TPTP Problem File: PRO025^1.p
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%------------------------------------------------------------------------------
% File : PRO025^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Processes
% Problem : Process algebra 199
% 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__199.p [Bla16]
% Status : Theorem
% Rating : 0.00 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% Syntax : Number of formulae : 325 ( 143 unt; 66 typ; 0 def)
% Number of atoms : 887 ( 371 equ; 0 cnn)
% Maximal formula atoms : 31 ( 3 avg)
% Number of connectives : 8625 ( 169 ~; 10 |; 49 &;8017 @)
% ( 0 <=>; 380 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 12 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1385 (1385 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 64 usr; 8 con; 0-14 aty)
% Number of variables : 2035 ( 238 ^;1668 !; 23 ?;2035 :)
% ( 106 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2016-07-13 14:40:06.073
%------------------------------------------------------------------------------
%----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 (59)
thf(sy_c_BNF__Def_Orel__fun,type,
bNF_rel_fun:
!>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
thf(sy_c_HOL_Oundefined,type,
undefined:
!>[A: $tType] : A ).
thf(sy_c_If,type,
if:
!>[A: $tType] : ( $o > A > A > A ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
proces1239275103le_CH1:
!>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
proces1869379930H1_rel:
!>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
proces1239275104le_CH2:
!>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
proces93903513H2_rel:
!>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
proces126235999e_CONT:
!>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
proces1004198490NT_rel:
!>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
proces1708129104e_PREF:
!>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
proces527360425EF_rel:
!>[A: $tType,B: $tType,C: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
proces1121166967uarded:
!>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
proces687458811_isACT:
!>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
proces896239806CT_rel:
!>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
proces1525233512Action:
!>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
proces1915862579Choice:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
proces1406508781rocess:
!>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
proces979765041_ch1Of:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
proces988026546_ch2Of:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
proces1778668539contOf:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
proces894737309rocess:
!>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
proces10484146Action:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
proces401113213Choice:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
proces370407749rocess:
!>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
proces1205983068rocess:
!>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
proces745025900prefOf:
!>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
proces749077512rocess:
!>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
proces1454156180ss_ACT:
!>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
proces89589571ess_CH:
!>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
proces1062592052s_PROC:
!>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
proces1627516585ss_VAR:
!>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
proces460752237s_term:
!>[Pvar: $tType,B: $tType,A: $tType] : ( ( Pvar > B ) > ( ( proces634752977rocess @ A ) > B ) > ( A > ( proces554692349s_term @ A @ Pvar ) > B ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B ) > ( proces554692349s_term @ A @ Pvar ) > B ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term,type,
proces224683037s_term:
!>[A: $tType,Aa: $tType,Pvar: $tType,Pvara: $tType] : ( ( A > Aa ) > ( Pvar > Pvara ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ Aa @ Pvara ) ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
proces2118920028s_term:
!>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term,type,
proces2117273769s_term:
!>[Pvar: $tType,D: $tType,A: $tType] : ( ( Pvar > D ) > ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
proces2029722208s_term:
!>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_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_Product__Type_Ocurry,type,
product_curry:
!>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
thf(sy_c_Product__Type_Ointernal__case__prod,type,
produc2004651681e_prod:
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
product_rec_prod:
!>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
thf(sy_c_Pure_Otype,type,
type:
!>[A: $tType] : ( itself @ A ) ).
thf(sy_c_Relation_Oinv__image,type,
inv_image:
!>[B: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ B ) ) > ( A > B ) > ( set @ ( product_prod @ A @ A ) ) ) ).
thf(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
thf(sy_c_Wellfounded_Oacc,type,
acc:
!>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ A ) ) ).
thf(sy_c_Wellfounded_Oaccp,type,
accp:
!>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
thf(sy_c_Wellfounded_Olex__prod,type,
lex_prod:
!>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
thf(sy_c_Wfrec_Oadm__wf,type,
adm_wf:
!>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( ( A > B ) > A > B ) > $o ) ).
thf(sy_c_Wfrec_Ocut,type,
cut:
!>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ ( product_prod @ A @ A ) ) > A > A > B ) ).
thf(sy_c_Wfrec_Osame__fst,type,
same_fst:
!>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
thf(sy_c_member,type,
member:
!>[A: $tType] : ( A > ( set @ A ) > $o ) ).
thf(sy_v_a_H____,type,
a2: a ).
thf(sy_v_a____,type,
a3: a ).
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_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_1_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_2_Action,axiom,
( ( proces1525233512Action @ a @ a2 @ p2 )
= ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) ) ).
% Action
thf(fact_3__C0_C,axiom,
proces687458811_isACT @ b @ a @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ).
% "0"
thf(fact_4__092_060open_062solution_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_A_061_AAction_A_IPREF_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_A_Isolution_Asys_A_ICONT_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_J_092_060close_062,axiom,
( ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) )
= ( proces1525233512Action @ a @ ( proces1708129104e_PREF @ b @ a @ b @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) @ ( proces1652378886lution @ b @ a @ sys @ ( proces126235999e_CONT @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) ) ) ) ).
% \<open>solution sys (PROC (Action a p)) = Action (PREF sys (PROC (Action a p))) (solution sys (CONT sys (PROC (Action a p))))\<close>
thf(fact_5_process__term_Osimps_I22_J,axiom,
! [Pvar: $tType,D: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X2: proces634752977rocess @ A] :
( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
= ( F2 @ X2 ) ) ).
% process_term.simps(22)
thf(fact_6_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_7_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_8_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_9_process__term_Odistinct_I1_J,axiom,
! [Pvar: $tType,A: $tType,X1: Pvar,X2: proces634752977rocess @ A] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
!= ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% process_term.distinct(1)
thf(fact_10_process_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
@ ^ [X12: A,X22: proces634752977rocess @ A] : ( H @ ( F1 @ X12 @ X22 ) )
@ ^ [X12: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( H @ ( F2 @ X12 @ X22 ) )
@ Process ) ) ).
% process.case_distrib
thf(fact_11_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 ) )
@ ^ [X12: A,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X12 @ X22 ) )
@ ^ [X12: proces554692349s_term @ A @ Pvar,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X12 @ X22 ) )
@ Process_term ) ) ).
% process_term.case_distrib
thf(fact_12_solution__VAR,axiom,
! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces1121166967uarded @ A @ B @ A @ Sys )
=> ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X3 ) ) ) ) ).
% solution_VAR
thf(fact_13_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_14_process__term_Opred__inject_I2_J,axiom,
! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces634752977rocess @ A] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1062592052s_PROC @ A @ Pvar @ A2 ) )
= ( proces1205983068rocess @ A @ P1 @ A2 ) ) ).
% process_term.pred_inject(2)
thf(fact_15_process__term_Oinject_I1_J,axiom,
! [A: $tType,Pvar: $tType,X1: Pvar,Y1: Pvar] :
( ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
= ( proces1627516585ss_VAR @ Pvar @ A @ Y1 ) )
= ( X1 = Y1 ) ) ).
% process_term.inject(1)
thf(fact_16_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_17_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_18_process_Oinject_I1_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
( ( ( proces1525233512Action @ A @ X11 @ X122 )
= ( proces1525233512Action @ A @ Y11 @ Y12 ) )
= ( ( X11 = Y11 )
& ( X122 = Y12 ) ) ) ).
% process.inject(1)
thf(fact_19_process__term_Opred__inject_I1_J,axiom,
! [A: $tType,Pvar: $tType,P1: A > $o,P2: Pvar > $o,A2: Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
= ( P2 @ A2 ) ) ).
% process_term.pred_inject(1)
thf(fact_20_process__term_Opred__inject_I4_J,axiom,
! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
= ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ A2 )
& ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% process_term.pred_inject(4)
thf(fact_21_process__term_Opred__inject_I3_J,axiom,
! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
= ( ( P1 @ A2 )
& ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% process_term.pred_inject(3)
thf(fact_22_process_Opred__inject_I1_J,axiom,
! [A: $tType,P3: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
( ( proces1205983068rocess @ A @ P3 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
= ( ( P3 @ A2 )
& ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% process.pred_inject(1)
thf(fact_23_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_24_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_25_isACT_Osimps_I4_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T1: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T1 @ T22 ) ) ).
