ) ) ) )
=> ( ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 @ X7 @ Y3 )
= ( proces2029722208s_term @ A @ C @ B @ D @ R1a @ R2a @ Ya2 @ Xa2 ) ) ) ) ) ) ).
% process_term.rel_cong
thf(fact_87_process__term_Oinj__map__strong,axiom,
! [C: $tType,D: $tType,B: $tType,A: $tType,X7: proces554692349s_term @ A @ B,Xa2: proces554692349s_term @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
( ! [Z1: A,Z1a: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X7 ) )
=> ( ( member @ A @ Z1a @ ( proces1264666542s_term @ A @ B @ Xa2 ) )
=> ( ( ( F1 @ Z1 )
= ( F1a @ Z1a ) )
=> ( Z1 = Z1a ) ) ) )
=> ( ! [Z2: B,Z2a: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X7 ) )
=> ( ( member @ B @ Z2a @ ( proces1493547885s_term @ A @ B @ Xa2 ) )
=> ( ( ( F2 @ Z2 )
= ( F2a @ Z2a ) )
=> ( Z2 = Z2a ) ) ) )
=> ( ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X7 )
= ( proces224683037s_term @ A @ C @ B @ D @ F1a @ F2a @ Xa2 ) )
=> ( X7 = Xa2 ) ) ) ) ).
% process_term.inj_map_strong
thf(fact_88_process__term_Omap__cong0,axiom,
! [D: $tType,C: $tType,B: $tType,A: $tType,X7: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X7 ) )
=> ( ( F1 @ Z1 )
= ( G1 @ Z1 ) ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X7 ) )
=> ( ( F2 @ Z2 )
= ( G2 @ Z2 ) ) )
=> ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X7 )
= ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ X7 ) ) ) ) ).
% process_term.map_cong0
thf(fact_89_old_Oprod_Oinject,axiom,
! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
( ( ( product_Pair @ A @ B @ A2 @ B2 )
= ( product_Pair @ A @ B @ A5 @ B3 ) )
= ( ( A2 = A5 )
& ( B2 = B3 ) ) ) ).
% old.prod.inject
thf(fact_90_prod_Oinject,axiom,
! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
( ( ( product_Pair @ A @ B @ X1 @ X2 )
= ( product_Pair @ A @ B @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_91_process__term_Oset__cases_I1_J,axiom,
! [Pvar: $tType,A: $tType,E: A,A2: proces554692349s_term @ A @ Pvar] :
( ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ A2 ) )
=> ( ! [Z3: proces634752977rocess @ A] :
( ( A2
= ( proces1062592052s_PROC @ A @ Pvar @ Z3 ) )
=> ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z3 ) ) )
=> ( ! [Z2: proces554692349s_term @ A @ Pvar] :
( A2
!= ( proces1454156180ss_ACT @ A @ Pvar @ E @ Z2 ) )
=> ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z2 ) ) )
=> ( ! [Z1: proces554692349s_term @ A @ Pvar] :
( ? [Z2: proces554692349s_term @ A @ Pvar] :
( A2
= ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z1 ) ) )
=> ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ A @ E @ ( proces1264666542s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ) ).
% process_term.set_cases(1)
thf(fact_92_solution_Odisc__iff_I2_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ T3 ) )
= ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 ) ) ) ).
% solution.disc_iff(2)
thf(fact_93_process__term_Opred__set,axiom,
! [B: $tType,A: $tType] :
( ( proces2118920028s_term @ A @ B )
= ( ^ [P12: A > $o,P22: B > $o,X4: proces554692349s_term @ A @ B] :
( ! [Y6: A] :
( ( member @ A @ Y6 @ ( proces1264666542s_term @ A @ B @ X4 ) )
=> ( P12 @ Y6 ) )
& ! [Y6: B] :
( ( member @ B @ Y6 @ ( proces1493547885s_term @ A @ B @ X4 ) )
=> ( P22 @ Y6 ) ) ) ) ) ).
% process_term.pred_set
thf(fact_94_solution__CH,axiom,
! [B: $tType,A: $tType,Sys2: B > ( proces554692349s_term @ A @ B ),T1: proces554692349s_term @ A @ B,T2: proces554692349s_term @ A @ B] :
( ( proces1652378886lution @ B @ A @ Sys2 @ ( proces89589571ess_CH @ A @ B @ T1 @ T2 ) )
= ( proces1915862579Choice @ A @ ( proces1652378886lution @ B @ A @ Sys2 @ T1 ) @ ( proces1652378886lution @ B @ A @ Sys2 @ T2 ) ) ) ).
% solution_CH
thf(fact_95_process_Oinject_I2_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y222: proces634752977rocess @ A] :
( ( ( proces1915862579Choice @ A @ X21 @ X222 )
= ( proces1915862579Choice @ A @ Y21 @ Y222 ) )
= ( ( X21 = Y21 )
& ( X222 = Y222 ) ) ) ).
% process.inject(2)
thf(fact_96_process_Orel__inject_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y222: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X222 ) @ ( proces1915862579Choice @ B @ Y21 @ Y222 ) )
= ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
& ( proces749077512rocess @ A @ B @ R @ X222 @ Y222 ) ) ) ).
% process.rel_inject(2)
thf(fact_97_process_Opred__inject_I2_J,axiom,
! [A: $tType,P: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
( ( proces1205983068rocess @ A @ P @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
= ( ( proces1205983068rocess @ A @ P @ A2 )
& ( proces1205983068rocess @ A @ P @ Aa2 ) ) ) ).
% process.pred_inject(2)
thf(fact_98_process_Opred__set,axiom,
! [A: $tType] :
( ( proces1205983068rocess @ A )
= ( ^ [P5: A > $o,X4: proces634752977rocess @ A] :
! [Y6: A] :
( ( member @ A @ Y6 @ ( proces1148692671rocess @ A @ X4 ) )
=> ( P5 @ Y6 ) ) ) ) ).
% process.pred_set
thf(fact_99_process_Odisc_I4_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% process.disc(4)
thf(fact_100_process_OdiscI_I2_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
( ( Process
= ( proces1915862579Choice @ A @ X21 @ X222 ) )
=> ( proces401113213Choice @ A @ Process ) ) ).
% process.discI(2)
thf(fact_101_process_Oset__intros_I4_J,axiom,
! [A: $tType,Xb: A,A2a: proces634752977rocess @ A,A1a: proces634752977rocess @ A] :
( ( member @ A @ Xb @ ( proces1148692671rocess @ A @ A2a ) )
=> ( member @ A @ Xb @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% process.set_intros(4)
thf(fact_102_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 ) ) ) ) ).
% process.set_intros(3)
thf(fact_103_isChoice__def,axiom,
! [A: $tType] :
( ( proces401113213Choice @ A )
= ( ^ [Process2: proces634752977rocess @ A] :
? [X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
( Process2
= ( proces1915862579Choice @ A @ X212 @ X223 ) ) ) ) ).
% isChoice_def
thf(fact_104_process_Orel__intros_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X222: proces634752977rocess @ A,Y222: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
=> ( ( proces749077512rocess @ A @ B @ R @ X222 @ Y222 )
=> ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X222 ) @ ( proces1915862579Choice @ B @ Y21 @ Y222 ) ) ) ) ).
% process.rel_intros(2)
thf(fact_105_process_Orel__cong,axiom,
! [A: $tType,B: $tType,X7: proces634752977rocess @ A,Ya2: proces634752977rocess @ A,Y3: proces634752977rocess @ B,Xa2: proces634752977rocess @ B,R: A > B > $o,Ra: A > B > $o] :
( ( X7 = Ya2 )
=> ( ( Y3 = Xa2 )
=> ( ! [Z3: A,Yb: B] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ Ya2 ) )
=> ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( proces749077512rocess @ A @ B @ R @ X7 @ Y3 )
= ( proces749077512rocess @ A @ B @ Ra @ Ya2 @ Xa2 ) ) ) ) ) ).
% process.rel_cong
thf(fact_106_process_Orel__mono__strong,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B,Ra: A > B > $o] :
( ( proces749077512rocess @ A @ B @ R @ X7 @ Y3 )
=> ( ! [Z3: A,Yb: B] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X7 ) )
=> ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Y3 ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( proces749077512rocess @ A @ B @ Ra @ X7 @ Y3 ) ) ) ).
