TPTP Problem File: PRO023^1.p
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%------------------------------------------------------------------------------
% File : PRO023^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Processes
% Problem : Process algebra 186
% 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__186.p [Bla16]
% Status : Theorem
% Rating : 0.00 v7.5.0, 0.67 v7.2.0, 0.75 v7.1.0
% Syntax : Number of formulae : 316 ( 143 unt; 57 typ; 0 def)
% Number of atoms : 846 ( 424 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 7470 ( 177 ~; 13 |; 55 &;6773 @)
% ( 0 <=>; 452 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 742 ( 742 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 6 con; 0-14 aty)
% Number of variables : 1929 ( 205 ^;1617 !; 23 ?;1929 :)
% ( 84 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2016-07-13 14:39:58.045
%------------------------------------------------------------------------------
%----Could-be-implicit typings (7)
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_Set_Oset,type,
set: $tType > $tType ).
thf(ty_t_itself,type,
itself: $tType > $tType ).
thf(ty_tf_b,type,
b: $tType ).
thf(ty_tf_a,type,
a: $tType ).
%----Explicit typings (50)
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_Orderings_Obot__class_Obot,type,
bot_bot:
!>[A: $tType] : 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_Omap__process,type,
proces370407749rocess:
!>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
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_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_Product__Type_OPair,type,
product_Pair:
!>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
thf(sy_c_Pure_Otype,type,
type:
!>[A: $tType] : ( itself @ A ) ).
thf(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
thf(sy_c_Set_Oinsert,type,
insert:
!>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
thf(sy_c_Set_Othe__elem,type,
the_elem:
!>[A: $tType] : ( ( set @ A ) > 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 ) ).
thf(sy_v_p,type,
p: proces634752977rocess @ a ).
thf(sy_v_p_H____,type,
p2: proces634752977rocess @ a ).
thf(sy_v_pa____,type,
pa: proces634752977rocess @ a ).
thf(sy_v_q____,type,
q: proces634752977rocess @ a ).
thf(sy_v_sys,type,
sys: b > ( proces554692349s_term @ a @ b ) ).
%----Relevant facts (255)
thf(fact_0__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062,axiom,
( ( proces10484146Action @ a @ pa )
| ( proces401113213Choice @ a @ pa ) ) ).
% \<open>isAction p \<or> isChoice p\<close>
thf(fact_1_process_Odistinct__disc_I2_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ( proces401113213Choice @ A @ Process )
=> ~ ( proces10484146Action @ A @ Process ) ) ).
% process.distinct_disc(2)
thf(fact_2_process_Odistinct__disc_I1_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ( proces10484146Action @ A @ Process )
=> ~ ( proces401113213Choice @ A @ Process ) ) ).
% process.distinct_disc(1)
thf(fact_3_isAction__isChoice,axiom,
! [A: $tType,P: proces634752977rocess @ A] :
( ( proces10484146Action @ A @ P )
| ( proces401113213Choice @ A @ P ) ) ).
% isAction_isChoice
thf(fact_4_process_Oexhaust__disc,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ~ ( proces10484146Action @ A @ Process )
=> ( proces401113213Choice @ A @ Process ) ) ).
% process.exhaust_disc
thf(fact_5_not__isAction__isChoice,axiom,
! [A: $tType,P: proces634752977rocess @ A] :
~ ( ( proces10484146Action @ A @ P )
& ( proces401113213Choice @ A @ P ) ) ).
% not_isAction_isChoice
thf(fact_6_process_Ocorec__disc__iff_I2_J,axiom,
! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( ~ ( P @ A2 ) ) ) ).
% process.corec_disc_iff(2)
thf(fact_7_process_Ocorec__disc__iff_I1_J,axiom,
! [A: $tType,C: $tType,P: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A2: C] :
( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( P @ A2 ) ) ).
% process.corec_disc_iff(1)
thf(fact_8_iss,axiom,
( p2
= ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ) ).
% iss
thf(fact_9_process_Omap__disc__iff_I2_J,axiom,
! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
= ( proces401113213Choice @ A @ A2 ) ) ).
% process.map_disc_iff(2)
thf(fact_10_process_Ocorec__disc_I2_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
( ~ ( P @ A2 )
=> ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% process.corec_disc(2)
thf(fact_11_process_Omap__disc__iff_I1_J,axiom,
! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
= ( proces10484146Action @ A @ A2 ) ) ).
% process.map_disc_iff(1)
thf(fact_12_process_Ocorec__disc_I1_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
( ( P @ A2 )
=> ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) ) ) ).
% process.corec_disc(1)
thf(fact_13_process_Odisc_I4_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% process.disc(4)
thf(fact_14_process_Odisc_I3_J,axiom,
! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% process.disc(3)
thf(fact_15_process_OdiscI_I2_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
( ( Process
= ( proces1915862579Choice @ A @ X21 @ X22 ) )
=> ( proces401113213Choice @ A @ Process ) ) ).
% process.discI(2)
thf(fact_16_isChoice__def,axiom,
! [A: $tType] :
( ( proces401113213Choice @ A )
= ( ^ [Process2: proces634752977rocess @ A] :
? [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
( Process2
= ( proces1915862579Choice @ A @ X212 @ X222 ) ) ) ) ).
% isChoice_def
thf(fact_17_process_Odisc_I2_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% process.disc(2)
thf(fact_18_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_19_process_Oinject_I1_J,axiom,
! [A: $tType,X11: A,X12: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
( ( ( proces1525233512Action @ A @ X11 @ X12 )
= ( proces1525233512Action @ A @ Y11 @ Y12 ) )
= ( ( X11 = Y11 )
& ( X12 = Y12 ) ) ) ).
% process.inject(1)
thf(fact_20_process_Oinject_I2_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
( ( ( proces1915862579Choice @ A @ X21 @ X22 )
= ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% process.inject(2)
thf(fact_21__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062,axiom,
( q
= ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ) ).
% \<open>q = solution sys (PROC p)\<close>
thf(fact_22_process_Ocorec_I2_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
( ~ ( P @ A2 )
=> ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
= ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A2 ) @ ( G211 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A2 ) @ ( G221 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% process.corec(2)
thf(fact_23_process_Ocorec_I1_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
( ( P @ A2 )
=> ( ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 )
= ( proces1525233512Action @ A @ ( G11 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A2 ) @ ( G121 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% process.corec(1)
thf(fact_24_process_Osimps_I16_J,axiom,
! [B: $tType,A: $tType,F: A > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
( ( proces370407749rocess @ A @ B @ F @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
= ( proces1915862579Choice @ B @ ( proces370407749rocess @ A @ B @ F @ X21 ) @ ( proces370407749rocess @ A @ B @ F @ X22 ) ) ) ).
% process.simps(16)
thf(fact_25_process_Osimps_I15_J,axiom,
! [B: $tType,A: $tType,F: A > B,X11: A,X12: proces634752977rocess @ A] :
( ( proces370407749rocess @ A @ B @ F @ ( proces1525233512Action @ A @ X11 @ X12 ) )
= ( proces1525233512Action @ B @ ( F @ X11 ) @ ( proces370407749rocess @ A @ B @ F @ X12 ) ) ) ).
% process.simps(15)
thf(fact_26_process_Odistinct_I1_J,axiom,
! [A: $tType,X11: A,X12: proces634752977rocess @ A,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
( ( proces1525233512Action @ A @ X11 @ X12 )
!= ( proces1915862579Choice @ A @ X21 @ X22 ) ) ).
% process.distinct(1)
thf(fact_27_process_Oexhaust,axiom,
! [A: $tType,Y: proces634752977rocess @ A] :
( ! [X112: A,X122: proces634752977rocess @ A] :
( Y
!= ( proces1525233512Action @ A @ X112 @ X122 ) )
=> ~ ! [X213: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
( Y
!= ( proces1915862579Choice @ A @ X213 @ X223 ) ) ) ).
% process.exhaust
thf(fact_28_process_Ocorec__code,axiom,
! [A: $tType,C: $tType] :
( ( proces894737309rocess @ C @ A )
= ( ^ [P2: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A3: C] : ( if @ ( proces634752977rocess @ A ) @ ( P2 @ A3 ) @ ( proces1525233512Action @ A @ ( G112 @ A3 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A3 ) @ ( G1212 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A3 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A3 ) @ ( G2112 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A3 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A3 ) @ ( G2212 @ A3 ) @ ( proces894737309rocess @ C @ A @ P2 @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A3 ) ) ) ) ) ) ) ).
% process.corec_code
thf(fact_29_process_Omap__ident,axiom,
! [A: $tType,T: proces634752977rocess @ A] :
( ( proces370407749rocess @ A @ A
@ ^ [X: A] : X
@ T )
= T ) ).
% process.map_ident
thf(fact_30_process__strong__coind,axiom,
! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P3: proces634752977rocess @ A] :
( ( Phi @ P @ P3 )
=> ( ! [P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
( ( Phi @ P4 @ P5 )
=> ( ( ( proces10484146Action @ A @ P4 )
= ( proces10484146Action @ A @ P5 ) )
& ( ( proces401113213Choice @ A @ P4 )
= ( proces401113213Choice @ A @ P5 ) ) ) )
=> ( ! [A4: A,A5: A,P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
( ( Phi @ ( proces1525233512Action @ A @ A4 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P5 ) )
=> ( ( A4 = A5 )
& ( ( Phi @ P4 @ P5 )
| ( P4 = P5 ) ) ) )
=> ( ! [P4: proces634752977rocess @ A,Q: proces634752977rocess @ A,P5: proces634752977rocess @ A,Q2: proces634752977rocess @ A] :
( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q ) @ ( proces1915862579Choice @ A @ P5 @ Q2 ) )
=> ( ( ( Phi @ P4 @ P5 )
| ( P4 = P5 ) )
& ( ( Phi @ Q @ Q2 )
| ( Q = Q2 ) ) ) )
=> ( P = P3 ) ) ) ) ) ).