% isACT.simps(4)
thf(fact_26_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_27_process_Osel_I1_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
= X11 ) ).
% process.sel(1)
thf(fact_28_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_29_process_Osimps_I5_J,axiom,
! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X122: proces634752977rocess @ A] :
( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X122 ) )
= ( F1 @ X11 @ X122 ) ) ).
% process.simps(5)
thf(fact_30_process__term_Osimps_I24_J,axiom,
! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
= ( F4 @ X41 @ X42 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X41 ) @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X42 ) ) ) ).
% process_term.simps(24)
thf(fact_31_process__term_Osimps_I23_J,axiom,
! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
= ( F3 @ X31 @ X32 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X32 ) ) ) ).
% process_term.simps(23)
thf(fact_32_process__term_Osimps_I21_J,axiom,
! [A: $tType,D: $tType,Pvar: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X1: Pvar] :
( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
= ( F1 @ X1 ) ) ).
% process_term.simps(21)
thf(fact_33_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_34_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_35_process__term_Osimps_I17_J,axiom,
! [A: $tType,B: $tType,Pvar: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X1: Pvar] :
( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
= ( F1 @ X1 ) ) ).
% process_term.simps(17)
thf(fact_36_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_37_process__term_Odistinct_I5_J,axiom,
! [Pvar: $tType,A: $tType,X1: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
!= ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% process_term.distinct(5)
thf(fact_38_process__term_Odistinct_I3_J,axiom,
! [Pvar: $tType,A: $tType,X1: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
!= ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% process_term.distinct(3)
thf(fact_39_isACT__VAR,axiom,
! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces1121166967uarded @ A @ B @ A @ Sys )
=> ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X3 ) )
= ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X3 ) ) ) ) ).
% isACT_VAR
thf(fact_40_CH2_Oinduct,axiom,
! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
=> ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( P3 @ A0 @ A1 ) ) ) ) ) ).
% CH2.induct
thf(fact_41_CONT_Oinduct,axiom,
! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
=> ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( P3 @ A0 @ A1 ) ) ) ) ) ).
% CONT.induct
thf(fact_42_PREF_Oinduct,axiom,
! [C: $tType,A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ B @ A] :
( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
=> ( ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( P3 @ A0 @ A1 ) ) ) ) ) ).
% PREF.induct
thf(fact_43_guarded__def,axiom,
! [C: $tType,B: $tType,A: $tType] :
( ( proces1121166967uarded @ A @ B @ C )
= ( ^ [Sys3: A > ( proces554692349s_term @ B @ C )] :
! [X5: A,Y: C] :
( ( Sys3 @ X5 )
!= ( proces1627516585ss_VAR @ C @ B @ Y ) ) ) ) ).
% guarded_def
thf(fact_44_isACT_Oinduct,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ D @ A] :
( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
=> ( P3 @ A0 @ A1 ) ) ) ) ) ).
% isACT.induct
thf(fact_45_mem__Collect__eq,axiom,
! [A: $tType,A2: A,P3: A > $o] :
( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
= ( P3 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_46_Collect__mem__eq,axiom,
! [A: $tType,A4: set @ A] :
( ( collect @ A
@ ^ [X: A] : ( member @ A @ X @ A4 ) )
= A4 ) ).
% Collect_mem_eq
thf(fact_47_Collect__cong,axiom,
! [A: $tType,P3: A > $o,Q: A > $o] :
( ! [X6: A] :
( ( P3 @ X6 )
= ( Q @ X6 ) )
=> ( ( collect @ A @ P3 )
= ( collect @ A @ Q ) ) ) ).
% Collect_cong
thf(fact_48_ext,axiom,
! [B: $tType,A: $tType,F: A > B,G: A > B] :
( ! [X6: A] :
( ( F @ X6 )
= ( G @ X6 ) )
=> ( F = G ) ) ).
% ext
thf(fact_49_process__term_Oinduct,axiom,
! [Pvar: $tType,A: $tType,P3: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
( ! [X6: Pvar] : ( P3 @ ( proces1627516585ss_VAR @ Pvar @ A @ X6 ) )
=> ( ! [X6: proces634752977rocess @ A] : ( P3 @ ( proces1062592052s_PROC @ A @ Pvar @ X6 ) )
=> ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
( ( P3 @ X2a )
=> ( P3 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
=> ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
( ( P3 @ X1a )
=> ( ( P3 @ X2a )
=> ( P3 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
=> ( P3 @ Process_term ) ) ) ) ) ).
% process_term.induct
thf(fact_50_process__term_Oexhaust,axiom,
! [Pvar: $tType,A: $tType,Y3: proces554692349s_term @ A @ Pvar] :
( ! [X13: Pvar] :
( Y3
!= ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
=> ( ! [X23: proces634752977rocess @ A] :
( Y3
!= ( proces1062592052s_PROC @ A @ Pvar @ X23 ) )
=> ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
( Y3
!= ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
=> ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
( Y3
!= ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% process_term.exhaust
thf(fact_51_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_52_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_53_process_Opred__True,axiom,
! [A: $tType] :
( ( proces1205983068rocess @ A
@ ^ [Uu: A] : $true )
= ( ^ [Uu: proces634752977rocess @ A] : $true ) ) ).
% process.pred_True
thf(fact_54_PREF_Oelims,axiom,
! [A: $tType,C: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y3: B] :
( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa )
= Y3 )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( Y3
!= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( X7 @ X4 ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( Y3
!= ( proces745025900prefOf @ B @ P4 ) ) )
=> ( ! [A3: B] :
( ? [T3: proces554692349s_term @ B @ A] :
( Xa
= ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
=> ( Y3 != A3 ) )
=> ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( Xa
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( Y3
!= ( undefined @ B ) ) ) ) ) ) ) ).
% PREF.elims
thf(fact_55_isACT_Oelims_I1_J,axiom,
! [D: $tType,A: $tType,B: $tType,C: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y3: $o] :
( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
= Y3 )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X4 ) )
=> ( Y3
= ( ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X4 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( Y3
= ( ~ ( proces10484146Action @ D @ P4 ) ) ) )
=> ( ( ? [A3: D,T3: proces554692349s_term @ D @ A] :
( Xa
= ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
=> ~ Y3 )
=> ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
( Xa
= ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
=> Y3 ) ) ) ) ) ).
% isACT.elims(1)
thf(fact_56_PREF_Osimps_I1_J,axiom,
! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X3: A] :
( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( Sys @ X3 ) ) ) ).
% PREF.simps(1)
thf(fact_57_isACT_Oelims_I2_J,axiom,
! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X4 ) )
=> ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X4 ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ~ ( proces10484146Action @ D @ P4 ) )
=> ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
( Xa
!= ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ).
% isACT.elims(2)
thf(fact_58_isACT_Oelims_I3_J,axiom,
! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X4 ) )
=> ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X4 ) ) )
=> ( ! [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_59_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_60_CH2_Ocases,axiom,
! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
=> ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% CH2.cases
thf(fact_61_CONT_Ocases,axiom,
! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
=> ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% CONT.cases
thf(fact_62_PREF_Ocases,axiom,
! [C: $tType,A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
=> ~ ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% PREF.cases
thf(fact_63_isACT_Ocases,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
=> ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) )
=> ~ ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
( X7
!= ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% isACT.cases
thf(fact_64_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_65_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_66_contOf__def,axiom,
! [A: $tType] :
( ( proces1778668539contOf @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [X112: A,X123: proces634752977rocess @ A] : X123
@ ^ [Uu2: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% contOf_def
thf(fact_67_process_Odisc__eq__case_I1_J,axiom,
! [A: $tType] :
( ( proces10484146Action @ A )
= ( proces1406508781rocess @ A @ $o
@ ^ [Uu: A,Uv2: proces634752977rocess @ A] : $true
@ ^ [Uu: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $false ) ) ).
% process.disc_eq_case(1)
thf(fact_68_isAction__def,axiom,
! [A: $tType] :
( ( proces10484146Action @ A )
= ( ^ [Process2: proces634752977rocess @ A] :
? [X112: A,X123: proces634752977rocess @ A] :
( Process2
= ( proces1525233512Action @ A @ X112 @ X123 ) ) ) ) ).