% process.rel_mono_strong
thf(fact_107_process_Orel__refl__strong,axiom,
! [A: $tType,X7: proces634752977rocess @ A,Ra: A > A > $o] :
( ! [Z3: A] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X7 ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( proces749077512rocess @ A @ A @ Ra @ X7 @ X7 ) ) ).
% process.rel_refl_strong
thf(fact_108_process_Opred__cong,axiom,
! [A: $tType,X7: proces634752977rocess @ A,Ya2: proces634752977rocess @ A,P: A > $o,Pa: A > $o] :
( ( X7 = Ya2 )
=> ( ! [Z3: A] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ Ya2 ) )
=> ( ( P @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( proces1205983068rocess @ A @ P @ X7 )
= ( proces1205983068rocess @ A @ Pa @ Ya2 ) ) ) ) ).
% process.pred_cong
thf(fact_109_process_Opred__mono__strong,axiom,
! [A: $tType,P: A > $o,X7: proces634752977rocess @ A,Pa: A > $o] :
( ( proces1205983068rocess @ A @ P @ X7 )
=> ( ! [Z3: A] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X7 ) )
=> ( ( P @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( proces1205983068rocess @ A @ Pa @ X7 ) ) ) ).
% process.pred_mono_strong
thf(fact_110_process__term_Osimps_I46_J,axiom,
! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A] :
( ( proces1264666542s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
= ( proces1148692671rocess @ A @ X2 ) ) ).
% process_term.simps(46)
thf(fact_111_process__term_Oset__intros_I1_J,axiom,
! [Pvar: $tType,A: $tType,X7: A,Aa2: proces634752977rocess @ A] :
( ( member @ A @ X7 @ ( proces1148692671rocess @ A @ Aa2 ) )
=> ( member @ A @ X7 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ Aa2 ) ) ) ) ).
% process_term.set_intros(1)
thf(fact_112_solution_Odisc_I2_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 )
=> ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ T3 ) ) ) ).
% solution.disc(2)
thf(fact_113_surj__pair,axiom,
! [A: $tType,B: $tType,P4: product_prod @ A @ B] :
? [X5: A,Y5: B] :
( P4
= ( product_Pair @ A @ B @ X5 @ Y5 ) ) ).
% surj_pair
thf(fact_114_prod__cases,axiom,
! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P4: product_prod @ A @ B] :
( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
=> ( P @ P4 ) ) ).
% prod_cases
thf(fact_115_Pair__inject,axiom,
! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
( ( ( product_Pair @ A @ B @ A2 @ B2 )
= ( product_Pair @ A @ B @ A5 @ B3 ) )
=> ~ ( ( A2 = A5 )
=> ( B2 != B3 ) ) ) ).
% Pair_inject
thf(fact_116_prod__cases3,axiom,
! [A: $tType,B: $tType,C: $tType,Y3: product_prod @ A @ ( product_prod @ B @ C )] :
~ ! [A4: A,B4: B,C2: C] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% prod_cases3
thf(fact_117_prod__cases4,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
~ ! [A4: A,B4: B,C2: C,D2: D] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% prod_cases4
thf(fact_118_prod__cases5,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) ) ).
% prod_cases5
thf(fact_119_prod__cases6,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F5: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) )] :
~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F5 ) @ D2 @ ( product_Pair @ E2 @ F5 @ E3 @ F6 ) ) ) ) ) ) ).
% prod_cases6
thf(fact_120_prod__cases7,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F5: $tType,G3: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
~ ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5,G4: G3] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F5 @ G3 ) @ E3 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) ) ).
% prod_cases7
thf(fact_121_prod__induct3,axiom,
! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ C )] :
( ! [A4: A,B4: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
=> ( P @ X7 ) ) ).
% prod_induct3
thf(fact_122_prod__induct4,axiom,
! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
( ! [A4: A,B4: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
=> ( P @ X7 ) ) ).
% prod_induct4
thf(fact_123_prod__induct5,axiom,
! [E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
( ! [A4: A,B4: B,C2: C,D2: D,E3: E2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) )
=> ( P @ X7 ) ) ).
% prod_induct5
thf(fact_124_prod__induct6,axiom,
! [F5: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) )] :
( ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F5 ) @ D2 @ ( product_Pair @ E2 @ F5 @ E3 @ F6 ) ) ) ) ) )
=> ( P @ X7 ) ) ).
% prod_induct6
thf(fact_125_prod__induct7,axiom,
! [G3: $tType,F5: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) ) )] :
( ! [A4: A,B4: B,C2: C,D2: D,E3: E2,F6: F5,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F5 @ G3 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F5 @ G3 ) @ E3 @ ( product_Pair @ F5 @ G3 @ F6 @ G4 ) ) ) ) ) ) )
=> ( P @ X7 ) ) ).
% prod_induct7
thf(fact_126_old_Oprod_Oexhaust,axiom,
! [A: $tType,B: $tType,Y3: product_prod @ A @ B] :
~ ! [A4: A,B4: B] :
( Y3
!= ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% old.prod.exhaust
thf(fact_127_old_Oprod_Oinducts,axiom,
! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_128_old_Oprod_Orec,axiom,
! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
= ( F1 @ A2 @ B2 ) ) ).
% old.prod.rec
thf(fact_129_internal__case__prod__conv,axiom,
! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
= ( C3 @ A2 @ B2 ) ) ).
% internal_case_prod_conv
thf(fact_130_Ball__def,axiom,
! [A: $tType] :
( ( ball @ A )
= ( ^ [A6: set @ A,P5: A > $o] :
! [X4: A] :
( ( member @ A @ X4 @ A6 )
=> ( P5 @ X4 ) ) ) ) ).
% Ball_def
thf(fact_131_ball__reg,axiom,
! [A: $tType,R: set @ A,P: A > $o,Q: A > $o] :
( ! [X5: A] :
( ( member @ A @ X5 @ R )
=> ( ( P @ X5 )
=> ( Q @ X5 ) ) )
=> ( ! [X5: A] :
( ( member @ A @ X5 @ R )
=> ( P @ X5 ) )
=> ! [X8: A] :
( ( member @ A @ X8 @ R )
=> ( Q @ X8 ) ) ) ) ).
% ball_reg
thf(fact_132_solution_Octr_I2_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 )
=> ( ( proces1652378886lution @ A @ B @ Sys2 @ T3 )
= ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1239275103le_CH1 @ A @ B @ Sys2 @ T3 ) ) @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1239275104le_CH2 @ A @ B @ Sys2 @ T3 ) ) ) ) ) ).
% solution.ctr(2)
thf(fact_133_CH2_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T2: proces554692349s_term @ B @ A] :
( ( proces1239275104le_CH2 @ A @ B @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T1 @ T2 ) )
= T2 ) ).
% CH2.simps(3)
thf(fact_134_CH1_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T2: proces554692349s_term @ B @ A] :
( ( proces1239275103le_CH1 @ A @ B @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T1 @ T2 ) )
= T1 ) ).
% CH1.simps(3)
thf(fact_135_solution_Osimps_I5_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 )
=> ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ T3 ) )
= ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1239275103le_CH1 @ A @ B @ Sys2 @ T3 ) ) ) ) ).
% solution.simps(5)
thf(fact_136_solution_Osimps_I6_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 )
=> ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ T3 ) )
= ( proces1652378886lution @ A @ B @ Sys2 @ ( proces1239275104le_CH2 @ A @ B @ Sys2 @ T3 ) ) ) ) ).
% solution.simps(6)
thf(fact_137_solution__ACT,axiom,
! [B: $tType,A: $tType,Sys2: B > ( proces554692349s_term @ A @ B ),A2: A,T3: proces554692349s_term @ A @ B] :
( ( proces1652378886lution @ B @ A @ Sys2 @ ( proces1454156180ss_ACT @ A @ B @ A2 @ T3 ) )
= ( proces1525233512Action @ A @ A2 @ ( proces1652378886lution @ B @ A @ Sys2 @ T3 ) ) ) ).
% solution_ACT
thf(fact_138_CH1_Osimps_I2_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
( ( proces1239275103le_CH1 @ A @ B @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
= ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) ) ).
% CH1.simps(2)
thf(fact_139_process_Oinject_I1_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A,Y11: A,Y122: proces634752977rocess @ A] :
( ( ( proces1525233512Action @ A @ X11 @ X122 )
= ( proces1525233512Action @ A @ Y11 @ Y122 ) )
= ( ( X11 = Y11 )
& ( X122 = Y122 ) ) ) ).