% process_strong_coind
thf(fact_31_process__coind,axiom,
! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P3: proces634752977rocess @ A] :
( ( Phi @ P @ P3 )
=> ( ! [P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
( ( Phi @ P4 @ P5 )
=> ( ( ( proces10484146Action @ A @ P4 )
= ( proces10484146Action @ A @ P5 ) )
& ( ( proces401113213Choice @ A @ P4 )
= ( proces401113213Choice @ A @ P5 ) ) ) )
=> ( ! [A4: A,A5: A,P4: proces634752977rocess @ A,P5: proces634752977rocess @ A] :
( ( Phi @ ( proces1525233512Action @ A @ A4 @ P4 ) @ ( proces1525233512Action @ A @ A5 @ P5 ) )
=> ( ( A4 = A5 )
& ( Phi @ P4 @ P5 ) ) )
=> ( ! [P4: proces634752977rocess @ A,Q: proces634752977rocess @ A,P5: proces634752977rocess @ A,Q2: proces634752977rocess @ A] :
( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q ) @ ( proces1915862579Choice @ A @ P5 @ Q2 ) )
=> ( ( Phi @ P4 @ P5 )
& ( Phi @ Q @ Q2 ) ) )
=> ( P = P3 ) ) ) ) ) ).
% process_coind
thf(fact_32_isAction__def,axiom,
! [A: $tType] :
( ( proces10484146Action @ A )
= ( ^ [Process2: proces634752977rocess @ A] :
? [X113: A,X123: proces634752977rocess @ A] :
( Process2
= ( proces1525233512Action @ A @ X113 @ X123 ) ) ) ) ).
% isAction_def
thf(fact_33_process_OdiscI_I1_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A,X11: A,X12: proces634752977rocess @ A] :
( ( Process
= ( proces1525233512Action @ A @ X11 @ X12 ) )
=> ( proces10484146Action @ A @ Process ) ) ).
% process.discI(1)
thf(fact_34_process_Odisc_I1_J,axiom,
! [A: $tType,X11: A,X12: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) ) ).
% process.disc(1)
thf(fact_35_solution_Odisc__iff_I2_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
= ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% solution.disc_iff(2)
thf(fact_36_solution_Odisc__iff_I1_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
= ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% solution.disc_iff(1)
thf(fact_37_solution_Odisc_I2_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
=> ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% solution.disc(2)
thf(fact_38_solution_Odisc_I1_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
=> ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% solution.disc(1)
thf(fact_39_process_Omap__sel_I1_J,axiom,
! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
( ( proces10484146Action @ A @ A2 )
=> ( ( proces745025900prefOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
= ( F @ ( proces745025900prefOf @ A @ A2 ) ) ) ) ).
% process.map_sel(1)
thf(fact_40_process_Omap__sel_I3_J,axiom,
! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
( ( proces401113213Choice @ A @ A2 )
=> ( ( proces979765041_ch1Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
= ( proces370407749rocess @ A @ B @ F @ ( proces979765041_ch1Of @ A @ A2 ) ) ) ) ).
% process.map_sel(3)
thf(fact_41_process_Omap__sel_I4_J,axiom,
! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
( ( proces401113213Choice @ A @ A2 )
=> ( ( proces988026546_ch2Of @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
= ( proces370407749rocess @ A @ B @ F @ ( proces988026546_ch2Of @ A @ A2 ) ) ) ) ).
% process.map_sel(4)
thf(fact_42_isACT_Osimps_I2_J,axiom,
! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
= ( proces10484146Action @ D @ P ) ) ).
% isACT.simps(2)
thf(fact_43_process_Omap__sel_I2_J,axiom,
! [B: $tType,A: $tType,A2: proces634752977rocess @ A,F: A > B] :
( ( proces10484146Action @ A @ A2 )
=> ( ( proces1778668539contOf @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
= ( proces370407749rocess @ A @ B @ F @ ( proces1778668539contOf @ A @ A2 ) ) ) ) ).
% process.map_sel(2)
thf(fact_44_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_45_mem__Collect__eq,axiom,
! [A: $tType,A2: A,P6: A > $o] :
( ( member @ A @ A2 @ ( collect @ A @ P6 ) )
= ( P6 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_46_Collect__mem__eq,axiom,
! [A: $tType,A6: set @ A] :
( ( collect @ A
@ ^ [X: A] : ( member @ A @ X @ A6 ) )
= A6 ) ).
% Collect_mem_eq
thf(fact_47_Collect__cong,axiom,
! [A: $tType,P6: A > $o,Q3: A > $o] :
( ! [X3: A] :
( ( P6 @ X3 )
= ( Q3 @ X3 ) )
=> ( ( collect @ A @ P6 )
= ( collect @ A @ Q3 ) ) ) ).
% Collect_cong
thf(fact_48_ext,axiom,
! [B: $tType,A: $tType,F: A > B,G: A > B] :
( ! [X3: A] :
( ( F @ X3 )
= ( G @ X3 ) )
=> ( F = G ) ) ).
% ext
thf(fact_49_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_50_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_51_process_Osplit__sel,axiom,
! [B: $tType,A: $tType,P6: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
( ( P6 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
= ( ( ( Process
= ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
=> ( P6 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
& ( ( Process
= ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
=> ( P6 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% process.split_sel
thf(fact_52_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_53_process_Osplit__sel__asm,axiom,
! [B: $tType,A: $tType,P6: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
( ( P6 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
= ( ~ ( ( ( Process
= ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
& ~ ( P6 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
| ( ( Process
= ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
& ~ ( P6 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% process.split_sel_asm
thf(fact_54_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_55_process_Oexpand,axiom,
! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
( ( ( proces10484146Action @ A @ Process )
= ( proces10484146Action @ A @ Process3 ) )
=> ( ( ( proces10484146Action @ A @ Process )
=> ( ( proces10484146Action @ A @ Process3 )
=> ( ( ( proces745025900prefOf @ A @ Process )
= ( proces745025900prefOf @ A @ Process3 ) )
& ( ( proces1778668539contOf @ A @ Process )
= ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
=> ( ( ( proces401113213Choice @ A @ Process )
=> ( ( proces401113213Choice @ A @ Process3 )
=> ( ( ( proces979765041_ch1Of @ A @ Process )
= ( proces979765041_ch1Of @ A @ Process3 ) )
& ( ( proces988026546_ch2Of @ A @ Process )
= ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
=> ( Process = Process3 ) ) ) ) ).
% process.expand
thf(fact_56_process_Ocoinduct,axiom,
! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
( ( R @ Process @ Process3 )
=> ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
( ( R @ Process4 @ Process5 )
=> ( ( ( proces10484146Action @ A @ Process4 )
= ( proces10484146Action @ A @ Process5 ) )
& ( ( proces10484146Action @ A @ Process4 )
=> ( ( proces10484146Action @ A @ Process5 )
=> ( ( ( proces745025900prefOf @ A @ Process4 )
= ( proces745025900prefOf @ A @ Process5 ) )
& ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
& ( ( proces401113213Choice @ A @ Process4 )
=> ( ( proces401113213Choice @ A @ Process5 )
=> ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
& ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
=> ( Process = Process3 ) ) ) ).
% process.coinduct
thf(fact_57_process_Ocoinduct__strong,axiom,
! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
( ( R @ Process @ Process3 )
=> ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
( ( R @ Process4 @ Process5 )
=> ( ( ( proces10484146Action @ A @ Process4 )
= ( proces10484146Action @ A @ Process5 ) )
& ( ( proces10484146Action @ A @ Process4 )
=> ( ( proces10484146Action @ A @ Process5 )
=> ( ( ( proces745025900prefOf @ A @ Process4 )
= ( proces745025900prefOf @ A @ Process5 ) )
& ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
| ( ( proces1778668539contOf @ A @ Process4 )
= ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
& ( ( proces401113213Choice @ A @ Process4 )
=> ( ( proces401113213Choice @ A @ Process5 )
=> ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
| ( ( proces979765041_ch1Of @ A @ Process4 )
= ( proces979765041_ch1Of @ A @ Process5 ) ) )
& ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
| ( ( proces988026546_ch2Of @ A @ Process4 )
= ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
=> ( Process = Process3 ) ) ) ).
% process.coinduct_strong
thf(fact_58_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
@ ^ [X1: A,X23: proces634752977rocess @ A] : ( H @ ( F1 @ X1 @ X23 ) )
@ ^ [X1: proces634752977rocess @ A,X23: proces634752977rocess @ A] : ( H @ ( F2 @ X1 @ X23 ) )
@ Process ) ) ).
% process.case_distrib
thf(fact_59_process_Osel_I2_J,axiom,
! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
= X12 ) ).
% process.sel(2)
thf(fact_60_process_Osel_I3_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
= X21 ) ).
% process.sel(3)
thf(fact_61_process_Osel_I4_J,axiom,
! [A: $tType,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
= X22 ) ).