% isAction_def
thf(fact_69_process_OdiscI_I1_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A,X11: A,X122: proces634752977rocess @ A] :
( ( Process
= ( proces1525233512Action @ A @ X11 @ X122 ) )
=> ( proces10484146Action @ A @ Process ) ) ).
% process.discI(1)
thf(fact_70_process_Odisc_I1_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% process.disc(1)
thf(fact_71_process_Osel_I2_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
= X122 ) ).
% process.sel(2)
thf(fact_72_CONT_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
@ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( Sys @ X3 ) ) ) ).
% CONT.simps(1)
thf(fact_73_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_74_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_75_isACT_Osimps_I1_J,axiom,
! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X3: A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X3 ) )
= ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( Sys @ X3 ) ) ) ).
% isACT.simps(1)
thf(fact_76_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_77_prefOf__def,axiom,
! [A: $tType] :
( ( proces745025900prefOf @ A )
= ( proces1406508781rocess @ A @ A
@ ^ [X112: A,X123: proces634752977rocess @ A] : X112
@ ^ [Uu2: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% prefOf_def
thf(fact_78_CONT_Oelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa )
= Y3 )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( Y3
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
@ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( X7 @ X4 ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( Y3
!= ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) )
=> ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
=> ( Y3 != T3 ) )
=> ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( Xa
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( Y3
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CONT.elims
thf(fact_79_old_Oprod_Oinject,axiom,
! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
( ( ( product_Pair @ A @ B @ A2 @ B2 )
= ( product_Pair @ A @ B @ A6 @ B3 ) )
= ( ( A2 = A6 )
& ( B2 = B3 ) ) ) ).
% old.prod.inject
thf(fact_80_prod_Oinject,axiom,
! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
( ( ( product_Pair @ A @ B @ X1 @ X2 )
= ( product_Pair @ A @ B @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_81_PREF_Opelims,axiom,
! [C: $tType,A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y3: B] :
( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( ( Y3
= ( proces460752237s_term @ C @ B @ B
@ ^ [Aa3: C] : ( undefined @ B )
@ ( proces745025900prefOf @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
@ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
@ ( X7 @ X4 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ( Y3
= ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
=> ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
=> ( ( Y3 = A3 )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
=> ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( ( Y3
= ( undefined @ B ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% PREF.pelims
thf(fact_82_CONT_Opelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( ( Y3
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
@ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
@ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ( X7 @ X4 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ( Y3
= ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
=> ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
=> ( ( Y3 = T3 )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
=> ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ V @ Va ) )
=> ( ( Y3
= ( undefined @ ( proces554692349s_term @ B @ A ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CONT.pelims
thf(fact_83_isACT_Opelims_I1_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y3: $o] :
( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa ) )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X4 ) )
=> ( ( Y3
= ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X4 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ D] :
( ( Xa
= ( proces1062592052s_PROC @ D @ A @ P4 ) )
=> ( ( Y3
= ( 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 ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) ) ) )
=> ( ! [A3: D,T3: proces554692349s_term @ D @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
=> ( Y3
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) )
=> ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
( ( Xa
= ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
=> ( ~ Y3
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% isACT.pelims(1)
thf(fact_84_isACT_Opelims_I2_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ 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 ) @ X7 @ Xa ) )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X4 ) )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
=> ~ ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X4 ) ) ) )
=> ( ! [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 ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
=> ~ ( proces10484146Action @ D @ P4 ) ) )
=> ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ) ) ) ).
% isACT.pelims(2)
thf(fact_85_isACT_Opelims_I3_J,axiom,
! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ 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 ) @ X7 @ Xa ) )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ D @ X4 ) )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
=> ( proces460752237s_term @ C @ $o @ B
@ ^ [Pvar2: C] : $false
@ ( proces10484146Action @ B )
@ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
@ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
@ ( X7 @ X4 ) ) ) )
=> ( ! [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 ) @ X7 @ ( 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 ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% isACT.pelims(3)
thf(fact_86_surj__pair,axiom,
! [A: $tType,B: $tType,P: product_prod @ A @ B] :
? [X6: A,Y4: B] :
( P
= ( product_Pair @ A @ B @ X6 @ Y4 ) ) ).
% surj_pair
thf(fact_87_prod__cases,axiom,
! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
( ! [A3: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B4 ) )
=> ( P3 @ P ) ) ).
% prod_cases
thf(fact_88_Pair__inject,axiom,
! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
( ( ( product_Pair @ A @ B @ A2 @ B2 )
= ( product_Pair @ A @ B @ A6 @ B3 ) )
=> ~ ( ( A2 = A6 )
=> ( B2 != B3 ) ) ) ).
% Pair_inject
thf(fact_89_prod__cases3,axiom,
! [A: $tType,B: $tType,C: $tType,Y3: product_prod @ A @ ( product_prod @ B @ C )] :
~ ! [A3: A,B4: B,C2: C] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% prod_cases3
thf(fact_90_prod__cases4,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
~ ! [A3: A,B4: B,C2: C,D2: D] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% prod_cases4
thf(fact_91_prod__cases5,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
~ ! [A3: A,B4: B,C2: C,D2: D,E2: E] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% prod_cases5
thf(fact_92_prod__cases6,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
~ ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% prod_cases6
thf(fact_93_prod__cases7,axiom,
! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,G2: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
~ ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] :
( Y3
!= ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) ) ).
% prod_cases7
thf(fact_94_prod__induct3,axiom,
! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ C )] :
( ! [A3: A,B4: B,C2: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
=> ( P3 @ X7 ) ) ).
% prod_induct3
thf(fact_95_prod__induct4,axiom,
! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
( ! [A3: A,B4: B,C2: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
=> ( P3 @ X7 ) ) ).
% prod_induct4
thf(fact_96_prod__induct5,axiom,
! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
( ! [A3: A,B4: B,C2: C,D2: D,E2: E] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
=> ( P3 @ X7 ) ) ).
% prod_induct5
thf(fact_97_prod__induct6,axiom,
! [F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
( ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
=> ( P3 @ X7 ) ) ).
% prod_induct6
thf(fact_98_prod__induct7,axiom,
! [G2: $tType,F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
( ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) )
=> ( P3 @ X7 ) ) ).
% prod_induct7
thf(fact_99_old_Oprod_Oexhaust,axiom,
! [A: $tType,B: $tType,Y3: product_prod @ A @ B] :
~ ! [A3: A,B4: B] :
( Y3
!= ( product_Pair @ A @ B @ A3 @ B4 ) ) ).
% old.prod.exhaust
thf(fact_100_old_Oprod_Oinducts,axiom,
! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
( ! [A3: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B4 ) )
=> ( P3 @ Prod ) ) ).
% old.prod.inducts
thf(fact_101_old_Oprod_Orec,axiom,
! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
= ( F1 @ A2 @ B2 ) ) ).
% old.prod.rec
thf(fact_102_CH1_Oelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa )
= Y3 )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( Y3
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
@ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
@ ( X7 @ X4 ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( Y3
!= ( 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 ) )
=> ( Y3 != T12 ) )
=> ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
( Xa
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( Y3
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CH1.elims
thf(fact_103_CH2_Oelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa )
= Y3 )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( Y3
!= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
@ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
@ ( X7 @ X4 ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( Y3
!= ( 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 ) )
=> ( Y3 != T23 ) )
=> ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
( Xa
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( Y3
!= ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% CH2.elims
thf(fact_104_CH1_Opelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( ( Y3
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
@ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
@ ( X7 @ X4 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ( Y3
= ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
=> ( ( Y3 = T12 )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
=> ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( ( Y3
= ( undefined @ ( proces554692349s_term @ B @ A ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CH1.pelims
thf(fact_105_CH2_Opelims,axiom,
! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa )
= Y3 )
=> ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
=> ( ! [X4: A] :
( ( Xa
= ( proces1627516585ss_VAR @ A @ B @ X4 ) )
=> ( ( Y3
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
@ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
@ ( X7 @ X4 ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
=> ( ! [P4: proces634752977rocess @ B] :
( ( Xa
= ( proces1062592052s_PROC @ B @ A @ P4 ) )
=> ( ( Y3
= ( 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 ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
=> ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
=> ( ( Y3 = 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 ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
=> ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
( ( Xa
= ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
=> ( ( Y3
= ( undefined @ ( proces554692349s_term @ B @ A ) ) )
=> ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% CH2.pelims
thf(fact_106_ch1Of__def,axiom,
! [A: $tType] :
( ( proces979765041_ch1Of @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [Uu2: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
@ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X21 ) ) ).