% process.inject(1)
thf(fact_140_process_Orel__inject_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y11: B,Y122: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y122 ) )
= ( ( R @ X11 @ Y11 )
& ( proces749077512rocess @ A @ B @ R @ X122 @ Y122 ) ) ) ).
% process.rel_inject(1)
thf(fact_141_process_Opred__inject_I1_J,axiom,
! [A: $tType,P: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
( ( proces1205983068rocess @ A @ P @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
= ( ( P @ A2 )
& ( proces1205983068rocess @ A @ P @ Aa2 ) ) ) ).
% process.pred_inject(1)
thf(fact_142_process_Ocollapse_I2_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ( proces401113213Choice @ A @ Process )
=> ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
= Process ) ) ).
% process.collapse(2)
thf(fact_143_process_Orel__intros_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X122: proces634752977rocess @ A,Y122: proces634752977rocess @ B] :
( ( R @ X11 @ Y11 )
=> ( ( proces749077512rocess @ A @ B @ R @ X122 @ Y122 )
=> ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y122 ) ) ) ) ).
% process.rel_intros(1)
thf(fact_144_process_Oexhaust,axiom,
! [A: $tType,Y3: proces634752977rocess @ A] :
( ! [X112: A,X123: proces634752977rocess @ A] :
( Y3
!= ( proces1525233512Action @ A @ X112 @ X123 ) )
=> ~ ! [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] :
( Y3
!= ( proces1915862579Choice @ A @ X213 @ X224 ) ) ) ).
% process.exhaust
thf(fact_145_process_Odistinct_I1_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
( ( proces1525233512Action @ A @ X11 @ X122 )
!= ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% process.distinct(1)
thf(fact_146_process_Oset__intros_I1_J,axiom,
! [A: $tType,A1: A,A23: proces634752977rocess @ A] : ( member @ A @ A1 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A23 ) ) ) ).
% process.set_intros(1)
thf(fact_147_process_Oset__intros_I2_J,axiom,
! [A: $tType,X7: A,A23: proces634752977rocess @ A,A1: A] :
( ( member @ A @ X7 @ ( proces1148692671rocess @ A @ A23 ) )
=> ( member @ A @ X7 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A23 ) ) ) ) ).
% process.set_intros(2)
thf(fact_148_process_Odisc_I3_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% process.disc(3)
thf(fact_149_process_Osel_I4_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
= X222 ) ).
% process.sel(4)
thf(fact_150_process_Osel_I3_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
= X21 ) ).
% process.sel(3)
thf(fact_151_process_Orel__cases,axiom,
! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ A2 @ B2 )
=> ( ! [X12: A,X22: proces634752977rocess @ A] :
( ( A2
= ( proces1525233512Action @ A @ X12 @ X22 ) )
=> ! [Y12: B,Y22: proces634752977rocess @ B] :
( ( B2
= ( proces1525233512Action @ B @ Y12 @ Y22 ) )
=> ( ( R @ X12 @ Y12 )
=> ~ ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 ) ) ) )
=> ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
( ( A2
= ( proces1915862579Choice @ A @ X1a @ X2a ) )
=> ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
( ( B2
= ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
=> ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
=> ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% process.rel_cases
thf(fact_152_process_Orel__distinct_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y222: proces634752977rocess @ B] :
~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1915862579Choice @ B @ Y21 @ Y222 ) ) ).
% process.rel_distinct(1)
thf(fact_153_process_Orel__distinct_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y222: proces634752977rocess @ A,X11: B,X122: proces634752977rocess @ B] :
~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y222 ) @ ( proces1525233512Action @ B @ X11 @ X122 ) ) ).
% process.rel_distinct(2)
thf(fact_154_process_Oset__cases,axiom,
! [A: $tType,E: A,A2: proces634752977rocess @ A] :
( ( member @ A @ E @ ( proces1148692671rocess @ A @ A2 ) )
=> ( ! [Z2: proces634752977rocess @ A] :
( A2
!= ( proces1525233512Action @ A @ E @ Z2 ) )
=> ( ! [Z1: A,Z2: proces634752977rocess @ A] :
( ( A2
= ( proces1525233512Action @ A @ Z1 @ Z2 ) )
=> ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z2 ) ) )
=> ( ! [Z1: proces634752977rocess @ A] :
( ? [Z2: proces634752977rocess @ A] :
( A2
= ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
=> ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z1 ) ) )
=> ~ ! [Z1: proces634752977rocess @ A,Z2: proces634752977rocess @ A] :
( ( A2
= ( proces1915862579Choice @ A @ Z1 @ Z2 ) )
=> ~ ( member @ A @ E @ ( proces1148692671rocess @ A @ Z2 ) ) ) ) ) ) ) ).
% process.set_cases
thf(fact_155_process_Oset__induct,axiom,
! [A: $tType,X7: A,A2: proces634752977rocess @ A,P: A > ( proces634752977rocess @ A ) > $o] :
( ( member @ A @ X7 @ ( proces1148692671rocess @ A @ A2 ) )
=> ( ! [Z1: A,Z2: proces634752977rocess @ A] : ( P @ Z1 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) )
=> ( ! [Z1: A,Z2: proces634752977rocess @ A,Xa: A] :
( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ Z2 ) )
=> ( ( P @ Xa @ Z2 )
=> ( P @ Xa @ ( proces1525233512Action @ A @ Z1 @ Z2 ) ) ) )
=> ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xb2: A] :
( ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ Z1a ) )
=> ( ( P @ Xb2 @ Z1a )
=> ( P @ Xb2 @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
=> ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xc2: A] :
( ( member @ A @ Xc2 @ ( proces1148692671rocess @ A @ Z2a ) )
=> ( ( P @ Xc2 @ Z2a )
=> ( P @ Xc2 @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
=> ( P @ X7 @ A2 ) ) ) ) ) ) ).
% process.set_induct
thf(fact_156_process_Oset__sel_I4_J,axiom,
! [A: $tType,A2: proces634752977rocess @ A,Xb: A] :
( ( proces401113213Choice @ A @ A2 )
=> ( ( member @ A @ Xb @ ( proces1148692671rocess @ A @ ( proces988026546_ch2Of @ A @ A2 ) ) )
=> ( member @ A @ Xb @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% process.set_sel(4)
thf(fact_157_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 ) ) ) ) ).
% process.set_sel(3)
thf(fact_158_CH2_Osimps_I2_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
( ( proces1239275104le_CH2 @ A @ B @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
= ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) ) ).
% CH2.simps(2)
thf(fact_159_solution_Ocode,axiom,
! [B: $tType,A: $tType] :
( ( proces1652378886lution @ A @ B )
= ( ^ [Sys: A > ( proces554692349s_term @ B @ A ),T5: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T5 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T5 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T5 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T5 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T5 ) ) ) ) ) ) ).
% solution.code
thf(fact_160_process__strong__coind,axiom,
! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
( ( Phi @ P4 @ P6 )
=> ( ! [P3: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
( ( Phi @ P3 @ P7 )
=> ( ( ( proces10484146Action @ A @ P3 )
= ( proces10484146Action @ A @ P7 ) )
& ( ( proces401113213Choice @ A @ P3 )
= ( proces401113213Choice @ A @ P7 ) ) ) )
=> ( ! [A4: A,A7: A,P3: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
( ( Phi @ ( proces1525233512Action @ A @ A4 @ P3 ) @ ( proces1525233512Action @ A @ A7 @ P7 ) )
=> ( ( A4 = A7 )
& ( ( Phi @ P3 @ P7 )
| ( P3 = P7 ) ) ) )
=> ( ! [P3: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P7: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
( ( Phi @ ( proces1915862579Choice @ A @ P3 @ Q2 ) @ ( proces1915862579Choice @ A @ P7 @ Q3 ) )
=> ( ( ( Phi @ P3 @ P7 )
| ( P3 = P7 ) )
& ( ( Phi @ Q2 @ Q3 )
| ( Q2 = Q3 ) ) ) )
=> ( P4 = P6 ) ) ) ) ) ).