% process.sel(4)
thf(fact_62_process_Osel_I1_J,axiom,
! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
= X11 ) ).
% process.sel(1)
thf(fact_63_process_Ocorec__sel_I2_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,Q12: C > $o,G11: C > A,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
( ( P @ A2 )
=> ( ( ( Q12 @ A2 )
=> ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( G121 @ A2 ) ) )
& ( ~ ( Q12 @ A2 )
=> ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A2 ) ) ) ) ) ) ).
% process.corec_sel(2)
thf(fact_64_process_Ocorec__sel_I3_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,Q21: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
( ~ ( P @ A2 )
=> ( ( ( Q21 @ A2 )
=> ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( G211 @ A2 ) ) )
& ( ~ ( Q21 @ A2 )
=> ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A2 ) ) ) ) ) ) ).
% process.corec_sel(3)
thf(fact_65_process_Ocorec__sel_I4_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,Q22: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
( ~ ( P @ A2 )
=> ( ( ( Q22 @ A2 )
=> ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( G221 @ A2 ) ) )
& ( ~ ( Q22 @ A2 )
=> ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A2 ) ) ) ) ) ) ).
% process.corec_sel(4)
thf(fact_66_process_Ocorec__sel_I1_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C] :
( ( P @ A2 )
=> ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ A2 ) )
= ( G11 @ A2 ) ) ) ).
% process.corec_sel(1)
thf(fact_67_process_Osimps_I5_J,axiom,
! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X12: proces634752977rocess @ A] :
( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X12 ) )
= ( F1 @ X11 @ X12 ) ) ).
% process.simps(5)
thf(fact_68_process_Osimps_I6_J,axiom,
! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A] :
( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X21 @ X22 ) )
= ( F2 @ X21 @ X22 ) ) ).
% process.simps(6)
thf(fact_69_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_70_solution_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
=> ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
= ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% solution.simps(3)
thf(fact_71_solution_Osimps_I5_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
=> ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
= ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% solution.simps(5)
thf(fact_72_solution_Osimps_I6_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
=> ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
= ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% solution.simps(6)
thf(fact_73_solution_Osimps_I4_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
=> ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
= ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% solution.simps(4)
thf(fact_74_process_Orel__coinduct,axiom,
! [A: $tType,B: $tType,P6: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B,R: A > B > $o] :
( ( P6 @ X4 @ Y )
=> ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
( ( P6 @ Process4 @ Process5 )
=> ( ( ( proces10484146Action @ A @ Process4 )
= ( proces10484146Action @ B @ Process5 ) )
& ( ( proces10484146Action @ A @ Process4 )
=> ( ( proces10484146Action @ B @ Process5 )
=> ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
& ( P6 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
& ( ( proces401113213Choice @ A @ Process4 )
=> ( ( proces401113213Choice @ B @ Process5 )
=> ( ( P6 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
& ( P6 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
=> ( proces749077512rocess @ A @ B @ R @ X4 @ Y ) ) ) ).
% process.rel_coinduct
thf(fact_75_process_Orel__sel,axiom,
! [B: $tType,A: $tType] :
( ( proces749077512rocess @ A @ B )
= ( ^ [R2: A > B > $o,A3: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
( ( ( proces10484146Action @ A @ A3 )
= ( proces10484146Action @ B @ B2 ) )
& ( ( proces10484146Action @ A @ A3 )
=> ( ( proces10484146Action @ B @ B2 )
=> ( ( R2 @ ( proces745025900prefOf @ A @ A3 ) @ ( proces745025900prefOf @ B @ B2 ) )
& ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A3 ) @ ( proces1778668539contOf @ B @ B2 ) ) ) ) )
& ( ( proces401113213Choice @ A @ A3 )
=> ( ( proces401113213Choice @ B @ B2 )
=> ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A3 ) @ ( proces979765041_ch1Of @ B @ B2 ) )
& ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A3 ) @ ( proces988026546_ch2Of @ B @ B2 ) ) ) ) ) ) ) ) ).
% process.rel_sel
thf(fact_76_PREF_Osimps_I2_J,axiom,
! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
= ( proces745025900prefOf @ B @ P ) ) ).
% PREF.simps(2)
thf(fact_77_CH2_Osimps_I2_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
= ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% CH2.simps(2)
thf(fact_78_process_Orel__inject_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
= ( ( R @ X11 @ Y11 )
& ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 ) ) ) ).
% process.rel_inject(1)
thf(fact_79_process_Orel__inject_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,X22: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
= ( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
& ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% process.rel_inject(2)
thf(fact_80_process_Orel__eq,axiom,
! [A: $tType] :
( ( proces749077512rocess @ A @ A
@ ^ [Y3: A,Z: A] : Y3 = Z )
= ( ^ [Y3: proces634752977rocess @ A,Z: proces634752977rocess @ A] : Y3 = Z ) ) ).
% process.rel_eq
thf(fact_81_process_Orel__refl,axiom,
! [B: $tType,Ra: B > B > $o,X4: proces634752977rocess @ B] :
( ! [X3: B] : ( Ra @ X3 @ X3 )
=> ( proces749077512rocess @ B @ B @ Ra @ X4 @ X4 ) ) ).
% process.rel_refl
thf(fact_82_process_Orel__intros_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X12: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
( ( R @ X11 @ Y11 )
=> ( ( proces749077512rocess @ A @ B @ R @ X12 @ Y12 )
=> ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% process.rel_intros(1)
thf(fact_83_process_Orel__intros_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X21: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X22: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ X21 @ Y21 )
=> ( ( proces749077512rocess @ A @ B @ R @ X22 @ Y22 )
=> ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X21 @ X22 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% process.rel_intros(2)
thf(fact_84_process_Orel__map_I2_J,axiom,
! [A: $tType,C: $tType,B: $tType,Sa: A > C > $o,X4: proces634752977rocess @ A,G: B > C,Y: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ C @ Sa @ X4 @ ( proces370407749rocess @ B @ C @ G @ Y ) )
= ( proces749077512rocess @ A @ B
@ ^ [X: A,Y4: B] : ( Sa @ X @ ( G @ Y4 ) )
@ X4
@ Y ) ) ).
% process.rel_map(2)
thf(fact_85_process_Orel__map_I1_J,axiom,
! [A: $tType,C: $tType,B: $tType,Sb: C > B > $o,I: A > C,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B] :
( ( proces749077512rocess @ C @ B @ Sb @ ( proces370407749rocess @ A @ C @ I @ X4 ) @ Y )
= ( proces749077512rocess @ A @ B
@ ^ [X: A] : ( Sb @ ( I @ X ) )
@ X4
@ Y ) ) ).
% process.rel_map(1)
thf(fact_86_solution_Ocode,axiom,
! [B: $tType,A: $tType] :
( ( proces1652378886lution @ A @ B )
= ( ^ [Sys2: A > ( proces554692349s_term @ B @ A ),T3: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys2 @ T3 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys2 @ T3 ) @ ( proces1652378886lution @ A @ B @ Sys2 @ ( proces126235999e_CONT @ 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.code
thf(fact_87_process_Orel__distinct_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X12: proces634752977rocess @ B] :
~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X12 ) ) ).
% process.rel_distinct(2)
thf(fact_88_process_Orel__distinct_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,X12: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X12 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% process.rel_distinct(1)
thf(fact_89_process_Orel__cases,axiom,
! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B3: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ A2 @ B3 )
=> ( ! [X13: A,X24: proces634752977rocess @ A] :
( ( A2
= ( proces1525233512Action @ A @ X13 @ X24 ) )
=> ! [Y1: B,Y23: proces634752977rocess @ B] :
( ( B3
= ( proces1525233512Action @ B @ Y1 @ Y23 ) )
=> ( ( R @ X13 @ Y1 )
=> ~ ( proces749077512rocess @ A @ B @ R @ X24 @ Y23 ) ) ) )
=> ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
( ( A2
= ( proces1915862579Choice @ A @ X1a @ X2a ) )
=> ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
( ( B3
= ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
=> ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
=> ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% process.rel_cases
thf(fact_90_solution_Octr_I1_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
=> ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
= ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% solution.ctr(1)
thf(fact_91_solution_Octr_I2_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
=> ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
= ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% solution.ctr(2)
thf(fact_92_CONT_Osimps_I2_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
= ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% CONT.simps(2)
thf(fact_93_CH1_Osimps_I2_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
= ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% CH1.simps(2)
thf(fact_94_prefOf__def,axiom,
! [A: $tType] :
( ( proces745025900prefOf @ A )
= ( proces1406508781rocess @ A @ A
@ ^ [X113: A,X123: proces634752977rocess @ A] : X113
@ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% prefOf_def
thf(fact_95_process_Oset__sel_I3_J,axiom,
! [A: $tType,A2: proces634752977rocess @ A,Xa: A] :
( ( proces401113213Choice @ A @ A2 )
=> ( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ ( proces979765041_ch1Of @ A @ A2 ) ) )
=> ( member @ A @ Xa @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% process.set_sel(3)
thf(fact_96_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_97_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_98_process_Oset__sel_I2_J,axiom,
! [A: $tType,A2: proces634752977rocess @ A,X4: A] :
( ( proces10484146Action @ A @ A2 )
=> ( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ ( proces1778668539contOf @ A @ A2 ) ) )
=> ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A2 ) ) ) ) ).