% ch1Of_def
thf(fact_107_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_108_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_109_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_110_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_111_CH2_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
= T22 ) ).
% CH2.simps(3)
thf(fact_112_CH1_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
= T1 ) ).
% CH1.simps(3)
thf(fact_113_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_114_CH2_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
@ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
@ ( Sys @ X3 ) ) ) ).
% CH2.simps(1)
thf(fact_115_CH1_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
= ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
@ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
@ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
@ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
@ ( Sys @ X3 ) ) ) ).
% CH1.simps(1)
thf(fact_116_ch2Of__def,axiom,
! [A: $tType] :
( ( proces988026546_ch2Of @ A )
= ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
@ ^ [Uu2: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
@ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X222 ) ) ).
% ch2Of_def
thf(fact_117_solution_Ocode,axiom,
! [B: $tType,A: $tType] :
( ( proces1652378886lution @ A @ B )
= ( ^ [Sys3: A > ( proces554692349s_term @ B @ A ),T4: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys3 @ T4 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys3 @ T4 ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces126235999e_CONT @ A @ B @ Sys3 @ T4 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275103le_CH1 @ A @ B @ Sys3 @ T4 ) ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275104le_CH2 @ A @ B @ Sys3 @ T4 ) ) ) ) ) ) ).
% solution.code
thf(fact_118_process_Osplit__sel__asm,axiom,
! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
= ( ~ ( ( ( Process
= ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
& ~ ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
| ( ( Process
= ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
& ~ ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% process.split_sel_asm
thf(fact_119_process_Osplit__sel,axiom,
! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
= ( ( ( Process
= ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
=> ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
& ( ( Process
= ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
=> ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% process.split_sel
thf(fact_120_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_121_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_122_process_Oinject_I2_J,axiom,
! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
( ( ( proces1915862579Choice @ A @ X212 @ X223 )
= ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
= ( ( X212 = Y21 )
& ( X223 = Y22 ) ) ) ).
% process.inject(2)
thf(fact_123_process_Opred__inject_I2_J,axiom,
! [A: $tType,P3: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
( ( proces1205983068rocess @ A @ P3 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
= ( ( proces1205983068rocess @ A @ P3 @ A2 )
& ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% process.pred_inject(2)
thf(fact_124_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_125_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_126_process_Odisc_I4_J,axiom,
! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% process.disc(4)
thf(fact_127_process_OdiscI_I2_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
( ( Process
= ( proces1915862579Choice @ A @ X212 @ X223 ) )
=> ( proces401113213Choice @ A @ Process ) ) ).
% process.discI(2)
thf(fact_128_isChoice__def,axiom,
! [A: $tType] :
( ( proces401113213Choice @ A )
= ( ^ [Process2: proces634752977rocess @ A] :
? [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
( Process2
= ( proces1915862579Choice @ A @ X21 @ X222 ) ) ) ) ).
% isChoice_def
thf(fact_129_process__strong__coind,axiom,
! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
( ( Phi @ P @ P6 )
=> ( ! [P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
( ( Phi @ P4 @ P7 )
=> ( ( ( proces10484146Action @ A @ P4 )
= ( proces10484146Action @ A @ P7 ) )
& ( ( proces401113213Choice @ A @ P4 )
= ( proces401113213Choice @ A @ P7 ) ) ) )
=> ( ! [A3: A,A7: A,P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A7 @ P7 ) )
=> ( ( A3 = A7 )
& ( ( Phi @ P4 @ P7 )
| ( P4 = P7 ) ) ) )
=> ( ! [P4: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P7: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q2 ) @ ( proces1915862579Choice @ A @ P7 @ Q3 ) )
=> ( ( ( Phi @ P4 @ P7 )
| ( P4 = P7 ) )
& ( ( Phi @ Q2 @ Q3 )
| ( Q2 = Q3 ) ) ) )
=> ( P = P6 ) ) ) ) ) ).
% process_strong_coind
thf(fact_130_process__coind,axiom,
! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
( ( Phi @ P @ P6 )
=> ( ! [P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
( ( Phi @ P4 @ P7 )
=> ( ( ( proces10484146Action @ A @ P4 )
= ( proces10484146Action @ A @ P7 ) )
& ( ( proces401113213Choice @ A @ P4 )
= ( proces401113213Choice @ A @ P7 ) ) ) )
=> ( ! [A3: A,A7: A,P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A7 @ P7 ) )
=> ( ( A3 = A7 )
& ( Phi @ P4 @ P7 ) ) )
=> ( ! [P4: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P7: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q2 ) @ ( proces1915862579Choice @ A @ P7 @ Q3 ) )
=> ( ( Phi @ P4 @ P7 )
& ( Phi @ Q2 @ Q3 ) ) )
=> ( P = P6 ) ) ) ) ) ).
% process_coind
thf(fact_131_process_Odisc_I2_J,axiom,
! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% process.disc(2)
thf(fact_132_process_Odistinct_I1_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
( ( proces1525233512Action @ A @ X11 @ X122 )
!= ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% process.distinct(1)
thf(fact_133_process_Oexhaust,axiom,
! [A: $tType,Y3: proces634752977rocess @ A] :
( ! [X113: A,X124: proces634752977rocess @ A] :
( Y3
!= ( proces1525233512Action @ A @ X113 @ X124 ) )
=> ~ ! [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] :
( Y3
!= ( proces1915862579Choice @ A @ X213 @ X224 ) ) ) ).
% process.exhaust
thf(fact_134_process_Osel_I4_J,axiom,
! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
= X223 ) ).
% process.sel(4)
thf(fact_135_process_Osel_I3_J,axiom,
! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
= X212 ) ).
% process.sel(3)
thf(fact_136_process_Odistinct__disc_I2_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ( proces401113213Choice @ A @ Process )
=> ~ ( proces10484146Action @ A @ Process ) ) ).
% process.distinct_disc(2)
thf(fact_137_process_Odistinct__disc_I1_J,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ( proces10484146Action @ A @ Process )
=> ~ ( proces401113213Choice @ A @ Process ) ) ).
% process.distinct_disc(1)
thf(fact_138_isAction__isChoice,axiom,
! [A: $tType,P: proces634752977rocess @ A] :
( ( proces10484146Action @ A @ P )
| ( proces401113213Choice @ A @ P ) ) ).
% isAction_isChoice
thf(fact_139_process_Oexhaust__disc,axiom,
! [A: $tType,Process: proces634752977rocess @ A] :
( ~ ( proces10484146Action @ A @ Process )
=> ( proces401113213Choice @ A @ Process ) ) ).
% process.exhaust_disc
thf(fact_140_not__isAction__isChoice,axiom,
! [A: $tType,P: proces634752977rocess @ A] :
~ ( ( proces10484146Action @ A @ P )
& ( proces401113213Choice @ A @ P ) ) ).
% not_isAction_isChoice
thf(fact_141_process_Odisc_I3_J,axiom,
! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% process.disc(3)
thf(fact_142_process_Osimps_I6_J,axiom,
! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
= ( F2 @ X212 @ X223 ) ) ).
% process.simps(6)
thf(fact_143_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_144_process_Odisc__eq__case_I2_J,axiom,
! [A: $tType] :
( ( proces401113213Choice @ A )
= ( proces1406508781rocess @ A @ $o
@ ^ [Uu: A,Uv2: proces634752977rocess @ A] : $false
@ ^ [Uu: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $true ) ) ).
% process.disc_eq_case(2)
thf(fact_145_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_146_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_147_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_148_process_Orel__sel,axiom,
! [B: $tType,A: $tType] :
( ( proces749077512rocess @ A @ B )
= ( ^ [R2: A > B > $o,A5: proces634752977rocess @ A,B5: proces634752977rocess @ B] :
( ( ( proces10484146Action @ A @ A5 )
= ( proces10484146Action @ B @ B5 ) )
& ( ( proces10484146Action @ A @ A5 )
=> ( ( proces10484146Action @ B @ B5 )
=> ( ( R2 @ ( proces745025900prefOf @ A @ A5 ) @ ( proces745025900prefOf @ B @ B5 ) )
& ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A5 ) @ ( proces1778668539contOf @ B @ B5 ) ) ) ) )
& ( ( proces401113213Choice @ A @ A5 )
=> ( ( proces401113213Choice @ B @ B5 )
=> ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A5 ) @ ( proces979765041_ch1Of @ B @ B5 ) )
& ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A5 ) @ ( proces988026546_ch2Of @ B @ B5 ) ) ) ) ) ) ) ) ).