% process_strong_coind
thf(fact_161_process__coind,axiom,
! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P4: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
( ( Phi @ P4 @ P6 )
=> ( ! [P3: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
( ( Phi @ P3 @ P7 )
=> ( ( ( proces10484146Action @ A @ P3 )
= ( proces10484146Action @ A @ P7 ) )
& ( ( proces401113213Choice @ A @ P3 )
= ( proces401113213Choice @ A @ P7 ) ) ) )
=> ( ! [A4: A,A7: A,P3: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
( ( Phi @ ( proces1525233512Action @ A @ A4 @ P3 ) @ ( proces1525233512Action @ A @ A7 @ P7 ) )
=> ( ( A4 = A7 )
& ( Phi @ P3 @ P7 ) ) )
=> ( ! [P3: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P7: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
( ( Phi @ ( proces1915862579Choice @ A @ P3 @ Q2 ) @ ( proces1915862579Choice @ A @ P7 @ Q3 ) )
=> ( ( Phi @ P3 @ P7 )
& ( Phi @ Q2 @ Q3 ) ) )
=> ( P4 = P6 ) ) ) ) ) ).
% process_coind
thf(fact_162_solution_Octr_I1_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 )
=> ( ( proces1652378886lution @ A @ B @ Sys2 @ T3 )
= ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys2 @ T3 ) @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces126235999e_CONT @ A @ B @ Sys2 @ T3 ) ) ) ) ) ).
% solution.ctr(1)
thf(fact_163_solution_Odisc__iff_I1_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ T3 ) )
= ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 ) ) ).
% solution.disc_iff(1)
thf(fact_164_process_Odisc_I1_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% process.disc(1)
thf(fact_165_process_OdiscI_I1_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A,X11: A,X122: proces634752977rocess @ A] :
( ( Process
= ( proces1525233512Action @ A @ X11 @ X122 ) )
=> ( proces10484146Action @ A @ Process ) ) ).
% process.discI(1)
thf(fact_166_isAction__def,axiom,
! [A: $tType] :
( ( proces10484146Action @ A )
= ( ^ [Process2: proces634752977rocess @ A] :
? [X113: A,X124: proces634752977rocess @ A] :
( Process2
= ( proces1525233512Action @ A @ X113 @ X124 ) ) ) ) ).
% isAction_def
thf(fact_167_process_Odistinct__disc_I2_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ( proces401113213Choice @ A @ Process )
=> ~ ( proces10484146Action @ A @ Process ) ) ).
% process.distinct_disc(2)
thf(fact_168_process_Odistinct__disc_I1_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ( proces10484146Action @ A @ Process )
=> ~ ( proces401113213Choice @ A @ Process ) ) ).
% process.distinct_disc(1)
thf(fact_169_isAction__isChoice,axiom,
! [A: $tType,P4: proces634752977rocess @ A] :
( ( proces10484146Action @ A @ P4 )
| ( proces401113213Choice @ A @ P4 ) ) ).
% isAction_isChoice
thf(fact_170_process_Oexhaust__disc,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ~ ( proces10484146Action @ A @ Process )
=> ( proces401113213Choice @ A @ Process ) ) ).
% process.exhaust_disc
thf(fact_171_not__isAction__isChoice,axiom,
! [A: $tType,P4: proces634752977rocess @ A] :
~ ( ( proces10484146Action @ A @ P4 )
& ( proces401113213Choice @ A @ P4 ) ) ).
% not_isAction_isChoice
thf(fact_172_process_Odisc_I2_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X21 @ X222 ) ) ).
% process.disc(2)
thf(fact_173_PREF_Osimps_I3_J,axiom,
! [A: $tType,C: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ C ),A2: B,T3: proces554692349s_term @ B @ A] :
( ( proces1708129104e_PREF @ A @ B @ C @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T3 ) )
= A2 ) ).
% PREF.simps(3)
thf(fact_174_CONT_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),A2: B,T3: proces554692349s_term @ B @ A] :
( ( proces126235999e_CONT @ A @ B @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T3 ) )
= T3 ) ).
% CONT.simps(3)
thf(fact_175_isACT_Osimps_I2_J,axiom,
! [A: $tType,C: $tType,B: $tType,D: $tType,Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
( ( proces687458811_isACT @ A @ B @ C @ D @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
= ( proces10484146Action @ D @ P4 ) ) ).
% isACT.simps(2)
thf(fact_176_solution_Odisc_I1_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 )
=> ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ T3 ) ) ) ).
% solution.disc(1)
thf(fact_177_solution_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 )
=> ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ T3 ) )
= ( proces1708129104e_PREF @ A @ B @ A @ Sys2 @ T3 ) ) ) ).
% solution.simps(3)
thf(fact_178_solution_Osimps_I4_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] :
( ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 )
=> ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys2 @ T3 ) )
= ( proces1652378886lution @ A @ B @ Sys2 @ ( proces126235999e_CONT @ A @ B @ Sys2 @ T3 ) ) ) ) ).
% solution.simps(4)
thf(fact_179_process_Orel__coinduct,axiom,
! [A: $tType,B: $tType,P: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B,R: A > B > $o] :
( ( P @ X7 @ Y3 )
=> ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ B] :
( ( P @ Process3 @ Process4 )
=> ( ( ( proces10484146Action @ A @ Process3 )
= ( proces10484146Action @ B @ Process4 ) )
& ( ( proces10484146Action @ A @ Process3 )
=> ( ( proces10484146Action @ B @ Process4 )
=> ( ( R @ ( proces745025900prefOf @ A @ Process3 ) @ ( proces745025900prefOf @ B @ Process4 ) )
& ( P @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ B @ Process4 ) ) ) ) )
& ( ( proces401113213Choice @ A @ Process3 )
=> ( ( proces401113213Choice @ B @ Process4 )
=> ( ( P @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ B @ Process4 ) )
& ( P @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ B @ Process4 ) ) ) ) ) ) )
=> ( proces749077512rocess @ A @ B @ R @ X7 @ Y3 ) ) ) ).
% process.rel_coinduct
thf(fact_180_process_Ocollapse_I1_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ( proces10484146Action @ A @ Process )
=> ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
= Process ) ) ).
% process.collapse(1)
thf(fact_181_process_Osel_I2_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
= X122 ) ).
% process.sel(2)
thf(fact_182_process_Osel_I1_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
= X11 ) ).
% process.sel(1)
thf(fact_183_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 ) ) ) ) ).
% process.exhaust_sel
thf(fact_184_process_Oexpand,axiom,
! [A: $tType,Process: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
( ( ( proces10484146Action @ A @ Process )
= ( proces10484146Action @ A @ Process5 ) )
=> ( ( ( proces10484146Action @ A @ Process )
=> ( ( proces10484146Action @ A @ Process5 )
=> ( ( ( proces745025900prefOf @ A @ Process )
= ( proces745025900prefOf @ A @ Process5 ) )
& ( ( proces1778668539contOf @ A @ Process )
= ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
=> ( ( ( proces401113213Choice @ A @ Process )
=> ( ( proces401113213Choice @ A @ Process5 )
=> ( ( ( proces979765041_ch1Of @ A @ Process )
= ( proces979765041_ch1Of @ A @ Process5 ) )
& ( ( proces988026546_ch2Of @ A @ Process )
= ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) )
=> ( Process = Process5 ) ) ) ) ).
% process.expand
thf(fact_185_process_Ocoinduct,axiom,
! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
( ( R @ Process @ Process5 )
=> ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ A] :
( ( R @ Process3 @ Process4 )
=> ( ( ( proces10484146Action @ A @ Process3 )
= ( proces10484146Action @ A @ Process4 ) )
& ( ( proces10484146Action @ A @ Process3 )
=> ( ( proces10484146Action @ A @ Process4 )
=> ( ( ( proces745025900prefOf @ A @ Process3 )
= ( proces745025900prefOf @ A @ Process4 ) )
& ( R @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ A @ Process4 ) ) ) ) )
& ( ( proces401113213Choice @ A @ Process3 )
=> ( ( proces401113213Choice @ A @ Process4 )
=> ( ( R @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ A @ Process4 ) )
& ( R @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ A @ Process4 ) ) ) ) ) ) )
=> ( Process = Process5 ) ) ) ).