% process.set_sel(2)
thf(fact_99_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_100_process_Orel__refl__strong,axiom,
! [A: $tType,X4: proces634752977rocess @ A,Ra: A > A > $o] :
( ! [Z3: A] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( proces749077512rocess @ A @ A @ Ra @ X4 @ X4 ) ) ).
% process.rel_refl_strong
thf(fact_101_process_Orel__mono__strong,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X4: proces634752977rocess @ A,Y: proces634752977rocess @ B,Ra: A > B > $o] :
( ( proces749077512rocess @ A @ B @ R @ X4 @ Y )
=> ( ! [Z3: A,Yb: B] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
=> ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Y ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( proces749077512rocess @ A @ B @ Ra @ X4 @ Y ) ) ) ).
% process.rel_mono_strong
thf(fact_102_process_Orel__cong,axiom,
! [A: $tType,B: $tType,X4: proces634752977rocess @ A,Ya: proces634752977rocess @ A,Y: proces634752977rocess @ B,Xa: proces634752977rocess @ B,R: A > B > $o,Ra: A > B > $o] :
( ( X4 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z3: A,Yb: B] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ Ya ) )
=> ( ( member @ B @ Yb @ ( proces1148692671rocess @ B @ Xa ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( proces749077512rocess @ A @ B @ R @ X4 @ Y )
= ( proces749077512rocess @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% process.rel_cong
thf(fact_103_process_Oset__intros_I1_J,axiom,
! [A: $tType,A1: A,A22: proces634752977rocess @ A] : ( member @ A @ A1 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ).
% process.set_intros(1)
thf(fact_104_process_Oset__intros_I2_J,axiom,
! [A: $tType,X4: A,A22: proces634752977rocess @ A,A1: A] :
( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A22 ) )
=> ( member @ A @ X4 @ ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ A1 @ A22 ) ) ) ) ).
% process.set_intros(2)
thf(fact_105_process_Oset__intros_I3_J,axiom,
! [A: $tType,Xa: A,A1a: proces634752977rocess @ A,A2a: proces634752977rocess @ A] :
( ( member @ A @ Xa @ ( proces1148692671rocess @ A @ A1a ) )
=> ( member @ A @ Xa @ ( proces1148692671rocess @ A @ ( proces1915862579Choice @ A @ A1a @ A2a ) ) ) ) ).
% process.set_intros(3)
thf(fact_106_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_107_process_Oinj__map__strong,axiom,
! [B: $tType,A: $tType,X4: proces634752977rocess @ A,Xa: proces634752977rocess @ A,F: A > B,Fa: A > B] :
( ! [Z3: A,Za: A] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
=> ( ( member @ A @ Za @ ( proces1148692671rocess @ A @ Xa ) )
=> ( ( ( F @ Z3 )
= ( Fa @ Za ) )
=> ( Z3 = Za ) ) ) )
=> ( ( ( proces370407749rocess @ A @ B @ F @ X4 )
= ( proces370407749rocess @ A @ B @ Fa @ Xa ) )
=> ( X4 = Xa ) ) ) ).
% process.inj_map_strong
thf(fact_108_process_Omap__cong0,axiom,
! [B: $tType,A: $tType,X4: proces634752977rocess @ A,F: A > B,G: A > B] :
( ! [Z3: A] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ X4 ) )
=> ( ( F @ Z3 )
= ( G @ Z3 ) ) )
=> ( ( proces370407749rocess @ A @ B @ F @ X4 )
= ( proces370407749rocess @ A @ B @ G @ X4 ) ) ) ).
% process.map_cong0
thf(fact_109_process_Omap__cong,axiom,
! [B: $tType,A: $tType,X4: proces634752977rocess @ A,Ya: proces634752977rocess @ A,F: A > B,G: A > B] :
( ( X4 = Ya )
=> ( ! [Z3: A] :
( ( member @ A @ Z3 @ ( proces1148692671rocess @ A @ Ya ) )
=> ( ( F @ Z3 )
= ( G @ Z3 ) ) )
=> ( ( proces370407749rocess @ A @ B @ F @ X4 )
= ( proces370407749rocess @ A @ B @ G @ Ya ) ) ) ) ).
% process.map_cong
thf(fact_110_contOf__def,axiom,
! [A: $tType] :
( ( proces1778668539contOf @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [X113: A,X123: proces634752977rocess @ A] : X123
@ ^ [Uu2: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% contOf_def
thf(fact_111_ch1Of__def,axiom,
! [A: $tType] :
( ( proces979765041_ch1Of @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
@ ^ [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X212 ) ) ).
% ch1Of_def
thf(fact_112_ch2Of__def,axiom,
! [A: $tType] :
( ( proces988026546_ch2Of @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [Uu2: A,Uv2: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
@ ^ [X212: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X222 ) ) ).
% ch2Of_def
thf(fact_113_process_Oset__induct,axiom,
! [A: $tType,X4: A,A2: proces634752977rocess @ A,P6: A > ( proces634752977rocess @ A ) > $o] :
( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ A2 ) )
=> ( ! [Z1: A,Z2: proces634752977rocess @ A] : ( P6 @ Z1 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) )
=> ( ! [Z1: A,Z2: proces634752977rocess @ A,Xa2: A] :
( ( member @ A @ Xa2 @ ( proces1148692671rocess @ A @ Z2 ) )
=> ( ( P6 @ Xa2 @ Z2 )
=> ( P6 @ Xa2 @ ( proces1525233512Action @ A @ Z1 @ Z2 ) ) ) )
=> ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xb2: A] :
( ( member @ A @ Xb2 @ ( proces1148692671rocess @ A @ Z1a ) )
=> ( ( P6 @ Xb2 @ Z1a )
=> ( P6 @ Xb2 @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
=> ( ! [Z1a: proces634752977rocess @ A,Z2a: proces634752977rocess @ A,Xc: A] :
( ( member @ A @ Xc @ ( proces1148692671rocess @ A @ Z2a ) )
=> ( ( P6 @ Xc @ Z2a )
=> ( P6 @ Xc @ ( proces1915862579Choice @ A @ Z1a @ Z2a ) ) ) )
=> ( P6 @ X4 @ A2 ) ) ) ) ) ) ).
% process.set_induct
thf(fact_114_process_Osimps_I21_J,axiom,
! [A: $tType,X11: A,X12: proces634752977rocess @ A] :
( ( proces1148692671rocess @ A @ ( proces1525233512Action @ A @ X11 @ X12 ) )
= ( insert @ A @ X11 @ ( proces1148692671rocess @ A @ X12 ) ) ) ).
% process.simps(21)
thf(fact_115_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_116_process__term_Oset__intros_I1_J,axiom,
! [Pvar: $tType,A: $tType,X4: A,Aa2: proces634752977rocess @ A] :
( ( member @ A @ X4 @ ( proces1148692671rocess @ A @ Aa2 ) )
=> ( member @ A @ X4 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ Aa2 ) ) ) ) ).
% process_term.set_intros(1)
thf(fact_117_process__term_Osimps_I26_J,axiom,
! [Pvar: $tType,C: $tType,B: $tType,A: $tType,F1: A > B,F2: Pvar > C,X2: proces634752977rocess @ A] :
( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
= ( proces1062592052s_PROC @ B @ C @ ( proces370407749rocess @ A @ B @ F1 @ X2 ) ) ) ).
% process_term.simps(26)
thf(fact_118_PREF_Osimps_I1_J,axiom,
! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X5: A] :
( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( Sys @ X5 ) ) ) ).
% PREF.simps(1)
thf(fact_119_process__term_Oinject_I1_J,axiom,
! [A: $tType,Pvar: $tType,X14: Pvar,Y13: Pvar] :
( ( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
= ( proces1627516585ss_VAR @ Pvar @ A @ Y13 ) )
= ( X14 = Y13 ) ) ).
% process_term.inject(1)
thf(fact_120_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
@ ^ [X: Pvar] : ( H @ ( F1 @ X ) )
@ ^ [X: proces634752977rocess @ A] : ( H @ ( F2 @ X ) )
@ ^ [X1: A,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X1 @ X23 ) )
@ ^ [X1: proces554692349s_term @ A @ Pvar,X23: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X1 @ X23 ) )
@ Process_term ) ) ).
% process_term.case_distrib
thf(fact_121_process__term_Omap__ident,axiom,
! [B: $tType,A: $tType,T: proces554692349s_term @ A @ B] :
( ( proces224683037s_term @ A @ A @ B @ B
@ ^ [X: A] : X
@ ^ [X: B] : X
@ T )
= T ) ).
% process_term.map_ident
thf(fact_122_process__term_Osimps_I25_J,axiom,
! [A: $tType,B: $tType,C: $tType,Pvar: $tType,F1: A > B,F2: Pvar > C,X14: Pvar] :
( ( proces224683037s_term @ A @ B @ Pvar @ C @ F1 @ F2 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
= ( proces1627516585ss_VAR @ C @ B @ ( F2 @ X14 ) ) ) ).
% process_term.simps(25)
thf(fact_123_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,X14: Pvar] :
( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
= ( F1 @ X14 ) ) ).
% process_term.simps(17)
thf(fact_124_process__term_Odistinct_I1_J,axiom,
! [Pvar: $tType,A: $tType,X14: Pvar,X2: proces634752977rocess @ A] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
!= ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% process_term.distinct(1)
thf(fact_125_isACT_Osimps_I1_J,axiom,
! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X5: A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X5 ) )
= ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( Sys @ X5 ) ) ) ).