% process.rel_sel
thf(fact_149_process_Orel__coinduct,axiom,
! [A: $tType,B: $tType,P3: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B,R: A > B > $o] :
( ( P3 @ X7 @ Y3 )
=> ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
( ( P3 @ Process4 @ Process5 )
=> ( ( ( proces10484146Action @ A @ Process4 )
= ( proces10484146Action @ B @ Process5 ) )
& ( ( proces10484146Action @ A @ Process4 )
=> ( ( proces10484146Action @ B @ Process5 )
=> ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
& ( P3 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
& ( ( proces401113213Choice @ A @ Process4 )
=> ( ( proces401113213Choice @ B @ Process5 )
=> ( ( P3 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
& ( P3 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
=> ( proces749077512rocess @ A @ B @ R @ X7 @ Y3 ) ) ) ).
% process.rel_coinduct
thf(fact_150_pred__equals__eq2,axiom,
! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
( ( ( ^ [X: A,Y5: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y5 ) @ R ) )
= ( ^ [X: A,Y5: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y5 ) @ S ) ) )
= ( R = S ) ) ).
% pred_equals_eq2
thf(fact_151_internal__case__prod__conv,axiom,
! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
= ( C3 @ A2 @ B2 ) ) ).
% internal_case_prod_conv
thf(fact_152_process_Orel__inject_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
= ( ( R @ X11 @ Y11 )
& ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 ) ) ) ).
% process.rel_inject(1)
thf(fact_153_process_Orel__inject_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
= ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
& ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 ) ) ) ).
% process.rel_inject(2)
thf(fact_154_process_Orel__intros_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X223: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
=> ( ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 )
=> ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% process.rel_intros(2)
thf(fact_155_process_Orel__refl,axiom,
! [B: $tType,Ra: B > B > $o,X7: proces634752977rocess @ B] :
( ! [X6: B] : ( Ra @ X6 @ X6 )
=> ( proces749077512rocess @ B @ B @ Ra @ X7 @ X7 ) ) ).
% process.rel_refl
thf(fact_156_process_Orel__eq,axiom,
! [A: $tType] :
( ( proces749077512rocess @ A @ A
@ ^ [Y6: A,Z: A] : Y6 = Z )
= ( ^ [Y6: proces634752977rocess @ A,Z: proces634752977rocess @ A] : Y6 = Z ) ) ).
% process.rel_eq
thf(fact_157_process_Orel__intros_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X122: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
( ( R @ X11 @ Y11 )
=> ( ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 )
=> ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% process.rel_intros(1)
thf(fact_158_process_Orel__distinct_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X122: proces634752977rocess @ B] :
~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X122 ) ) ).
% process.rel_distinct(2)
thf(fact_159_process_Orel__distinct_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% process.rel_distinct(1)
thf(fact_160_process_Orel__cases,axiom,
! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R @ A2 @ B2 )
=> ( ! [X13: A,X23: proces634752977rocess @ A] :
( ( A2
= ( proces1525233512Action @ A @ X13 @ X23 ) )
=> ! [Y13: B,Y23: proces634752977rocess @ B] :
( ( B2
= ( proces1525233512Action @ B @ Y13 @ Y23 ) )
=> ( ( R @ X13 @ Y13 )
=> ~ ( proces749077512rocess @ A @ B @ R @ X23 @ Y23 ) ) ) )
=> ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
( ( A2
= ( proces1915862579Choice @ A @ X1a @ X2a ) )
=> ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
( ( B2
= ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
=> ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
=> ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% process.rel_cases
thf(fact_161_process__term_Orel__induct,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X7: proces554692349s_term @ A @ Pvar,Y3: proces554692349s_term @ B @ C,Q: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X7 @ Y3 )
=> ( ! [A12: Pvar,B1: C] :
( ( R22 @ A12 @ B1 )
=> ( Q @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
=> ( ! [A22: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
( ( proces749077512rocess @ A @ B @ R1 @ A22 @ B22 )
=> ( Q @ ( proces1062592052s_PROC @ A @ Pvar @ A22 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
=> ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
( ( R1 @ A31 @ B31 )
=> ( ( Q @ A32 @ B32 )
=> ( Q @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
=> ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
( ( Q @ A41 @ B41 )
=> ( ( Q @ A42 @ B42 )
=> ( Q @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
=> ( Q @ X7 @ Y3 ) ) ) ) ) ) ).
% process_term.rel_induct
thf(fact_162_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,B2: proces554692349s_term @ B @ C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B2 )
=> ( ! [X6: Pvar] :
( ( A2
= ( proces1627516585ss_VAR @ Pvar @ A @ X6 ) )
=> ! [Y4: C] :
( ( B2
= ( proces1627516585ss_VAR @ C @ B @ Y4 ) )
=> ~ ( R22 @ X6 @ Y4 ) ) )
=> ( ! [Xa2: proces634752977rocess @ A] :
( ( A2
= ( proces1062592052s_PROC @ A @ Pvar @ Xa2 ) )
=> ! [Ya: proces634752977rocess @ B] :
( ( B2
= ( proces1062592052s_PROC @ B @ C @ Ya ) )
=> ~ ( proces749077512rocess @ A @ B @ R1 @ Xa2 @ Ya ) ) )
=> ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
=> ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
( ( B2
= ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
=> ( ( R1 @ X1a @ Y1a )
=> ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ 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] :
( ( B2
= ( 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_163_process__term_Oset__cases_I2_J,axiom,
! [Pvar: $tType,A: $tType,E3: Pvar,A2: proces554692349s_term @ A @ Pvar] :
( ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
=> ( ( A2
!= ( proces1627516585ss_VAR @ Pvar @ A @ E3 ) )
=> ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
=> ( ! [Z1: proces554692349s_term @ A @ Pvar] :
( ? [Z2: proces554692349s_term @ A @ Pvar] :
( A2
= ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
=> ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
( ( A2
= ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
=> ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% process_term.set_cases(2)
thf(fact_164_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_165_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_166_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_167_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_168_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_169_process__term_Orel__intros_I1_J,axiom,
! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X1: Pvar,Y1: C,R1: A > B > $o] :
( ( R22 @ X1 @ Y1 )
=> ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) ) ) ).
% process_term.rel_intros(1)
thf(fact_170_process__term_Orel__inject_I1_J,axiom,
! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y1: C] :
( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) )
= ( R22 @ X1 @ Y1 ) ) ).
% process_term.rel_inject(1)
thf(fact_171_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_172_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_173_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_174_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_175_process__term_Orel__eq,axiom,
! [B: $tType,A: $tType] :
( ( proces2029722208s_term @ A @ A @ B @ B
@ ^ [Y6: A,Z: A] : Y6 = Z
@ ^ [Y6: B,Z: B] : Y6 = Z )
= ( ^ [Y6: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : Y6 = Z ) ) ).
% process_term.rel_eq
thf(fact_176_process__term_Orel__refl,axiom,
! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X7: proces554692349s_term @ C @ D] :
( ! [X6: C] : ( R1a @ X6 @ X6 )
=> ( ! [X6: D] : ( R2a @ X6 @ X6 )
=> ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X7 @ X7 ) ) ) ).
% process_term.rel_refl
thf(fact_177_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_178_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_179_process__term_Orel__distinct_I1_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y2: proces634752977rocess @ B] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% process_term.rel_distinct(1)
thf(fact_180_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,X1: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% process_term.rel_distinct(2)
thf(fact_181_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_182_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_183_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_184_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_185_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,X1: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% process_term.rel_distinct(6)
thf(fact_186_process__term_Orel__distinct_I5_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% process_term.rel_distinct(5)
thf(fact_187_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,X1: D] :
~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% process_term.rel_distinct(4)
thf(fact_188_process__term_Orel__distinct_I3_J,axiom,
! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% process_term.rel_distinct(3)
thf(fact_189_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_190_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_191_accp_Ocases,axiom,
! [A: $tType,R3: A > A > $o,A2: A] :
( ( accp @ A @ R3 @ A2 )
=> ! [Y7: A] :
( ( R3 @ Y7 @ A2 )
=> ( accp @ A @ R3 @ Y7 ) ) ) ).