% process.coinduct
thf(fact_186_process_Ocoinduct__strong,axiom,
! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
( ( R @ Process @ Process5 )
=> ( ! [Process3: proces634752977rocess @ A,Process4: proces634752977rocess @ A] :
( ( R @ Process3 @ Process4 )
=> ( ( ( proces10484146Action @ A @ Process3 )
= ( proces10484146Action @ A @ Process4 ) )
& ( ( proces10484146Action @ A @ Process3 )
=> ( ( proces10484146Action @ A @ Process4 )
=> ( ( ( proces745025900prefOf @ A @ Process3 )
= ( proces745025900prefOf @ A @ Process4 ) )
& ( ( R @ ( proces1778668539contOf @ A @ Process3 ) @ ( proces1778668539contOf @ A @ Process4 ) )
| ( ( proces1778668539contOf @ A @ Process3 )
= ( proces1778668539contOf @ A @ Process4 ) ) ) ) ) )
& ( ( proces401113213Choice @ A @ Process3 )
=> ( ( proces401113213Choice @ A @ Process4 )
=> ( ( ( R @ ( proces979765041_ch1Of @ A @ Process3 ) @ ( proces979765041_ch1Of @ A @ Process4 ) )
| ( ( proces979765041_ch1Of @ A @ Process3 )
= ( proces979765041_ch1Of @ A @ Process4 ) ) )
& ( ( R @ ( proces988026546_ch2Of @ A @ Process3 ) @ ( proces988026546_ch2Of @ A @ Process4 ) )
| ( ( proces988026546_ch2Of @ A @ Process3 )
= ( proces988026546_ch2Of @ A @ Process4 ) ) ) ) ) ) ) )
=> ( Process = Process5 ) ) ) ).
% process.coinduct_strong
thf(fact_187_process_Oset__sel_I2_J,axiom,
! [A: $tType,A2: proces634752977rocess @ A,X7: A] :
( ( proces10484146Action @ A @ A2 )
=> ( ( member @ A @ X7 @ ( proces1148692671rocess @ A @ ( proces1778668539contOf @ A @ A2 ) ) )
=> ( member @ A @ X7 @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% process.set_sel(2)
thf(fact_188_process_Oset__sel_I1_J,axiom,
! [A: $tType,A2: proces634752977rocess @ A] :
( ( proces10484146Action @ A @ A2 )
=> ( member @ A @ ( proces745025900prefOf @ A @ A2 ) @ ( proces1148692671rocess @ A @ A2 ) ) ) ).
% process.set_sel(1)
thf(fact_189_CONT_Osimps_I2_J,axiom,
! [A: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
( ( proces126235999e_CONT @ A @ B @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
= ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) ).
% CONT.simps(2)
thf(fact_190_PREF_Osimps_I2_J,axiom,
! [A: $tType,C: $tType,B: $tType,Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
( ( proces1708129104e_PREF @ A @ B @ C @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
= ( proces745025900prefOf @ B @ P4 ) ) ).
% PREF.simps(2)
thf(fact_191_process_Orel__sel,axiom,
! [B: $tType,A: $tType] :
( ( proces749077512rocess @ A @ B )
= ( ^ [R3: A > B > $o,A8: proces634752977rocess @ A,B5: proces634752977rocess @ B] :
( ( ( proces10484146Action @ A @ A8 )
= ( proces10484146Action @ B @ B5 ) )
& ( ( proces10484146Action @ A @ A8 )
=> ( ( proces10484146Action @ B @ B5 )
=> ( ( R3 @ ( proces745025900prefOf @ A @ A8 ) @ ( proces745025900prefOf @ B @ B5 ) )
& ( proces749077512rocess @ A @ B @ R3 @ ( proces1778668539contOf @ A @ A8 ) @ ( proces1778668539contOf @ B @ B5 ) ) ) ) )
& ( ( proces401113213Choice @ A @ A8 )
=> ( ( proces401113213Choice @ B @ B5 )
=> ( ( proces749077512rocess @ A @ B @ R3 @ ( proces979765041_ch1Of @ A @ A8 ) @ ( proces979765041_ch1Of @ B @ B5 ) )
& ( proces749077512rocess @ A @ B @ R3 @ ( proces988026546_ch2Of @ A @ A8 ) @ ( proces988026546_ch2Of @ B @ B5 ) ) ) ) ) ) ) ) ).
% process.rel_sel
thf(fact_192_process_Osplit__sel__asm,axiom,
! [B: $tType,A: $tType,P: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
( ( P @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
= ( ~ ( ( ( Process
= ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
& ~ ( P @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
| ( ( Process
= ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
& ~ ( P @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% process.split_sel_asm
thf(fact_193_process_Osplit__sel,axiom,
! [B: $tType,A: $tType,P: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
( ( P @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
= ( ( ( Process
= ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
=> ( P @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
& ( ( Process
= ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
=> ( P @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% process.split_sel
thf(fact_194_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 ) ) ) ) ) ).
% process.case_eq_if
thf(fact_195_process_Osimps_I5_J,axiom,
! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X122: proces634752977rocess @ A] :
( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X122 ) )
= ( F1 @ X11 @ X122 ) ) ).
% process.simps(5)
thf(fact_196_process_Osimps_I6_J,axiom,
! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X21 @ X222 ) )
= ( F2 @ X21 @ X222 ) ) ).
% process.simps(6)
thf(fact_197_ssubst__Pair__rhs,axiom,
! [B: $tType,A: $tType,R4: A,S: B,R: set @ ( product_prod @ A @ B ),S2: B] :
( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R4 @ S ) @ R )
=> ( ( S2 = S )
=> ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R4 @ S2 ) @ R ) ) ) ).
% ssubst_Pair_rhs
thf(fact_198_curry__conv,axiom,
! [A: $tType,C: $tType,B: $tType] :
( ( product_curry @ B @ C @ A )
= ( ^ [F7: ( product_prod @ B @ C ) > A,A8: B,B5: C] : ( F7 @ ( product_Pair @ B @ C @ A8 @ B5 ) ) ) ) ).
% curry_conv
thf(fact_199_curryI,axiom,
! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
=> ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% curryI
thf(fact_200_curryD,axiom,
! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
=> ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% curryD
thf(fact_201_curryE,axiom,
! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
=> ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% curryE
thf(fact_202_process__term_Octr__transfer_I2_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces749077512rocess @ A @ B @ R1 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( proces1062592052s_PROC @ A @ Pvar ) @ ( proces1062592052s_PROC @ B @ C ) ) ).
% process_term.ctr_transfer(2)
thf(fact_203_isACT_Oelims_I1_J,axiom,
! [D: $tType,A: $tType,B: $tType,C: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A,Y3: $o] :
( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
= Y3 )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ D @ X6 ) )
=> ( Y3
= ( ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X6 ) ) ) ) )
=> ( ! [P3: proces634752977rocess @ D] :
( ( Xa2
= ( proces1062592052s_PROC @ D @ A @ P3 ) )
=> ( Y3
= ( ~ ( proces10484146Action @ D @ P3 ) ) ) )
=> ( ( ? [A4: D,T4: proces554692349s_term @ D @ A] :
( Xa2
= ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
=> ~ Y3 )
=> ~ ( ? [T12: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
( Xa2
= ( proces89589571ess_CH @ D @ A @ T12 @ T22 ) )
=> Y3 ) ) ) ) ) ).
% isACT.elims(1)
thf(fact_204_curry__def,axiom,
! [C: $tType,B: $tType,A: $tType] :
( ( product_curry @ A @ B @ C )
= ( ^ [C4: ( product_prod @ A @ B ) > C,X4: A,Y6: B] : ( C4 @ ( product_Pair @ A @ B @ X4 @ Y6 ) ) ) ) ).
% curry_def
thf(fact_205_curry__K,axiom,
! [B: $tType,C: $tType,A: $tType,C3: C] :
( ( product_curry @ A @ B @ C
@ ^ [X4: product_prod @ A @ B] : C3 )
= ( ^ [X4: A,Y6: B] : C3 ) ) ).
% curry_K
thf(fact_206_process__term_Octr__transfer_I1_J,axiom,
! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R2: Pvar > C > $o,R1: A > B > $o] : ( bNF_rel_fun @ Pvar @ C @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ R2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( proces1627516585ss_VAR @ Pvar @ A ) @ ( proces1627516585ss_VAR @ C @ B ) ) ).
% process_term.ctr_transfer(1)
thf(fact_207_process__term_Orel__map_I2_J,axiom,
! [A: $tType,B: $tType,E2: $tType,F5: $tType,D: $tType,C: $tType,S1a: A > E2 > $o,S2a: B > F5 > $o,X7: proces554692349s_term @ A @ B,G1: C > E2,G2: D > F5,Y3: proces554692349s_term @ C @ D] :
( ( proces2029722208s_term @ A @ E2 @ B @ F5 @ S1a @ S2a @ X7 @ ( proces224683037s_term @ C @ E2 @ D @ F5 @ G1 @ G2 @ Y3 ) )
= ( proces2029722208s_term @ A @ C @ B @ D
@ ^ [X4: A,Y6: C] : ( S1a @ X4 @ ( G1 @ Y6 ) )
@ ^ [X4: B,Y6: D] : ( S2a @ X4 @ ( G2 @ Y6 ) )
@ X7
@ Y3 ) ) ).