% isACT.simps(1)
thf(fact_126_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_127_CONT_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
@ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( Sys @ X5 ) ) ) ).
% CONT.simps(1)
thf(fact_128_CH2_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
@ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
@ ( Sys @ X5 ) ) ) ).
% CH2.simps(1)
thf(fact_129_CH1_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
@ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
@ ( Sys @ X5 ) ) ) ).
% CH1.simps(1)
thf(fact_130_insertCI,axiom,
! [A: $tType,A2: A,B4: set @ A,B3: A] :
( ( ~ ( member @ A @ A2 @ B4 )
=> ( A2 = B3 ) )
=> ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% insertCI
thf(fact_131_insert__iff,axiom,
! [A: $tType,A2: A,B3: A,A6: set @ A] :
( ( member @ A @ A2 @ ( insert @ A @ B3 @ A6 ) )
= ( ( A2 = B3 )
| ( member @ A @ A2 @ A6 ) ) ) ).
% insert_iff
thf(fact_132_insert__absorb2,axiom,
! [A: $tType,X4: A,A6: set @ A] :
( ( insert @ A @ X4 @ ( insert @ A @ X4 @ A6 ) )
= ( insert @ A @ X4 @ A6 ) ) ).
% insert_absorb2
thf(fact_133_solution__VAR,axiom,
! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
( ( proces1121166967uarded @ A @ B @ A @ Sys )
=> ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X5 ) )
= ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X5 ) ) ) ) ).
% solution_VAR
thf(fact_134_mk__disjoint__insert,axiom,
! [A: $tType,A2: A,A6: set @ A] :
( ( member @ A @ A2 @ A6 )
=> ? [B5: set @ A] :
( ( A6
= ( insert @ A @ A2 @ B5 ) )
& ~ ( member @ A @ A2 @ B5 ) ) ) ).
% mk_disjoint_insert
thf(fact_135_insert__commute,axiom,
! [A: $tType,X4: A,Y: A,A6: set @ A] :
( ( insert @ A @ X4 @ ( insert @ A @ Y @ A6 ) )
= ( insert @ A @ Y @ ( insert @ A @ X4 @ A6 ) ) ) ).
% insert_commute
thf(fact_136_insert__eq__iff,axiom,
! [A: $tType,A2: A,A6: set @ A,B3: A,B4: set @ A] :
( ~ ( member @ A @ A2 @ A6 )
=> ( ~ ( member @ A @ B3 @ B4 )
=> ( ( ( insert @ A @ A2 @ A6 )
= ( insert @ A @ B3 @ B4 ) )
= ( ( ( A2 = B3 )
=> ( A6 = B4 ) )
& ( ( A2 != B3 )
=> ? [C2: set @ A] :
( ( A6
= ( insert @ A @ B3 @ C2 ) )
& ~ ( member @ A @ B3 @ C2 )
& ( B4
= ( insert @ A @ A2 @ C2 ) )
& ~ ( member @ A @ A2 @ C2 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_137_insert__absorb,axiom,
! [A: $tType,A2: A,A6: set @ A] :
( ( member @ A @ A2 @ A6 )
=> ( ( insert @ A @ A2 @ A6 )
= A6 ) ) ).
% insert_absorb
thf(fact_138_insert__ident,axiom,
! [A: $tType,X4: A,A6: set @ A,B4: set @ A] :
( ~ ( member @ A @ X4 @ A6 )
=> ( ~ ( member @ A @ X4 @ B4 )
=> ( ( ( insert @ A @ X4 @ A6 )
= ( insert @ A @ X4 @ B4 ) )
= ( A6 = B4 ) ) ) ) ).
% insert_ident
thf(fact_139_Set_Oset__insert,axiom,
! [A: $tType,X4: A,A6: set @ A] :
( ( member @ A @ X4 @ A6 )
=> ~ ! [B5: set @ A] :
( ( A6
= ( insert @ A @ X4 @ B5 ) )
=> ( member @ A @ X4 @ B5 ) ) ) ).
% Set.set_insert
thf(fact_140_insertI2,axiom,
! [A: $tType,A2: A,B4: set @ A,B3: A] :
( ( member @ A @ A2 @ B4 )
=> ( member @ A @ A2 @ ( insert @ A @ B3 @ B4 ) ) ) ).
% insertI2
thf(fact_141_insertI1,axiom,
! [A: $tType,A2: A,B4: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B4 ) ) ).
% insertI1
thf(fact_142_insertE,axiom,
! [A: $tType,A2: A,B3: A,A6: set @ A] :
( ( member @ A @ A2 @ ( insert @ A @ B3 @ A6 ) )
=> ( ( A2 != B3 )
=> ( member @ A @ A2 @ A6 ) ) ) ).
% insertE
thf(fact_143_guarded__def,axiom,
! [C: $tType,B: $tType,A: $tType] :
( ( proces1121166967uarded @ A @ B @ C )
= ( ^ [Sys2: A > ( proces554692349s_term @ B @ C )] :
! [X6: A,Y5: C] :
( ( Sys2 @ X6 )
!= ( proces1627516585ss_VAR @ C @ B @ Y5 ) ) ) ) ).
% guarded_def
thf(fact_144_insert__compr,axiom,
! [A: $tType] :
( ( insert @ A )
= ( ^ [A3: A,B6: set @ A] :
( collect @ A
@ ^ [X: A] :
( ( X = A3 )
| ( member @ A @ X @ B6 ) ) ) ) ) ).
% insert_compr
thf(fact_145_insert__Collect,axiom,
! [A: $tType,A2: A,P6: A > $o] :
( ( insert @ A @ A2 @ ( collect @ A @ P6 ) )
= ( collect @ A
@ ^ [U: A] :
( ( U != A2 )
=> ( P6 @ U ) ) ) ) ).
% insert_Collect
thf(fact_146_isACT__VAR,axiom,
! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X5: A] :
( ( proces1121166967uarded @ A @ B @ A @ Sys )
=> ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X5 ) )
= ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X5 ) ) ) ) ).
% isACT_VAR
thf(fact_147_isACT_Oelims_I2_J,axiom,
! [C: $tType,B: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X7 ) )
=> ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X4 @ X7 ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ~ ( proces10484146Action @ D @ P4 ) )
=> ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
( Xa
!= ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ).
% isACT.elims(2)
thf(fact_148_isACT_Oelims_I3_J,axiom,
! [C: $tType,B: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X7 ) )
=> ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X4 @ X7 ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( proces10484146Action @ D @ P4 ) )
=> ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
( Xa
!= ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% isACT.elims(3)
thf(fact_149_CH2_Oelims,axiom,
! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
( ( ( proces1239275104le_CH2 @ A @ B @ X4 @ Xa )
= Y )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( Y
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
@ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
@ ( X4 @ X7 ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( Y
!= ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
=> ( Y != T23 ) )
=> ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
( Xa
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( Y
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CH2.elims
thf(fact_150_CH1_Oelims,axiom,
! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
( ( ( proces1239275103le_CH1 @ A @ B @ X4 @ Xa )
= Y )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( Y
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
@ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
@ ( X4 @ X7 ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( Y
!= ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A] :
( ? [T23: proces554692349s_term @ B @ A] :
( Xa
= ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
=> ( Y != T12 ) )
=> ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
( Xa
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( Y
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CH1.elims
thf(fact_151_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_152_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_153_process__term_Osimps_I47_J,axiom,
! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
= ( insert @ A @ X31 @ ( proces1264666542s_term @ A @ Pvar @ X32 ) ) ) ).
% process_term.simps(47)
thf(fact_154_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_155_isACT_Osimps_I4_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T13: proces554692349s_term @ D @ A,T24: proces554692349s_term @ D @ A] :
~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T13 @ T24 ) ) ).
% isACT.simps(4)
thf(fact_156_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_157_isACT_Osimps_I3_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: D,T2: proces554692349s_term @ D @ A] : ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1454156180ss_ACT @ D @ A @ A2 @ T2 ) ) ).
% isACT.simps(3)
thf(fact_158_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_159_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_160_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_161_process__term_Oset__intros_I2_J,axiom,
! [Pvar: $tType,A: $tType,A1: A,A22: proces554692349s_term @ A @ Pvar] : ( member @ A @ A1 @ ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1 @ A22 ) ) ) ).
% process_term.set_intros(2)
thf(fact_162_process__term_Oset__intros_I3_J,axiom,
! [Pvar: $tType,A: $tType,Xa: A,A22: proces554692349s_term @ A @ Pvar,A1: A] :
( ( member @ A @ Xa @ ( proces1264666542s_term @ A @ Pvar @ A22 ) )
=> ( member @ A @ Xa @ ( proces1264666542s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1 @ A22 ) ) ) ) ).
% process_term.set_intros(3)
thf(fact_163_process__term_Oset__intros_I4_J,axiom,
! [Pvar: $tType,A: $tType,Xc2: A,A1a: proces554692349s_term @ A @ Pvar,A2a: proces554692349s_term @ A @ Pvar] :
( ( member @ A @ Xc2 @ ( proces1264666542s_term @ A @ Pvar @ A1a ) )
=> ( member @ A @ Xc2 @ ( proces1264666542s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1a @ A2a ) ) ) ) ).