% accp.cases
thf(fact_192_accp_Osimps,axiom,
! [A: $tType] :
( ( accp @ A )
= ( ^ [R4: A > A > $o,A5: A] :
? [X: A] :
( ( A5 = X )
& ! [Y5: A] :
( ( R4 @ Y5 @ X )
=> ( accp @ A @ R4 @ Y5 ) ) ) ) ) ).
% accp.simps
thf(fact_193_accp_Ointros,axiom,
! [A: $tType,R3: A > A > $o,X7: A] :
( ! [Y4: A] :
( ( R3 @ Y4 @ X7 )
=> ( accp @ A @ R3 @ Y4 ) )
=> ( accp @ A @ R3 @ X7 ) ) ).
% accp.intros
thf(fact_194_accp__induct__rule,axiom,
! [A: $tType,R3: A > A > $o,A2: A,P3: A > $o] :
( ( accp @ A @ R3 @ A2 )
=> ( ! [X6: A] :
( ( accp @ A @ R3 @ X6 )
=> ( ! [Y7: A] :
( ( R3 @ Y7 @ X6 )
=> ( P3 @ Y7 ) )
=> ( P3 @ X6 ) ) )
=> ( P3 @ A2 ) ) ) ).
% accp_induct_rule
thf(fact_195_not__accp__down,axiom,
! [A: $tType,R: A > A > $o,X7: A] :
( ~ ( accp @ A @ R @ X7 )
=> ~ ! [Z3: A] :
( ( R @ Z3 @ X7 )
=> ( accp @ A @ R @ Z3 ) ) ) ).
% not_accp_down
thf(fact_196_accp__downward,axiom,
! [A: $tType,R3: A > A > $o,B2: A,A2: A] :
( ( accp @ A @ R3 @ B2 )
=> ( ( R3 @ A2 @ B2 )
=> ( accp @ A @ R3 @ A2 ) ) ) ).
% accp_downward
thf(fact_197_accp_Oinducts,axiom,
! [A: $tType,R3: A > A > $o,X7: A,P3: A > $o] :
( ( accp @ A @ R3 @ X7 )
=> ( ! [X6: A] :
( ! [Y7: A] :
( ( R3 @ Y7 @ X6 )
=> ( accp @ A @ R3 @ Y7 ) )
=> ( ! [Y7: A] :
( ( R3 @ Y7 @ X6 )
=> ( P3 @ Y7 ) )
=> ( P3 @ X6 ) ) )
=> ( P3 @ X7 ) ) ) ).
% accp.inducts
thf(fact_198_accp__induct,axiom,
! [A: $tType,R3: A > A > $o,A2: A,P3: A > $o] :
( ( accp @ A @ R3 @ A2 )
=> ( ! [X6: A] :
( ( accp @ A @ R3 @ X6 )
=> ( ! [Y7: A] :
( ( R3 @ Y7 @ X6 )
=> ( P3 @ Y7 ) )
=> ( P3 @ X6 ) ) )
=> ( P3 @ A2 ) ) ) ).
% accp_induct
thf(fact_199_in__lex__prod,axiom,
! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B,R3: set @ ( product_prod @ A @ A ),S2: set @ ( product_prod @ B @ B )] :
( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A6 @ B3 ) ) @ ( lex_prod @ A @ B @ R3 @ S2 ) )
= ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A6 ) @ R3 )
| ( ( A2 = A6 )
& ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B3 ) @ S2 ) ) ) ) ).
% in_lex_prod
thf(fact_200_process_Ocorec__code,axiom,
! [A: $tType,C: $tType] :
( ( proces894737309rocess @ C @ A )
= ( ^ [P5: 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,A5: C] : ( if @ ( proces634752977rocess @ A ) @ ( P5 @ A5 ) @ ( proces1525233512Action @ A @ ( G11 @ A5 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A5 ) @ ( G121 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A5 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A5 ) @ ( G211 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A5 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A5 ) @ ( G221 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A5 ) ) ) ) ) ) ) ).
% process.corec_code
thf(fact_201_process_Ocorec__disc__iff_I1_J,axiom,
! [A: $tType,C: $tType,P: 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,A2: C] :
( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( P @ A2 ) ) ).
% process.corec_disc_iff(1)
thf(fact_202_process_Ocorec__disc__iff_I2_J,axiom,
! [A: $tType,C: $tType,P: 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,A2: C] :
( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( ~ ( P @ A2 ) ) ) ).
% process.corec_disc_iff(2)
thf(fact_203_process_Ocorec__disc_I1_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
( ( P @ A2 )
=> ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% process.corec_disc(1)
thf(fact_204_process_Ocorec_I1_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
( ( P @ A2 )
=> ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
= ( proces1525233512Action @ A @ ( G112 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A2 ) @ ( G1212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% process.corec(1)
thf(fact_205_process_Ocorec_I2_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
( ~ ( P @ A2 )
=> ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
= ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A2 ) @ ( G2112 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% process.corec(2)
thf(fact_206_process_Ocorec__disc_I2_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
( ~ ( P @ A2 )
=> ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% process.corec_disc(2)
thf(fact_207_process_Ocorec__sel_I2_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,Q122: C > $o,G112: C > A,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] :
( ( P @ A2 )
=> ( ( ( Q122 @ A2 )
=> ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( G1212 @ A2 ) ) )
& ( ~ ( Q122 @ A2 )
=> ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% process.corec_sel(2)
thf(fact_208_process_Ocorec__sel_I3_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,Q212: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
( ~ ( P @ A2 )
=> ( ( ( Q212 @ A2 )
=> ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( G2112 @ A2 ) ) )
& ( ~ ( Q212 @ A2 )
=> ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) ) ) ) ).
% process.corec_sel(3)
thf(fact_209_process_Ocorec__sel_I4_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,Q222: 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,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
( ~ ( P @ A2 )
=> ( ( ( Q222 @ A2 )
=> ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( G2212 @ A2 ) ) )
& ( ~ ( Q222 @ A2 )
=> ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% process.corec_sel(4)
thf(fact_210_process_Ocorec__sel_I1_J,axiom,
! [A: $tType,C: $tType,P: C > $o,A2: C,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] :
( ( P @ A2 )
=> ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
= ( G112 @ A2 ) ) ) ).
% process.corec_sel(1)
thf(fact_211_same__fstI,axiom,
! [B: $tType,A: $tType,P3: A > $o,X7: A,Y8: B,Y3: B,R: A > ( set @ ( product_prod @ B @ B ) )] :
( ( P3 @ X7 )
=> ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y8 @ Y3 ) @ ( R @ X7 ) )
=> ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X7 @ Y8 ) @ ( product_Pair @ A @ B @ X7 @ Y3 ) ) @ ( same_fst @ A @ B @ P3 @ R ) ) ) ) ).
% same_fstI
thf(fact_212_ssubst__Pair__rhs,axiom,
! [B: $tType,A: $tType,R3: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R )
=> ( ( S3 = S2 )
=> ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S3 ) @ R ) ) ) ).
% ssubst_Pair_rhs
thf(fact_213_cut__def,axiom,
! [B: $tType,A: $tType] :
( ( cut @ A @ B )
= ( ^ [F7: A > B,R2: set @ ( product_prod @ A @ A ),X: A,Y5: A] : ( if @ B @ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X ) @ R2 ) @ ( F7 @ Y5 ) @ ( undefined @ B ) ) ) ) ).
% cut_def
thf(fact_214_curry__conv,axiom,
! [A: $tType,C: $tType,B: $tType] :
( ( product_curry @ B @ C @ A )
= ( ^ [F7: ( product_prod @ B @ C ) > A,A5: B,B5: C] : ( F7 @ ( product_Pair @ B @ C @ A5 @ B5 ) ) ) ) ).
% curry_conv
thf(fact_215_curryI,axiom,
! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
=> ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% curryI
thf(fact_216_cuts__eq,axiom,
! [B: $tType,A: $tType,F: A > B,R: set @ ( product_prod @ A @ A ),X7: A,G: A > B] :
( ( ( cut @ A @ B @ F @ R @ X7 )
= ( cut @ A @ B @ G @ R @ X7 ) )
= ( ! [Y5: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X7 ) @ R )
=> ( ( F @ Y5 )
= ( G @ Y5 ) ) ) ) ) ).