% process_term.rel_map(2)
thf(fact_208_process__term_Orel__map_I1_J,axiom,
! [A: $tType,B: $tType,E2: $tType,F5: $tType,D: $tType,C: $tType,S1b: E2 > C > $o,S2b: F5 > D > $o,I1: A > E2,I2: B > F5,X7: proces554692349s_term @ A @ B,Y3: proces554692349s_term @ C @ D] :
( ( proces2029722208s_term @ E2 @ C @ F5 @ D @ S1b @ S2b @ ( proces224683037s_term @ A @ E2 @ B @ F5 @ I1 @ I2 @ X7 ) @ Y3 )
= ( proces2029722208s_term @ A @ C @ B @ D
@ ^ [X4: A] : ( S1b @ ( I1 @ X4 ) )
@ ^ [X4: B] : ( S2b @ ( I2 @ X4 ) )
@ X7
@ Y3 ) ) ).
% process_term.rel_map(1)
thf(fact_209_process__term_Omap__cong__pred,axiom,
! [D: $tType,C: $tType,B: $tType,A: $tType,X7: proces554692349s_term @ A @ B,Ya2: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
( ( X7 = Ya2 )
=> ( ( proces2118920028s_term @ A @ B
@ ^ [Z12: A] :
( ( F1 @ Z12 )
= ( G1 @ Z12 ) )
@ ^ [Z22: B] :
( ( F2 @ Z22 )
= ( G2 @ Z22 ) )
@ Ya2 )
=> ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X7 )
= ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ Ya2 ) ) ) ) ).
% process_term.map_cong_pred
thf(fact_210_process__term_Omap__transfer,axiom,
! [A: $tType,C: $tType,B: $tType,D: $tType,L: $tType,J: $tType,K: $tType,I: $tType,R1b: A > I > $o,S1d: C > K > $o,R2b: B > J > $o,S2d: D > L > $o] : ( bNF_rel_fun @ ( A > C ) @ ( I > K ) @ ( ( B > D ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( J > L ) > ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ A @ I @ C @ K @ R1b @ S1d ) @ ( bNF_rel_fun @ ( B > D ) @ ( J > L ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ B @ J @ D @ L @ R2b @ S2d ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ I @ J ) @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ K @ L ) @ ( proces2029722208s_term @ A @ I @ B @ J @ R1b @ R2b ) @ ( proces2029722208s_term @ C @ K @ D @ L @ S1d @ S2d ) ) ) @ ( proces224683037s_term @ A @ C @ B @ D ) @ ( proces224683037s_term @ I @ K @ J @ L ) ) ).
% process_term.map_transfer
thf(fact_211_process__term_Opred__True,axiom,
! [B: $tType,A: $tType] :
( ( proces2118920028s_term @ A @ B
@ ^ [Uu: A] : $true
@ ^ [Uu: B] : $true )
= ( ^ [Uu: proces554692349s_term @ A @ B] : $true ) ) ).
% process_term.pred_True
thf(fact_212_process__term_Ocase__distrib,axiom,
! [B: $tType,C: $tType,Pvar: $tType,A: $tType,H: B > C,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,Process_term: proces554692349s_term @ A @ Pvar] :
( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
= ( proces460752237s_term @ Pvar @ C @ A
@ ^ [X4: Pvar] : ( H @ ( F1 @ X4 ) )
@ ^ [X4: proces634752977rocess @ A] : ( H @ ( F2 @ X4 ) )
@ ^ [X13: A,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X13 @ X23 ) )
@ ^ [X13: proces554692349s_term @ A @ Pvar,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X13 @ X23 ) )
@ Process_term ) ) ).
% process_term.case_distrib
thf(fact_213_process__term_Omap__ident,axiom,
! [B: $tType,A: $tType,T6: proces554692349s_term @ A @ B] :
( ( proces224683037s_term @ A @ A @ B @ B
@ ^ [X4: A] : X4
@ ^ [X4: B] : X4
@ T6 )
= T6 ) ).
% process_term.map_ident
thf(fact_214_process_Opred__True,axiom,
! [A: $tType] :
( ( proces1205983068rocess @ A
@ ^ [Uu: A] : $true )
= ( ^ [Uu: proces634752977rocess @ A] : $true ) ) ).
% process.pred_True
thf(fact_215_process__term_Ocase__transfer,axiom,
! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E2: $tType,C: $tType,R2: Pvar > C > $o,S3: D > E2 > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E2 ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E2 ) > ( B > ( proces554692349s_term @ B @ C ) > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E2 @ R2 @ S3 ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E2 ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E2 @ ( proces749077512rocess @ A @ B @ R1 ) @ S3 ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E2 ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ S3 ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ S3 ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ S3 ) ) ) ) @ ( proces460752237s_term @ Pvar @ D @ A ) @ ( proces460752237s_term @ C @ E2 @ B ) ) ).
% process_term.case_transfer
thf(fact_216_process__term_Orec__transfer,axiom,
! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E2: $tType,C: $tType,R2: Pvar > C > $o,S3: D > E2 > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E2 ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E2 ) > ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E2 @ R2 @ S3 ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E2 ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E2 @ ( proces749077512rocess @ A @ B @ R1 ) @ S3 ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E2 > E2 ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) > ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 > E2 ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D ) @ ( E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( bNF_rel_fun @ D @ E2 @ D @ E2 @ S3 @ S3 ) ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E2 > E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D > D ) @ ( E2 > E2 > E2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( bNF_rel_fun @ D @ E2 @ ( D > D ) @ ( E2 > E2 ) @ S3 @ ( bNF_rel_fun @ D @ E2 @ D @ E2 @ S3 @ S3 ) ) ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E2 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ S3 ) ) ) ) @ ( proces2117273769s_term @ Pvar @ D @ A ) @ ( proces2117273769s_term @ C @ E2 @ B ) ) ).
% process_term.rec_transfer
thf(fact_217_let__rsp,axiom,
! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o] :
( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ R1 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 ) @ R2 )
@ ^ [S4: A,F7: A > C] : ( F7 @ S4 )
@ ^ [S4: B,F7: B > D] : ( F7 @ S4 ) ) ).
% let_rsp
thf(fact_218_isACT_Osimps_I1_J,axiom,
! [D: $tType,B: $tType,C: $tType,A: $tType,Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X3 ) )
= ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( Sys2 @ X3 ) ) ) ).
% isACT.simps(1)
thf(fact_219_process_Odisc__eq__case_I1_J,axiom,
! [A: $tType] :
( ( proces10484146Action @ A )
= ( proces1406508781rocess @ A @ $o
@ ^ [Uu: A,Uv: proces634752977rocess @ A] : $true
@ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $false ) ) ).
% process.disc_eq_case(1)
thf(fact_220_process_Ocase__distrib,axiom,
! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
= ( proces1406508781rocess @ A @ C
@ ^ [X13: A,X23: proces634752977rocess @ A] : ( H @ ( F1 @ X13 @ X23 ) )
@ ^ [X13: proces634752977rocess @ A,X23: proces634752977rocess @ A] : ( H @ ( F2 @ X13 @ X23 ) )
@ Process ) ) ).
% process.case_distrib
thf(fact_221_process_Odisc__eq__case_I2_J,axiom,
! [A: $tType] :
( ( proces401113213Choice @ A )
= ( proces1406508781rocess @ A @ $o
@ ^ [Uu: A,Uv: proces634752977rocess @ A] : $false
@ ^ [Uu: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : $true ) ) ).
% process.disc_eq_case(2)
thf(fact_222_isACT_Oelims_I2_J,axiom,
! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ D @ X6 ) )
=> ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X6 ) ) )
=> ( ! [P3: proces634752977rocess @ D] :
( ( Xa2
= ( proces1062592052s_PROC @ D @ A @ P3 ) )
=> ~ ( proces10484146Action @ D @ P3 ) )
=> ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
( Xa2
!= ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ).
% isACT.elims(2)
thf(fact_223_isACT_Oelims_I3_J,axiom,
! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ D @ X6 ) )
=> ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X6 ) ) )
=> ( ! [P3: proces634752977rocess @ D] :
( ( Xa2
= ( proces1062592052s_PROC @ D @ A @ P3 ) )
=> ( proces10484146Action @ D @ P3 ) )
=> ~ ! [T12: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
( Xa2
!= ( proces89589571ess_CH @ D @ A @ T12 @ T22 ) ) ) ) ) ).