% process_term.set_intros(4)
thf(fact_164_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_165_process__term_Odistinct_I3_J,axiom,
! [Pvar: $tType,A: $tType,X14: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
!= ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% process_term.distinct(3)
thf(fact_166_process__term_Odistinct_I5_J,axiom,
! [Pvar: $tType,A: $tType,X14: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X14 )
!= ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% process_term.distinct(5)
thf(fact_167_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_168_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_169_process__term_Oexhaust,axiom,
! [Pvar: $tType,A: $tType,Y: proces554692349s_term @ A @ Pvar] :
( ! [X13: Pvar] :
( Y
!= ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
=> ( ! [X24: proces634752977rocess @ A] :
( Y
!= ( proces1062592052s_PROC @ A @ Pvar @ X24 ) )
=> ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
( Y
!= ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
=> ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
( Y
!= ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% process_term.exhaust
thf(fact_170_process__term_Oinduct,axiom,
! [Pvar: $tType,A: $tType,P6: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
( ! [X3: Pvar] : ( P6 @ ( proces1627516585ss_VAR @ Pvar @ A @ X3 ) )
=> ( ! [X3: proces634752977rocess @ A] : ( P6 @ ( proces1062592052s_PROC @ A @ Pvar @ X3 ) )
=> ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
( ( P6 @ X2a )
=> ( P6 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
=> ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
( ( P6 @ X1a )
=> ( ( P6 @ X2a )
=> ( P6 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
=> ( P6 @ Process_term ) ) ) ) ) ).
% process_term.induct
thf(fact_171_isACT_Oinduct,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,P6: ( 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 ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P6 @ Sys3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
=> ( P6 @ A0 @ A1 ) ) ) ) ) ).
% isACT.induct
thf(fact_172_PREF_Oinduct,axiom,
! [C: $tType,A: $tType,B: $tType,P6: ( 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 ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( ! [A4: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( P6 @ A0 @ A1 ) ) ) ) ) ).
% PREF.induct
thf(fact_173_CONT_Oinduct,axiom,
! [A: $tType,B: $tType,P6: ( 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 ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( P6 @ A0 @ A1 ) ) ) ) ) ).
% CONT.induct
thf(fact_174_CH2_Oinduct,axiom,
! [A: $tType,B: $tType,P6: ( 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 ),X7: A] : ( P6 @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P6 @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P6 @ Sys3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
=> ( ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P6 @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( P6 @ A0 @ A1 ) ) ) ) ) ).
% CH2.induct
thf(fact_175_CH1_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] :
( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T13 @ T24 ) )
= T13 ) ).
% CH1.simps(3)
thf(fact_176_CH2_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] :
( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T13 @ T24 ) )
= T24 ) ).
% CH2.simps(3)
thf(fact_177_CONT_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
= T2 ) ).
% CONT.simps(3)
thf(fact_178_PREF_Osimps_I3_J,axiom,
! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
= A2 ) ).
% PREF.simps(3)
thf(fact_179_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_180_isACT_Oelims_I1_J,axiom,
! [D: $tType,A: $tType,B: $tType,C: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
( ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
= Y )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X7 ) )
=> ( Y
= ( ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X4 @ X7 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( Y
= ( ~ ( proces10484146Action @ D @ P4 ) ) ) )
=> ( ( ? [A4: D,T4: proces554692349s_term @ D @ A] :
( Xa
= ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
=> ~ Y )
=> ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
( Xa
= ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
=> Y ) ) ) ) ) ).
% isACT.elims(1)
thf(fact_181_PREF_Oelims,axiom,
! [A: $tType,C: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
( ( ( proces1708129104e_PREF @ A @ B @ C @ X4 @ Xa )
= Y )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( Y
!= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( X4 @ X7 ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( Y
!= ( proces745025900prefOf @ B @ P4 ) ) )
=> ( ! [A4: B] :
( ? [T4: proces554692349s_term @ B @ A] :
( Xa
= ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( Y != A4 ) )
=> ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( Xa
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( Y
!= ( undefined @ B ) ) ) ) ) ) ) ).
% PREF.elims
thf(fact_182_CONT_Oelims,axiom,
! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
( ( ( proces126235999e_CONT @ A @ B @ X4 @ Xa )
= Y )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( Y
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
@ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( X4 @ X7 ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( Y
!= ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) )
=> ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( Y != T4 ) )
=> ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( Xa
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( Y
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CONT.elims
thf(fact_183_process__term_Orel__cases,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,A2: proces554692349s_term @ A @ Pvar,B3: proces554692349s_term @ B @ C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B3 )
=> ( ! [X3: Pvar] :
( ( A2
= ( proces1627516585ss_VAR @ Pvar @ A @ X3 ) )
=> ! [Y6: C] :
( ( B3
= ( proces1627516585ss_VAR @ C @ B @ Y6 ) )
=> ~ ( R22 @ X3 @ Y6 ) ) )
=> ( ! [Xa2: proces634752977rocess @ A] :
( ( A2
= ( proces1062592052s_PROC @ A @ Pvar @ Xa2 ) )
=> ! [Ya2: proces634752977rocess @ B] :
( ( B3
= ( proces1062592052s_PROC @ B @ C @ Ya2 ) )
=> ~ ( proces749077512rocess @ A @ B @ R1 @ Xa2 @ Ya2 ) ) )
=> ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
=> ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
( ( B3
= ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
=> ( ( R1 @ X1a @ Y1a )
=> ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ 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] :
( ( B3
= ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
=> ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
=> ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% process_term.rel_cases
thf(fact_184_process__term_Orel__induct,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X4: proces554692349s_term @ A @ Pvar,Y: proces554692349s_term @ B @ C,Q3: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X4 @ Y )
=> ( ! [A12: Pvar,B1: C] :
( ( R22 @ A12 @ B1 )
=> ( Q3 @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
=> ( ! [A23: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R1 @ A23 @ B22 )
=> ( Q3 @ ( proces1062592052s_PROC @ A @ Pvar @ A23 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
=> ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
( ( R1 @ A31 @ B31 )
=> ( ( Q3 @ A32 @ B32 )
=> ( Q3 @ ( 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] :
( ( Q3 @ A41 @ B41 )
=> ( ( Q3 @ A42 @ B42 )
=> ( Q3 @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
=> ( Q3 @ X4 @ Y ) ) ) ) ) ) ).
% process_term.rel_induct
thf(fact_185_isACT_Ocases,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: D,T4: proces554692349s_term @ D @ A] :
( X4
!= ( 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,T23: proces554692349s_term @ D @ A] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys3 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% isACT.cases
thf(fact_186_process__term_Orel__inject_I4_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: 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 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
= ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
& ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% process_term.rel_inject(4)
thf(fact_187_process__term_Orel__inject_I3_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
= ( ( R1 @ X31 @ Y31 )
& ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% process_term.rel_inject(3)
thf(fact_188_process__term_Orel__intros_I4_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: 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 @ R22 @ X41 @ Y41 )
=> ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% process_term.rel_intros(4)
thf(fact_189_process__term_Orel__intros_I3_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X31: A,Y31: B,R22: Pvar > C > $o,X32: proces554692349s_term @ A @ Pvar,Y32: proces554692349s_term @ B @ C] :
( ( R1 @ X31 @ Y31 )
=> ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% process_term.rel_intros(3)
thf(fact_190_process__term_Orel__inject_I1_J,axiom,
! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y13: C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1627516585ss_VAR @ C @ B @ Y13 ) )
= ( R22 @ X14 @ Y13 ) ) ).
% process_term.rel_inject(1)
thf(fact_191_process__term_Orel__intros_I1_J,axiom,
! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X14: Pvar,Y13: C,R1: A > B > $o] :
( ( R22 @ X14 @ Y13 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1627516585ss_VAR @ C @ B @ Y13 ) ) ) ).
% process_term.rel_intros(1)
thf(fact_192_process__term_Orel__refl,axiom,
! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X4: proces554692349s_term @ C @ D] :
( ! [X3: C] : ( R1a @ X3 @ X3 )
=> ( ! [X3: D] : ( R2a @ X3 @ X3 )
=> ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X4 @ X4 ) ) ) ).
% process_term.rel_refl
thf(fact_193_process__term_Orel__eq,axiom,
! [B: $tType,A: $tType] :
( ( proces2029722208s_term @ A @ A @ B @ B
@ ^ [Y3: A,Z: A] : Y3 = Z
@ ^ [Y3: B,Z: B] : Y3 = Z )
= ( ^ [Y3: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : Y3 = Z ) ) ).
% process_term.rel_eq
thf(fact_194_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,X4: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D] :
( ( proces2029722208s_term @ E2 @ C @ F5 @ D @ S1b @ S2b @ ( proces224683037s_term @ A @ E2 @ B @ F5 @ I1 @ I2 @ X4 ) @ Y )
= ( proces2029722208s_term @ A @ C @ B @ D
@ ^ [X: A] : ( S1b @ ( I1 @ X ) )
@ ^ [X: B] : ( S2b @ ( I2 @ X ) )
@ X4
@ Y ) ) ).
% process_term.rel_map(1)
thf(fact_195_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,X4: proces554692349s_term @ A @ B,G1: C > E2,G2: D > F5,Y: proces554692349s_term @ C @ D] :
( ( proces2029722208s_term @ A @ E2 @ B @ F5 @ S1a @ S2a @ X4 @ ( proces224683037s_term @ C @ E2 @ D @ F5 @ G1 @ G2 @ Y ) )
= ( proces2029722208s_term @ A @ C @ B @ D
@ ^ [X: A,Y4: C] : ( S1a @ X @ ( G1 @ Y4 ) )
@ ^ [X: B,Y4: D] : ( S2a @ X @ ( G2 @ Y4 ) )
@ X4
@ Y ) ) ).