% cuts_eq
thf(fact_217_cut__apply,axiom,
! [B: $tType,A: $tType,X7: A,A2: A,R: set @ ( product_prod @ A @ A ),F: A > B] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ A2 ) @ R )
=> ( ( cut @ A @ B @ F @ R @ A2 @ X7 )
= ( F @ X7 ) ) ) ).
% cut_apply
thf(fact_218_curry__K,axiom,
! [B: $tType,C: $tType,A: $tType,C3: C] :
( ( product_curry @ A @ B @ C
@ ^ [X: product_prod @ A @ B] : C3 )
= ( ^ [X: A,Y5: B] : C3 ) ) ).
% curry_K
thf(fact_219_curryD,axiom,
! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
=> ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% curryD
thf(fact_220_curryE,axiom,
! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
=> ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% curryE
thf(fact_221_curry__def,axiom,
! [C: $tType,B: $tType,A: $tType] :
( ( product_curry @ A @ B @ C )
= ( ^ [C4: ( product_prod @ A @ B ) > C,X: A,Y5: B] : ( C4 @ ( product_Pair @ A @ B @ X @ Y5 ) ) ) ) ).
% curry_def
thf(fact_222_adm__lemma,axiom,
! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F8: ( A > B ) > A > B] :
( adm_wf @ A @ B @ R
@ ^ [F7: A > B,X: A] : ( F8 @ ( cut @ A @ B @ F7 @ R @ X ) @ X ) ) ).
% adm_lemma
thf(fact_223_accp__acc__eq,axiom,
! [A: $tType,R3: set @ ( product_prod @ A @ A )] :
( ( accp @ A
@ ^ [X: A,Y5: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y5 ) @ R3 ) )
= ( ^ [X: A] : ( member @ A @ X @ ( acc @ A @ R3 ) ) ) ) ).
% accp_acc_eq
thf(fact_224_acc_Ocases,axiom,
! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A )] :
( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
=> ! [Y7: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ A2 ) @ R3 )
=> ( member @ A @ Y7 @ ( acc @ A @ R3 ) ) ) ) ).
% acc.cases
thf(fact_225_acc_Osimps,axiom,
! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A )] :
( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
= ( ? [X: A] :
( ( A2 = X )
& ! [Y5: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X ) @ R3 )
=> ( member @ A @ Y5 @ ( acc @ A @ R3 ) ) ) ) ) ) ).
% acc.simps
thf(fact_226_acc_Ointros,axiom,
! [A: $tType,X7: A,R3: set @ ( product_prod @ A @ A )] :
( ! [Y4: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X7 ) @ R3 )
=> ( member @ A @ Y4 @ ( acc @ A @ R3 ) ) )
=> ( member @ A @ X7 @ ( acc @ A @ R3 ) ) ) ).
% acc.intros
thf(fact_227_acc__induct,axiom,
! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
=> ( ! [X6: A] :
( ( member @ A @ X6 @ ( acc @ A @ R3 ) )
=> ( ! [Y7: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
=> ( P3 @ Y7 ) )
=> ( P3 @ X6 ) ) )
=> ( P3 @ A2 ) ) ) ).
% acc_induct
thf(fact_228_acc_Oinducts,axiom,
! [A: $tType,X7: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
( ( member @ A @ X7 @ ( acc @ A @ R3 ) )
=> ( ! [X6: A] :
( ! [Y7: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
=> ( member @ A @ Y7 @ ( acc @ A @ R3 ) ) )
=> ( ! [Y7: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
=> ( P3 @ Y7 ) )
=> ( P3 @ X6 ) ) )
=> ( P3 @ X7 ) ) ) ).
% acc.inducts
thf(fact_229_acc__downward,axiom,
! [A: $tType,B2: A,R3: set @ ( product_prod @ A @ A ),A2: A] :
( ( member @ A @ B2 @ ( acc @ A @ R3 ) )
=> ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R3 )
=> ( member @ A @ A2 @ ( acc @ A @ R3 ) ) ) ) ).
% acc_downward
thf(fact_230_not__acc__down,axiom,
! [A: $tType,X7: A,R: set @ ( product_prod @ A @ A )] :
( ~ ( member @ A @ X7 @ ( acc @ A @ R ) )
=> ~ ! [Z3: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z3 @ X7 ) @ R )
=> ( member @ A @ Z3 @ ( acc @ A @ R ) ) ) ) ).
% not_acc_down
thf(fact_231_acc__induct__rule,axiom,
! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
=> ( ! [X6: A] :
( ( member @ A @ X6 @ ( acc @ A @ R3 ) )
=> ( ! [Y7: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
=> ( P3 @ Y7 ) )
=> ( P3 @ X6 ) ) )
=> ( P3 @ A2 ) ) ) ).
% acc_induct_rule
thf(fact_232_adm__wf__def,axiom,
! [B: $tType,A: $tType] :
( ( adm_wf @ A @ B )
= ( ^ [R2: set @ ( product_prod @ A @ A ),F9: ( A > B ) > A > B] :
! [F7: A > B,G4: A > B,X: A] :
( ! [Z4: A] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z4 @ X ) @ R2 )
=> ( ( F7 @ Z4 )
= ( G4 @ Z4 ) ) )
=> ( ( F9 @ F7 @ X )
= ( F9 @ G4 @ X ) ) ) ) ) ).
% adm_wf_def
thf(fact_233_acc__def,axiom,
! [A: $tType] :
( ( acc @ A )
= ( ^ [R4: set @ ( product_prod @ A @ A )] :
( collect @ A
@ ( accp @ A
@ ^ [X: A,Y5: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y5 ) @ R4 ) ) ) ) ) ).
% acc_def
thf(fact_234_process__term_Octr__transfer_I2_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces749077512rocess @ A @ B @ R1 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1062592052s_PROC @ A @ Pvar ) @ ( proces1062592052s_PROC @ B @ C ) ) ).
% process_term.ctr_transfer(2)
thf(fact_235_in__inv__image,axiom,
! [A: $tType,B: $tType,X7: A,Y3: A,R3: set @ ( product_prod @ B @ B ),F: A > B] :
( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Y3 ) @ ( inv_image @ B @ A @ R3 @ F ) )
= ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ ( F @ X7 ) @ ( F @ Y3 ) ) @ R3 ) ) ).
% in_inv_image
thf(fact_236_process__term_Octr__transfer_I1_J,axiom,
! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,R1: A > B > $o] : ( bNF_rel_fun @ Pvar @ C @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ R22 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1627516585ss_VAR @ Pvar @ A ) @ ( proces1627516585ss_VAR @ C @ B ) ) ).
% process_term.ctr_transfer(1)
thf(fact_237_process__term_Orec__transfer,axiom,
! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D ) @ ( E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ D @ E @ S @ S ) ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D > D ) @ ( E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ ( D > D ) @ ( E > E ) @ S @ ( bNF_rel_fun @ D @ E @ D @ E @ S @ S ) ) ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces2117273769s_term @ Pvar @ D @ A ) @ ( proces2117273769s_term @ C @ E @ B ) ) ).
% process_term.rec_transfer
thf(fact_238_process__term_Ocase__transfer,axiom,
! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces460752237s_term @ Pvar @ D @ A ) @ ( proces460752237s_term @ C @ E @ B ) ) ).
% process_term.case_transfer
thf(fact_239_process_Ocorec__transfer,axiom,
! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] :
( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > B ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
@ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
@ ^ [Y6: $o,Z: $o] : Y6 = Z )
@ ( bNF_rel_fun @ ( C > A ) @ ( D > B ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ A @ B @ S @ R )
@ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
@ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
@ ^ [Y6: $o,Z: $o] : Y6 = Z )
@ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
@ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
@ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
@ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
@ ^ [Y6: $o,Z: $o] : Y6 = Z )
@ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
@ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
@ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
@ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
@ ^ [Y6: $o,Z: $o] : Y6 = Z )
@ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) ) ) ) ) ) ) ) ) ) )
@ ( proces894737309rocess @ C @ A )
@ ( proces894737309rocess @ D @ B ) ) ).