% isACT.elims(3)
thf(fact_224_PREF_Oelims,axiom,
! [A: $tType,C: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ B @ A,Y3: B] :
( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa2 )
= Y3 )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( Y3
!= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : A8
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( X7 @ X6 ) ) ) )
=> ( ! [P3: proces634752977rocess @ B] :
( ( Xa2
= ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( Y3
!= ( proces745025900prefOf @ B @ P3 ) ) )
=> ( ! [A4: B] :
( ? [T4: proces554692349s_term @ B @ A] :
( Xa2
= ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( Y3 != A4 ) )
=> ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( Xa2
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( Y3
!= ( undefined @ B ) ) ) ) ) ) ) ).
% PREF.elims
thf(fact_225_CH1_Oelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa2 )
= Y3 )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( Y3
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A8: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P8 ) )
@ ^ [A8: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : T13
@ ( X7 @ X6 ) ) ) )
=> ( ! [P3: proces634752977rocess @ B] :
( ( Xa2
= ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( Y3
!= ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P3 ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A] :
( ? [T22: proces554692349s_term @ B @ A] :
( Xa2
= ( proces89589571ess_CH @ B @ A @ T12 @ T22 ) )
=> ( Y3 != T12 ) )
=> ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
( Xa2
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( Y3
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CH1.elims
thf(fact_226_process_Octr__transfer_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1525233512Action @ A ) @ ( proces1525233512Action @ B ) ) ).
% process.ctr_transfer(1)
thf(fact_227_process_Octr__transfer_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1915862579Choice @ A ) @ ( proces1915862579Choice @ B ) ) ).
% process.ctr_transfer(2)
thf(fact_228_process__term_Octr__transfer_I3_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) ) @ ( proces1454156180ss_ACT @ A @ Pvar ) @ ( proces1454156180ss_ACT @ B @ C ) ) ).
% process_term.ctr_transfer(3)
thf(fact_229_process__term_Octr__transfer_I4_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R2: Pvar > C > $o] : ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R2 ) ) @ ( proces89589571ess_CH @ A @ Pvar ) @ ( proces89589571ess_CH @ B @ C ) ) ).
% process_term.ctr_transfer(4)
thf(fact_230_process__term_Orel__transfer,axiom,
! [A: $tType,C: $tType,B: $tType,D: $tType,H2: $tType,F5: $tType,G3: $tType,E2: $tType,S1a: A > E2 > $o,S1c: C > G3 > $o,S2a: B > F5 > $o,S2c: D > H2 > $o] :
( bNF_rel_fun @ ( A > C > $o ) @ ( E2 > G3 > $o ) @ ( ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( F5 > H2 > $o ) > ( proces554692349s_term @ E2 @ F5 ) > ( proces554692349s_term @ G3 @ H2 ) > $o )
@ ( bNF_rel_fun @ A @ E2 @ ( C > $o ) @ ( G3 > $o ) @ S1a
@ ( bNF_rel_fun @ C @ G3 @ $o @ $o @ S1c
@ ^ [Y4: $o,Z: $o] : Y4 = Z ) )
@ ( bNF_rel_fun @ ( B > D > $o ) @ ( F5 > H2 > $o ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ E2 @ F5 ) > ( proces554692349s_term @ G3 @ H2 ) > $o )
@ ( bNF_rel_fun @ B @ F5 @ ( D > $o ) @ ( H2 > $o ) @ S2a
@ ( bNF_rel_fun @ D @ H2 @ $o @ $o @ S2c
@ ^ [Y4: $o,Z: $o] : Y4 = Z ) )
@ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ E2 @ F5 ) @ ( ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ G3 @ H2 ) > $o ) @ ( proces2029722208s_term @ A @ E2 @ B @ F5 @ S1a @ S2a )
@ ( bNF_rel_fun @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ G3 @ H2 ) @ $o @ $o @ ( proces2029722208s_term @ C @ G3 @ D @ H2 @ S1c @ S2c )
@ ^ [Y4: $o,Z: $o] : Y4 = Z ) ) )
@ ( proces2029722208s_term @ A @ C @ B @ D )
@ ( proces2029722208s_term @ E2 @ G3 @ F5 @ H2 ) ) ).
% process_term.rel_transfer
thf(fact_231_process__term_Opred__transfer,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o] :
( bNF_rel_fun @ ( A > $o ) @ ( C > $o ) @ ( ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) @ ( ( D > $o ) > ( proces554692349s_term @ C @ D ) > $o )
@ ( bNF_rel_fun @ A @ C @ $o @ $o @ R1
@ ^ [Y4: $o,Z: $o] : Y4 = Z )
@ ( bNF_rel_fun @ ( B > $o ) @ ( D > $o ) @ ( ( proces554692349s_term @ A @ B ) > $o ) @ ( ( proces554692349s_term @ C @ D ) > $o )
@ ( bNF_rel_fun @ B @ D @ $o @ $o @ R2
@ ^ [Y4: $o,Z: $o] : Y4 = Z )
@ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ C @ D ) @ $o @ $o @ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R2 )
@ ^ [Y4: $o,Z: $o] : Y4 = Z ) )
@ ( proces2118920028s_term @ A @ B )
@ ( proces2118920028s_term @ C @ D ) ) ).
% process_term.pred_transfer
thf(fact_232_process_Orel__transfer,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ C ) > ( proces634752977rocess @ D ) > $o )
@ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
@ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
@ ^ [Y4: $o,Z: $o] : Y4 = Z ) )
@ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ C ) @ ( ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ D ) > $o ) @ ( proces749077512rocess @ A @ C @ Sa )
@ ( bNF_rel_fun @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ D ) @ $o @ $o @ ( proces749077512rocess @ B @ D @ Sc )
@ ^ [Y4: $o,Z: $o] : Y4 = Z ) )
@ ( proces749077512rocess @ A @ B )
@ ( proces749077512rocess @ C @ D ) ) ).
% process.rel_transfer
thf(fact_233_process_Opred__transfer,axiom,
! [A: $tType,B: $tType,R: A > B > $o] :
( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( proces634752977rocess @ A ) > $o ) @ ( ( proces634752977rocess @ B ) > $o )
@ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
@ ^ [Y4: $o,Z: $o] : Y4 = Z )
@ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
@ ^ [Y4: $o,Z: $o] : Y4 = Z )
@ ( proces1205983068rocess @ A )
@ ( proces1205983068rocess @ B ) ) ).
% process.pred_transfer
thf(fact_234_process_Odisc__transfer_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o] :
( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
@ ^ [Y4: $o,Z: $o] : Y4 = Z
@ ( proces401113213Choice @ A )
@ ( proces401113213Choice @ B ) ) ).
% process.disc_transfer(2)
thf(fact_235_process_Odisc__transfer_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o] :
( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
@ ^ [Y4: $o,Z: $o] : Y4 = Z
@ ( proces10484146Action @ A )
@ ( proces10484146Action @ B ) ) ).
% process.disc_transfer(1)
thf(fact_236_process_Ocase__transfer,axiom,
! [A: $tType,C: $tType,D: $tType,B: $tType,R: A > B > $o,S3: C > D > $o] : ( bNF_rel_fun @ ( A > ( proces634752977rocess @ A ) > C ) @ ( B > ( proces634752977rocess @ B ) > D ) @ ( ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) > ( proces634752977rocess @ A ) > C ) @ ( ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) > ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S3 ) ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S3 ) ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S3 ) ) @ ( proces1406508781rocess @ A @ C ) @ ( proces1406508781rocess @ B @ D ) ) ).
% process.case_transfer
thf(fact_237_ch2Of__def,axiom,
! [A: $tType] :
( ( proces988026546_ch2Of @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
@ ^ [X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] : X223 ) ) ).
% ch2Of_def
thf(fact_238_ch1Of__def,axiom,
! [A: $tType] :
( ( proces979765041_ch1Of @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
@ ^ [X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] : X212 ) ) ).
% ch1Of_def
thf(fact_239_contOf__def,axiom,
! [A: $tType] :
( ( proces1778668539contOf @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [X113: A,X124: proces634752977rocess @ A] : X124
@ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% contOf_def
thf(fact_240_prefOf__def,axiom,
! [A: $tType] :
( ( proces745025900prefOf @ A )
= ( proces1406508781rocess @ A @ A
@ ^ [X113: A,X124: proces634752977rocess @ A] : X113
@ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% prefOf_def
thf(fact_241_CONT_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces126235999e_CONT @ A @ B @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P8 ) )
@ ^ [A8: B,T5: proces554692349s_term @ B @ A] : T5
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( Sys2 @ X3 ) ) ) ).