% process_term.rel_map(2)
thf(fact_196_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,R22: Pvar > C > $o] :
( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% process_term.rel_intros(2)
thf(fact_197_process__term_Orel__inject_I2_J,axiom,
! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
= ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% process_term.rel_inject(2)
thf(fact_198_process__term_Orel__distinct_I2_J,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X14: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% process_term.rel_distinct(2)
thf(fact_199_process__term_Orel__distinct_I1_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y2: proces634752977rocess @ B] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% process_term.rel_distinct(1)
thf(fact_200_process__term_Orel__distinct_I10_J,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% process_term.rel_distinct(10)
thf(fact_201_process__term_Orel__distinct_I9_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% process_term.rel_distinct(9)
thf(fact_202_process__term_Orel__distinct_I8_J,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% process_term.rel_distinct(8)
thf(fact_203_process__term_Orel__distinct_I7_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y31: B,Y32: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% process_term.rel_distinct(7)
thf(fact_204_process__term_Orel__distinct_I6_J,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X14: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% process_term.rel_distinct(6)
thf(fact_205_process__term_Orel__distinct_I5_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% process_term.rel_distinct(5)
thf(fact_206_process__term_Orel__distinct_I4_J,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X14: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X14 ) ) ).
% process_term.rel_distinct(4)
thf(fact_207_process__term_Orel__distinct_I3_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X14: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% process_term.rel_distinct(3)
thf(fact_208_process__term_Orel__distinct_I11_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: 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 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% process_term.rel_distinct(11)
thf(fact_209_process__term_Orel__distinct_I12_J,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: 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 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% process_term.rel_distinct(12)
thf(fact_210_CH2_Ocases,axiom,
! [A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
=> ~ ! [A4: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% CH2.cases
thf(fact_211_CONT_Ocases,axiom,
! [A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys3: A > ( proces554692349s_term @ B @ A ),X7: A] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ A ),A4: B,T4: proces554692349s_term @ B @ A] :
( X4
!= ( 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] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% CONT.cases
thf(fact_212_PREF_Ocases,axiom,
! [C: $tType,A: $tType,B: $tType,X4: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys3: A > ( proces554692349s_term @ B @ C ),X7: A] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys3 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
=> ( ! [Sys3: A > ( proces554692349s_term @ B @ C ),A4: B,T4: proces554692349s_term @ B @ A] :
( X4
!= ( 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] :
( X4
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% PREF.cases
thf(fact_213_CH1_Opelims,axiom,
! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
( ( ( proces1239275103le_CH1 @ A @ B @ X4 @ Xa )
= Y )
=> ( ( 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 ) @ X4 @ Xa ) )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( ( Y
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P2 ) )
@ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T1
@ ( X4 @ X7 ) ) )
=> ~ ( 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 ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ( Y
= ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) )
=> ~ ( 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 ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
=> ( ( Y = 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 ) @ X4 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
=> ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( ( Y
= ( 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 ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CH1.pelims
thf(fact_214_CH2_Opelims,axiom,
! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
( ( ( proces1239275104le_CH2 @ A @ B @ X4 @ Xa )
= Y )
=> ( ( 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 ) @ X4 @ Xa ) )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( ( Y
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P2 ) )
@ ^ [A3: B,B2: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] : T22
@ ( X4 @ X7 ) ) )
=> ~ ( 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 ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ( Y
= ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) )
=> ~ ( 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 ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
=> ( ( Y = T23 )
=> ~ ( 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 ) @ X4 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
=> ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( ( Y
= ( 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 ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CH2.pelims
thf(fact_215_CONT_Opelims,axiom,
! [A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y: proces554692349s_term @ B @ A] :
( ( ( proces126235999e_CONT @ A @ B @ X4 @ Xa )
= Y )
=> ( ( 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 ) @ X4 @ Xa ) )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( ( Y
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P2: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P2 ) )
@ ^ [A3: B,T3: proces554692349s_term @ B @ A] : T3
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( X4 @ X7 ) ) )
=> ~ ( 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 ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ( Y
= ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) )
=> ~ ( 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 ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
=> ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( ( Y = 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 ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
=> ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( ( Y
= ( 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 ) @ X4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CONT.pelims
thf(fact_216_PREF_Opelims,axiom,
! [C: $tType,A: $tType,B: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y: B] :
( ( ( proces1708129104e_PREF @ A @ B @ C @ X4 @ Xa )
= Y )
=> ( ( 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 ) @ X4 @ Xa ) )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X7 ) )
=> ( ( Y
= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : A3
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( X4 @ X7 ) ) )
=> ~ ( 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 ) @ X4 @ ( proces1627516585ss_VAR @ A @ B @ X7 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ( Y
= ( proces745025900prefOf @ B @ P4 ) )
=> ~ ( 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 ) @ X4 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
=> ( ! [A4: B,T4: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) )
=> ( ( Y = 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 ) @ X4 @ ( proces1454156180ss_ACT @ B @ A @ A4 @ T4 ) ) ) ) )
=> ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( ( Y
= ( 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 ) @ X4 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% PREF.pelims
thf(fact_217_isACT_Opelims_I1_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y: $o] :
( ( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
= Y )
=> ( ( 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 ) @ X4 @ Xa ) )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X7 ) )
=> ( ( Y
= ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X4 @ X7 ) ) )
=> ~ ( 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 ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( ( Y
= ( proces10484146Action @ D @ P4 ) )
=> ~ ( 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 ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) ) ) )
=> ( ! [A4: D,T4: proces554692349s_term @ D @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) )
=> ( Y
=> ~ ( 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 ) @ X4 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) )
=> ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
( ( Xa
= ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
=> ( ~ Y
=> ~ ( 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 ) @ X4 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% isACT.pelims(1)
thf(fact_218_isACT_Opelims_I3_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
=> ( ( 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 ) @ X4 @ Xa ) )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X7 ) )
=> ( ( 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 ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
=> ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X4 @ X7 ) ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( ( 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 ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
=> ( proces10484146Action @ D @ P4 ) ) )
=> ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
( ( Xa
= ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
=> ~ ( 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 ) @ X4 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% isACT.pelims(3)
thf(fact_219_isACT_Opelims_I2_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X4: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ X4 @ Xa )
=> ( ( 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 ) @ X4 @ Xa ) )
=> ( ! [X7: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X7 ) )
=> ( ( 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 ) @ X4 @ ( proces1627516585ss_VAR @ A @ D @ X7 ) ) )
=> ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A3: B,T3: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X4 @ X7 ) ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( ( 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 ) @ X4 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
=> ~ ( proces10484146Action @ D @ P4 ) ) )
=> ~ ! [A4: D,T4: proces554692349s_term @ D @ A] :
( ( Xa
= ( 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 ) @ X4 @ ( proces1454156180ss_ACT @ D @ A @ A4 @ T4 ) ) ) ) ) ) ) ) ).
% isACT.pelims(2)
thf(fact_220_pred__equals__eq2,axiom,
! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
( ( ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ R ) )
= ( ^ [X: A,Y4: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y4 ) @ S ) ) )
= ( R = S ) ) ).
% pred_equals_eq2
thf(fact_221_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_222_process__term_Oset__intros_I6_J,axiom,
! [A: $tType,Pvar: $tType,Ab2: Pvar] : ( member @ Pvar @ Ab2 @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab2 ) ) ) ).
% process_term.set_intros(6)
thf(fact_223_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_224_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_225_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_226_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_227_process__term_Orel__refl__strong,axiom,
! [B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
=> ( R1a @ Z1 @ Z1 ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
=> ( R2a @ Z2 @ Z2 ) )
=> ( proces2029722208s_term @ A @ A @ B @ B @ R1a @ R2a @ X4 @ X4 ) ) ) ).
% process_term.rel_refl_strong
thf(fact_228_process__term_Orel__mono__strong,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,X4: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
( ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ X4 @ Y )
=> ( ! [Z1: A,Y1: C] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
=> ( ( member @ C @ Y1 @ ( proces1264666542s_term @ C @ D @ Y ) )
=> ( ( R1 @ Z1 @ Y1 )
=> ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z2: B,Y23: D] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
=> ( ( member @ D @ Y23 @ ( proces1493547885s_term @ C @ D @ Y ) )
=> ( ( R22 @ Z2 @ Y23 )
=> ( R2a @ Z2 @ Y23 ) ) ) )
=> ( proces2029722208s_term @ A @ C @ B @ D @ R1a @ R2a @ X4 @ Y ) ) ) ) ).
% process_term.rel_mono_strong
thf(fact_229_process__term_Orel__cong,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,Y: proces554692349s_term @ C @ D,Xa: proces554692349s_term @ C @ D,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
( ( X4 = Ya )
=> ( ( Y = Xa )
=> ( ! [Z1: A,Y1: C] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
=> ( ( member @ C @ Y1 @ ( proces1264666542s_term @ C @ D @ Xa ) )
=> ( ( R1 @ Z1 @ Y1 )
= ( R1a @ Z1 @ Y1 ) ) ) )
=> ( ! [Z2: B,Y23: D] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
=> ( ( member @ D @ Y23 @ ( proces1493547885s_term @ C @ D @ Xa ) )
=> ( ( R22 @ Z2 @ Y23 )
= ( R2a @ Z2 @ Y23 ) ) ) )
=> ( ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ X4 @ Y )
= ( proces2029722208s_term @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% process_term.rel_cong
thf(fact_230_process__term_Omap__cong,axiom,
! [D: $tType,C: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
( ( X4 = Ya )
=> ( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
=> ( ( F1 @ Z1 )
= ( G1 @ Z1 ) ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
=> ( ( F2 @ Z2 )
= ( G2 @ Z2 ) ) )
=> ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
= ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ) ).