% process.corec_transfer
thf(fact_240_process_Odisc__transfer_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o] :
( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
@ ^ [Y6: $o,Z: $o] : Y6 = Z
@ ( proces10484146Action @ A )
@ ( proces10484146Action @ B ) ) ).
% process.disc_transfer(1)
thf(fact_241_process_Odisc__transfer_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o] :
( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
@ ^ [Y6: $o,Z: $o] : Y6 = Z
@ ( proces401113213Choice @ A )
@ ( proces401113213Choice @ B ) ) ).
% process.disc_transfer(2)
thf(fact_242_process_Octr__transfer_I2_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1915862579Choice @ A ) @ ( proces1915862579Choice @ B ) ) ).
% process.ctr_transfer(2)
thf(fact_243_process_Ocase__transfer,axiom,
! [A: $tType,C: $tType,D: $tType,B: $tType,R: A > B > $o,S: C > D > $o] : ( bNF_rel_fun @ ( A > ( proces634752977rocess @ A ) > C ) @ ( B > ( proces634752977rocess @ B ) > D ) @ ( ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) > ( proces634752977rocess @ A ) > C ) @ ( ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) > ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( proces1406508781rocess @ A @ C ) @ ( proces1406508781rocess @ B @ D ) ) ).
% process.case_transfer
thf(fact_244_process_Opred__transfer,axiom,
! [A: $tType,B: $tType,R: A > B > $o] :
( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( proces634752977rocess @ A ) > $o ) @ ( ( proces634752977rocess @ B ) > $o )
@ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
@ ^ [Y6: $o,Z: $o] : Y6 = Z )
@ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
@ ^ [Y6: $o,Z: $o] : Y6 = Z )
@ ( proces1205983068rocess @ A )
@ ( proces1205983068rocess @ B ) ) ).
% process.pred_transfer
thf(fact_245_process_Orel__transfer,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ C ) > ( proces634752977rocess @ D ) > $o )
@ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
@ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
@ ^ [Y6: $o,Z: $o] : Y6 = Z ) )
@ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ C ) @ ( ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ D ) > $o ) @ ( proces749077512rocess @ A @ C @ Sa )
@ ( bNF_rel_fun @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ D ) @ $o @ $o @ ( proces749077512rocess @ B @ D @ Sc )
@ ^ [Y6: $o,Z: $o] : Y6 = Z ) )
@ ( proces749077512rocess @ A @ B )
@ ( proces749077512rocess @ C @ D ) ) ).
% process.rel_transfer
thf(fact_246_process_Octr__transfer_I1_J,axiom,
! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1525233512Action @ A ) @ ( proces1525233512Action @ B ) ) ).
% process.ctr_transfer(1)
thf(fact_247_process__term_Octr__transfer_I4_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces89589571ess_CH @ A @ Pvar ) @ ( proces89589571ess_CH @ B @ C ) ) ).
% process_term.ctr_transfer(4)
thf(fact_248_process__term_Octr__transfer_I3_J,axiom,
! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces1454156180ss_ACT @ A @ Pvar ) @ ( proces1454156180ss_ACT @ B @ C ) ) ).
% process_term.ctr_transfer(3)
thf(fact_249_process__term_Opred__transfer,axiom,
! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] :
( bNF_rel_fun @ ( A > $o ) @ ( C > $o ) @ ( ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) @ ( ( D > $o ) > ( proces554692349s_term @ C @ D ) > $o )
@ ( bNF_rel_fun @ A @ C @ $o @ $o @ R1
@ ^ [Y6: $o,Z: $o] : Y6 = Z )
@ ( bNF_rel_fun @ ( B > $o ) @ ( D > $o ) @ ( ( proces554692349s_term @ A @ B ) > $o ) @ ( ( proces554692349s_term @ C @ D ) > $o )
@ ( bNF_rel_fun @ B @ D @ $o @ $o @ R22
@ ^ [Y6: $o,Z: $o] : Y6 = Z )
@ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ C @ D ) @ $o @ $o @ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 )
@ ^ [Y6: $o,Z: $o] : Y6 = Z ) )
@ ( proces2118920028s_term @ A @ B )
@ ( proces2118920028s_term @ C @ D ) ) ).
% process_term.pred_transfer
thf(fact_250_process__term_Orel__transfer,axiom,
! [A: $tType,C: $tType,B: $tType,D: $tType,H2: $tType,F5: $tType,G2: $tType,E: $tType,S1a: A > E > $o,S1c: C > G2 > $o,S2a: B > F5 > $o,S2c: D > H2 > $o] :
( bNF_rel_fun @ ( A > C > $o ) @ ( E > G2 > $o ) @ ( ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( F5 > H2 > $o ) > ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
@ ( bNF_rel_fun @ A @ E @ ( C > $o ) @ ( G2 > $o ) @ S1a
@ ( bNF_rel_fun @ C @ G2 @ $o @ $o @ S1c
@ ^ [Y6: $o,Z: $o] : Y6 = Z ) )
@ ( bNF_rel_fun @ ( B > D > $o ) @ ( F5 > H2 > $o ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
@ ( bNF_rel_fun @ B @ F5 @ ( D > $o ) @ ( H2 > $o ) @ S2a
@ ( bNF_rel_fun @ D @ H2 @ $o @ $o @ S2c
@ ^ [Y6: $o,Z: $o] : Y6 = Z ) )
@ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ E @ F5 ) @ ( ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ G2 @ H2 ) > $o ) @ ( proces2029722208s_term @ A @ E @ B @ F5 @ S1a @ S2a )
@ ( bNF_rel_fun @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ G2 @ H2 ) @ $o @ $o @ ( proces2029722208s_term @ C @ G2 @ D @ H2 @ S1c @ S2c )
@ ^ [Y6: $o,Z: $o] : Y6 = Z ) ) )
@ ( proces2029722208s_term @ A @ C @ B @ D )
@ ( proces2029722208s_term @ E @ G2 @ F5 @ H2 ) ) ).
% process_term.rel_transfer
thf(fact_251_process__term_Omap__transfer,axiom,
! [A: $tType,C: $tType,B: $tType,D: $tType,L: $tType,J: $tType,K: $tType,I: $tType,R1b: A > I > $o,S1d: C > K > $o,R2b: B > J > $o,S2d: D > L > $o] : ( bNF_rel_fun @ ( A > C ) @ ( I > K ) @ ( ( B > D ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( J > L ) > ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ A @ I @ C @ K @ R1b @ S1d ) @ ( bNF_rel_fun @ ( B > D ) @ ( J > L ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ B @ J @ D @ L @ R2b @ S2d ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ I @ J ) @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ K @ L ) @ ( proces2029722208s_term @ A @ I @ B @ J @ R1b @ R2b ) @ ( proces2029722208s_term @ C @ K @ D @ L @ S1d @ S2d ) ) ) @ ( proces224683037s_term @ A @ C @ B @ D ) @ ( proces224683037s_term @ I @ K @ J @ L ) ) ).
% process_term.map_transfer
thf(fact_252_process_Omap__transfer,axiom,
! [A: $tType,B: $tType,F5: $tType,E: $tType,Rb: A > E > $o,Sd: B > F5 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( E > F5 ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) ) @ ( ( proces634752977rocess @ E ) > ( proces634752977rocess @ F5 ) ) @ ( bNF_rel_fun @ A @ E @ B @ F5 @ Rb @ Sd ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ E ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ F5 ) @ ( proces749077512rocess @ A @ E @ Rb ) @ ( proces749077512rocess @ B @ F5 @ Sd ) ) @ ( proces370407749rocess @ A @ B ) @ ( proces370407749rocess @ E @ F5 ) ) ).
% process.map_transfer
thf(fact_253_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_254_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)
%----Helper facts (3)
thf(help_If_3_1_T,axiom,
! [P3: $o] :
( ( P3 = $true )
| ( P3 = $false ) ) ).
thf(help_If_2_1_T,axiom,
! [A: $tType,X7: A,Y3: A] :
( ( if @ A @ $false @ X7 @ Y3 )
= Y3 ) ).
thf(help_If_1_1_T,axiom,
! [A: $tType,X7: A,Y3: A] :
( ( if @ A @ $true @ X7 @ Y3 )
= X7 ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
( ( a3 = a2 )
& ( p2
= ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ) ) ).
%------------------------------------------------------------------------------