% CONT.simps(1)
thf(fact_242_CH2_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces1239275104le_CH2 @ A @ B @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A8: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P8 ) )
@ ^ [A8: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : T23
@ ( Sys2 @ X3 ) ) ) ).
% CH2.simps(1)
thf(fact_243_CH1_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys2: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces1239275103le_CH1 @ A @ B @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A8: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P8 ) )
@ ^ [A8: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : T13
@ ( Sys2 @ X3 ) ) ) ).
% CH1.simps(1)
thf(fact_244_PREF_Osimps_I1_J,axiom,
! [B: $tType,C: $tType,A: $tType,Sys2: A > ( proces554692349s_term @ B @ C ),X3: A] :
( ( proces1708129104e_PREF @ A @ B @ C @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : A8
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( Sys2 @ X3 ) ) ) ).
% PREF.simps(1)
thf(fact_245_CONT_Oelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa2 )
= Y3 )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( Y3
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P8 ) )
@ ^ [A8: B,T5: proces554692349s_term @ B @ A] : T5
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( X7 @ X6 ) ) ) )
=> ( ! [P3: proces634752977rocess @ B] :
( ( Xa2
= ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( Y3
!= ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P3 ) ) ) )
=> ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( Y3 != T4 ) )
=> ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( Xa2
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( Y3
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CONT.elims
thf(fact_246_CH2_Oelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa2 )
= Y3 )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( Y3
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A8: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P8 ) )
@ ^ [A8: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : T23
@ ( X7 @ X6 ) ) ) )
=> ( ! [P3: proces634752977rocess @ B] :
( ( Xa2
= ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( Y3
!= ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P3 ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces89589571ess_CH @ B @ A @ T12 @ T22 ) )
=> ( Y3 != T22 ) )
=> ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
( Xa2
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( Y3
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CH2.elims
thf(fact_247_CH1_Opelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa2 )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa2 ) )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( ( Y3
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A8: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P8 ) )
@ ^ [A8: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : T13
@ ( X7 @ X6 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) ) ) ) )
=> ( ! [P3: proces634752977rocess @ B] :
( ( Xa2
= ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( ( Y3
= ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P3 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P3 ) ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces89589571ess_CH @ B @ A @ T12 @ T22 ) )
=> ( ( Y3 = T12 )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T22 ) ) ) ) )
=> ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( ( Y3
= ( undefined @ ( proces554692349s_term @ B @ A ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CH1.pelims
thf(fact_248_CH2_Opelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa2 )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa2 ) )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( ( Y3
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A8: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P8 ) )
@ ^ [A8: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : T23
@ ( X7 @ X6 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) ) ) ) )
=> ( ! [P3: proces634752977rocess @ B] :
( ( Xa2
= ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( ( Y3
= ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P3 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P3 ) ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces89589571ess_CH @ B @ A @ T12 @ T22 ) )
=> ( ( Y3 = T22 )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T22 ) ) ) ) )
=> ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( ( Y3
= ( undefined @ ( proces554692349s_term @ B @ A ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CH2.pelims
thf(fact_249_CONT_Opelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa2: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa2 )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa2 ) )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( ( Y3
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P8: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P8 ) )
@ ^ [A8: B,T5: proces554692349s_term @ B @ A] : T5
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( X7 @ X6 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) ) ) ) )
=> ( ! [P3: proces634752977rocess @ B] :
( ( Xa2
= ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( ( Y3
= ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P3 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P3 ) ) ) ) )
=> ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( ( Y3 = T4 )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
=> ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( ( Y3
= ( undefined @ ( proces554692349s_term @ B @ A ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CONT.pelims
thf(fact_250_PREF_Opelims,axiom,
! [C: $tType,A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ B @ A,Y3: B] :
( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa2 )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa2 ) )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ B @ X6 ) )
=> ( ( Y3
= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : A8
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab2: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( X7 @ X6 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X6 ) ) ) ) )
=> ( ! [P3: proces634752977rocess @ B] :
( ( Xa2
= ( proces1062592052s_PROC @ B @ A @ P3 ) )
=> ( ( Y3
= ( proces745025900prefOf @ B @ P3 ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P3 ) ) ) ) )
=> ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( ( Y3 = A4 )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
=> ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( ( Xa2
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( ( Y3
= ( undefined @ B ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% PREF.pelims
thf(fact_251_isACT_Opelims_I1_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A,Y3: $o] :
( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa2 ) )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ D @ X6 ) )
=> ( ( Y3
= ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X6 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X6 ) ) ) ) )
=> ( ! [P3: proces634752977rocess @ D] :
( ( Xa2
= ( proces1062592052s_PROC @ D @ A @ P3 ) )
=> ( ( Y3
= ( proces10484146Action @ D @ P3 ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P3 ) ) ) ) )
=> ( ! [A4: D,T4: proces554692349s_term @ D @ A] :
( ( Xa2
= ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
=> ( Y3
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) )
=> ~ ! [T12: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
( ( Xa2
= ( proces89589571ess_CH @ D @ A @ T12 @ T22 ) )
=> ( ~ Y3
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T22 ) ) ) ) ) ) ) ) ) ) ).
% isACT.pelims(1)
thf(fact_252_isACT_Opelims_I3_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa2 ) )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ D @ X6 ) )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X6 ) ) )
=> ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X6 ) ) ) )
=> ( ! [P3: proces634752977rocess @ D] :
( ( Xa2
= ( proces1062592052s_PROC @ D @ A @ P3 ) )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P3 ) ) )
=> ( proces10484146Action @ D @ P3 ) ) )
=> ~ ! [T12: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
( ( Xa2
= ( proces89589571ess_CH @ D @ A @ T12 @ T22 ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T22 ) ) ) ) ) ) ) ) ).
% isACT.pelims(3)
thf(fact_253_isACT_Opelims_I2_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa2: proces554692349s_term @ D @ A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa2 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa2 ) )
=> ( ! [X6: A] :
( ( Xa2
= ( proces1627516585ss_VAR @ A @ D @ X6 ) )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X6 ) ) )
=> ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A8: B,T5: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X6 ) ) ) )
=> ( ! [P3: proces634752977rocess @ D] :
( ( Xa2
= ( proces1062592052s_PROC @ D @ A @ P3 ) )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P3 ) ) )
=> ~ ( proces10484146Action @ D @ P3 ) ) )
=> ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
( ( Xa2
= ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ) ) ) ).
% isACT.pelims(2)
thf(fact_254_process_Ocorec__transfer,axiom,
! [C: $tType,A: $tType,B: $tType,D: $tType,S3: C > D > $o,R: A > B > $o] :
( bNF_rel_fun @ ( C > $o ) @ ( D > $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 ) ) @ ( ( D > B ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
@ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
@ ^ [Y4: $o,Z: $o] : Y4 = Z )
@ ( bNF_rel_fun @ ( C > A ) @ ( D > B ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ A @ B @ S3 @ R )
@ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
@ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
@ ^ [Y4: $o,Z: $o] : Y4 = Z )
@ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) )
@ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S3 @ S3 )
@ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
@ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
@ ^ [Y4: $o,Z: $o] : Y4 = Z )
@ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) )
@ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S3 @ S3 )
@ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
@ ( bNF_rel_fun @ C @ D @ $o @ $o @ S3
@ ^ [Y4: $o,Z: $o] : Y4 = Z )
@ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S3 @ S3 ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S3 @ ( proces749077512rocess @ A @ B @ R ) ) ) ) ) ) ) ) ) ) ) )
@ ( proces894737309rocess @ C @ A )
@ ( proces894737309rocess @ D @ B ) ) ).
% process.corec_transfer
%----Helper facts (3)
thf(help_If_3_1_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_T,axiom,
! [A: $tType,X7: A,Y3: A] :
( ( if @ A @ $false @ X7 @ Y3 )
= Y3 ) ).
thf(help_If_1_1_T,axiom,
! [A: $tType,X7: A,Y3: A] :
( ( if @ A @ $true @ X7 @ Y3 )
= X7 ) ).
%----Free types (1)
thf(tfree_0,hypothesis,
zero @ a @ ( type @ a ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
! [X6: nat,Y7: a] :
( ( proces1667721le_sys @ a @ X6 )
!= ( proces1627516585ss_VAR @ a @ ( list @ char ) @ Y7 ) ) ).
%------------------------------------------------------------------------------