% process_term.map_cong
thf(fact_231_process__term_Omap__cong0,axiom,
! [D: $tType,C: $tType,B: $tType,A: $tType,X4: 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 @ X4 ) )
=> ( ( F1 @ Z1 )
= ( G1 @ Z1 ) ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
=> ( ( F2 @ Z2 )
= ( G2 @ Z2 ) ) )
=> ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
= ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ X4 ) ) ) ) ).
% process_term.map_cong0
thf(fact_232_process__term_Oinj__map__strong,axiom,
! [C: $tType,D: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Xa: 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 @ X4 ) )
=> ( ( member @ A @ Z1a @ ( proces1264666542s_term @ A @ B @ Xa ) )
=> ( ( ( F1 @ Z1 )
= ( F1a @ Z1a ) )
=> ( Z1 = Z1a ) ) ) )
=> ( ! [Z2: B,Z2a: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
=> ( ( member @ B @ Z2a @ ( proces1493547885s_term @ A @ B @ Xa ) )
=> ( ( ( F2 @ Z2 )
= ( F2a @ Z2a ) )
=> ( Z2 = Z2a ) ) ) )
=> ( ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
= ( proces224683037s_term @ A @ C @ B @ D @ F1a @ F2a @ Xa ) )
=> ( X4 = Xa ) ) ) ) ).
% process_term.inj_map_strong
thf(fact_233_process__term_Osimps_I49_J,axiom,
! [A: $tType,Pvar: $tType,X14: Pvar] :
( ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
= ( insert @ Pvar @ X14 @ ( bot_bot @ ( set @ Pvar ) ) ) ) ).
% process_term.simps(49)
thf(fact_234_process__term_Opred__mono__strong,axiom,
! [B: $tType,A: $tType,P1: A > $o,P22: B > $o,X4: proces554692349s_term @ A @ B,P1a: A > $o,P2a: B > $o] :
( ( proces2118920028s_term @ A @ B @ P1 @ P22 @ X4 )
=> ( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ X4 ) )
=> ( ( P1 @ Z1 )
=> ( P1a @ Z1 ) ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ X4 ) )
=> ( ( P22 @ Z2 )
=> ( P2a @ Z2 ) ) )
=> ( proces2118920028s_term @ A @ B @ P1a @ P2a @ X4 ) ) ) ) ).
% process_term.pred_mono_strong
thf(fact_235_singletonI,axiom,
! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% singletonI
thf(fact_236_singleton__conv,axiom,
! [A: $tType,A2: A] :
( ( collect @ A
@ ^ [X: A] : X = A2 )
= ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% singleton_conv
thf(fact_237_singleton__conv2,axiom,
! [A: $tType,A2: A] :
( ( collect @ A
@ ( ^ [Y3: A,Z: A] : Y3 = Z
@ A2 ) )
= ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% singleton_conv2
thf(fact_238_process__term_Opred__inject_I1_J,axiom,
! [A: $tType,Pvar: $tType,P1: A > $o,P22: Pvar > $o,A2: Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
= ( P22 @ A2 ) ) ).
% process_term.pred_inject(1)
thf(fact_239_process__term_Opred__inject_I4_J,axiom,
! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
= ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ A2 )
& ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% process_term.pred_inject(4)
thf(fact_240_process__term_Opred__inject_I3_J,axiom,
! [Pvar: $tType,A: $tType,P1: A > $o,P22: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
= ( ( P1 @ A2 )
& ( proces2118920028s_term @ A @ Pvar @ P1 @ P22 @ Aa2 ) ) ) ).
% process_term.pred_inject(3)
thf(fact_241_process__term_Osimps_I50_J,axiom,
! [A: $tType,Pvar: $tType,X2: proces634752977rocess @ A] :
( ( proces1493547885s_term @ A @ Pvar @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
= ( bot_bot @ ( set @ Pvar ) ) ) ).
% process_term.simps(50)
thf(fact_242_process__term_Omap__cong__pred,axiom,
! [D: $tType,C: $tType,B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
( ( X4 = Ya )
=> ( ( proces2118920028s_term @ A @ B
@ ^ [Z12: A] :
( ( F1 @ Z12 )
= ( G1 @ Z12 ) )
@ ^ [Z22: B] :
( ( F2 @ Z22 )
= ( G2 @ Z22 ) )
@ Ya )
=> ( ( proces224683037s_term @ A @ C @ B @ D @ F1 @ F2 @ X4 )
= ( proces224683037s_term @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ).
% process_term.map_cong_pred
thf(fact_243_process__term_Osimps_I45_J,axiom,
! [Pvar: $tType,A: $tType,X14: Pvar] :
( ( proces1264666542s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ X14 ) )
= ( bot_bot @ ( set @ A ) ) ) ).
% process_term.simps(45)
thf(fact_244_Collect__conv__if,axiom,
! [A: $tType,P6: A > $o,A2: A] :
( ( ( P6 @ A2 )
=> ( ( collect @ A
@ ^ [X: A] :
( ( X = A2 )
& ( P6 @ X ) ) )
= ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
& ( ~ ( P6 @ A2 )
=> ( ( collect @ A
@ ^ [X: A] :
( ( X = A2 )
& ( P6 @ X ) ) )
= ( bot_bot @ ( set @ A ) ) ) ) ) ).
% Collect_conv_if
thf(fact_245_Collect__conv__if2,axiom,
! [A: $tType,P6: A > $o,A2: A] :
( ( ( P6 @ A2 )
=> ( ( collect @ A
@ ^ [X: A] :
( ( A2 = X )
& ( P6 @ X ) ) )
= ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
& ( ~ ( P6 @ A2 )
=> ( ( collect @ A
@ ^ [X: A] :
( ( A2 = X )
& ( P6 @ X ) ) )
= ( bot_bot @ ( set @ A ) ) ) ) ) ).
% Collect_conv_if2
thf(fact_246_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_247_empty__def,axiom,
! [A: $tType] :
( ( bot_bot @ ( set @ A ) )
= ( collect @ A
@ ^ [X: A] : $false ) ) ).
% empty_def
thf(fact_248_singleton__inject,axiom,
! [A: $tType,A2: A,B3: A] :
( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
= ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
=> ( A2 = B3 ) ) ).
% singleton_inject
thf(fact_249_insert__not__empty,axiom,
! [A: $tType,A2: A,A6: set @ A] :
( ( insert @ A @ A2 @ A6 )
!= ( bot_bot @ ( set @ A ) ) ) ).
% insert_not_empty
thf(fact_250_doubleton__eq__iff,axiom,
! [A: $tType,A2: A,B3: A,C3: A,D2: A] :
( ( ( insert @ A @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
= ( insert @ A @ C3 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
= ( ( ( A2 = C3 )
& ( B3 = D2 ) )
| ( ( A2 = D2 )
& ( B3 = C3 ) ) ) ) ).
% doubleton_eq_iff
thf(fact_251_singleton__iff,axiom,
! [A: $tType,B3: A,A2: A] :
( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
= ( B3 = A2 ) ) ).
% singleton_iff
thf(fact_252_singletonD,axiom,
! [A: $tType,B3: A,A2: A] :
( ( member @ A @ B3 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
=> ( B3 = A2 ) ) ).
% singletonD
thf(fact_253_process__term_Opred__cong,axiom,
! [B: $tType,A: $tType,X4: proces554692349s_term @ A @ B,Ya: proces554692349s_term @ A @ B,P1: A > $o,P1a: A > $o,P22: B > $o,P2a: B > $o] :
( ( X4 = Ya )
=> ( ! [Z1: A] :
( ( member @ A @ Z1 @ ( proces1264666542s_term @ A @ B @ Ya ) )
=> ( ( P1 @ Z1 )
= ( P1a @ Z1 ) ) )
=> ( ! [Z2: B] :
( ( member @ B @ Z2 @ ( proces1493547885s_term @ A @ B @ Ya ) )
=> ( ( P22 @ Z2 )
= ( P2a @ Z2 ) ) )
=> ( ( proces2118920028s_term @ A @ B @ P1 @ P22 @ X4 )
= ( proces2118920028s_term @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% process_term.pred_cong
thf(fact_254_the__elem__eq,axiom,
! [A: $tType,X4: A] :
( ( the_elem @ A @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) )
= X4 ) ).
% the_elem_eq
%----Helper facts (3)
thf(help_If_3_1_T,axiom,
! [P6: $o] :
( ( P6 = $true )
| ( P6 = $false ) ) ).
thf(help_If_2_1_T,axiom,
! [A: $tType,X4: A,Y: A] :
( ( if @ A @ $false @ X4 @ Y )
= Y ) ).
thf(help_If_1_1_T,axiom,
! [A: $tType,X4: A,Y: A] :
( ( if @ A @ $true @ X4 @ Y )
= X4 ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
( ( ( proces10484146Action @ a @ pa )
= ( proces10484146Action @ a @ p2 ) )
& ( ( proces401113213Choice @ a @ pa )
= ( proces401113213Choice @ a @ p2 ) ) ) ).
%------------------------------------------------------------------------------