TPTP Problem File: ITP181^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP181^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer Strong_Late_Sim_SC problem prob_189__3410182_1
% Version : Especial.
% English :
% Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source : [Des21]
% Names : Strong_Late_Sim_SC/prob_189__3410182_1 [Des21]
% Status : Theorem
% Rating : 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% Syntax : Number of formulae : 481 ( 181 unt; 128 typ; 0 def)
% Number of atoms : 968 ( 372 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 3651 ( 172 ~; 10 |; 86 &;2926 @)
% ( 0 <=>; 457 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Number of types : 36 ( 35 usr)
% Number of type conns : 366 ( 366 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 93 usr; 11 con; 0-5 aty)
% Number of variables : 1441 ( 26 ^;1373 !; 42 ?;1441 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:30:23.843
%------------------------------------------------------------------------------
% Could-be-implicit typings (35)
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% Explicit typings (93)
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thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
produc1189045204_pi_pi: ( name > noption_pi ) > produc629157763_pi_pi > produc1559976732_pi_pi ).
thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
produc703114481reeRes: ( name > noption_pi ) > produc1834551554reeRes > produc1961110975reeRes ).
thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
produc1275980869_pi_pi: ( name > noption_pi ) > produc1141751126_pi_pi > produc53907987_pi_pi ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
produc1570949143e_name: name > name > produc367475239e_name ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Opi,type,
product_Pair_name_pi: name > pi > product_prod_name_pi ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Oname,type,
product_Pair_pi_name: pi > name > product_prod_pi_name ).
thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Late____Semantics__OfreeRes,type,
produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(sy_c_Relation_OId_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
id_name_noption_pi: set_Pr1569510577ion_pi ).
thf(sy_c_Relation_OId_001t__Agent__Opi,type,
id_pi: set_Pr1834926343_pi_pi ).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(sy_c_Strong__Late__Sim_Oderivative,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(sy_c_Strong__Late__Sim_Osimulation,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
member1632198138ion_pi: produc1462499409ion_pi > set_Pr1569510577ion_pi > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
member695660714_pi_pi: produc53907987_pi_pi > set_Pr100209225_pi_pi > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(sy_v_P,type,
p: pi ).
thf(sy_v_PQ____,type,
pq: pi ).
thf(sy_v_Q,type,
q: pi ).
thf(sy_v_Rel,type,
rel: set_Pr1834926343_pi_pi ).
thf(sy_v_a____,type,
a: late_subject ).
thf(sy_v_x,type,
x: name ).
thf(sy_v_y____,type,
y: name ).
% Relevant facts (352)
thf(fact_0_Eqvt,axiom,
eqvt_pi @ rel ).
% Eqvt
thf(fact_1_Bound_Ohyps_I5_J,axiom,
fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% Bound.hyps(5)
thf(fact_2_Bound_Ohyps_I4_J,axiom,
fresh_717452603ubject @ y @ a ).
% Bound.hyps(4)
thf(fact_3_Bound_Ohyps_I3_J,axiom,
fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% Bound.hyps(3)
thf(fact_4_Bound_Ohyps_I2_J,axiom,
fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% Bound.hyps(2)
thf(fact_5_Bound_Ohyps_I1_J,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% Bound.hyps(1)
thf(fact_6_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y: late_freeRes] :
( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_7_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y: name] :
( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_name_name @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_8_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y: pi] :
( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_name_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_9_fresh__prod,axiom,
! [A: name,X: name,Y: late_freeRes] :
( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_10_fresh__prod,axiom,
! [A: name,X: name,Y: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_name_name @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_11_fresh__prod,axiom,
! [A: name,X: name,Y: pi] :
( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_name_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_12_fresh__prod,axiom,
! [A: name,X: pi,Y: late_freeRes] :
( ( fresh_1504024600reeRes @ A @ ( produc1638681944reeRes @ X @ Y ) )
= ( ( fresh_name_pi @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_13_fresh__prod,axiom,
! [A: name,X: pi,Y: name] :
( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
= ( ( fresh_name_pi @ A @ X )
& ( fresh_name_name @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_14_fresh__prod,axiom,
! [A: name,X: pi,Y: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
= ( ( fresh_name_pi @ A @ X )
& ( fresh_name_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_15_fresh__prod,axiom,
! [A: name,X: name,Y: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_16_pi_Ofresh_I7_J,axiom,
! [A: name,X2: pi,X1: pi] :
( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
= ( ( fresh_name_pi @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(7)
thf(fact_17_transitions_OResB,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_717452603ubject @ Y @ A )
=> ( ( Y != X )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_717452603ubject @ X @ A )
=> ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% transitions.ResB
thf(fact_18_freshBoundDerivative_I1_J,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_717452603ubject @ Y @ A ) ) ) ).
% freshBoundDerivative(1)
thf(fact_19_Late__Semantics_OResB,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_717452603ubject @ Y @ A )
=> ( ( Y != X )
=> ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% Late_Semantics.ResB
thf(fact_20_fresh__prodD_I2_J,axiom,
! [A: name,X: pi,Y: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
=> ( fresh_name_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_21_fresh__prodD_I2_J,axiom,
! [A: name,X: name,Y: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
=> ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_22_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: late_freeRes] :
( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
=> ( fresh_1641682979reeRes @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_23_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: name] :
( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
=> ( fresh_name_name @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_24_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: pi] :
( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
=> ( fresh_name_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_25_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: name > noption_pi] :
( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_26_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
=> ( fresh_1376661020_pi_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_27_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: produc1834551554reeRes] :
( ( fresh_1729533561reeRes @ A @ ( produc703114481reeRes @ X @ Y ) )
=> ( fresh_1711070152reeRes @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_28_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: produc405342261i_name] :
( ( fresh_1513292180i_name @ A @ ( produc1024533510i_name @ X @ Y ) )
=> ( fresh_453496559i_name @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_29_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: produc629157763_pi_pi] :
( ( fresh_1335311330_pi_pi @ A @ ( produc1189045204_pi_pi @ X @ Y ) )
=> ( fresh_253309757_pi_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_30_fresh__prodD_I1_J,axiom,
! [A: name,X: pi,Y: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
=> ( fresh_name_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_31_fresh__prodD_I1_J,axiom,
! [A: name,X: name,Y: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
=> ( fresh_name_name @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_32_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: late_freeRes] :
( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_33_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: name] :
( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_34_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: pi] :
( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_35_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: name > noption_pi] :
( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_36_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_37_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: produc1834551554reeRes] :
( ( fresh_1729533561reeRes @ A @ ( produc703114481reeRes @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_38_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: produc405342261i_name] :
( ( fresh_1513292180i_name @ A @ ( produc1024533510i_name @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_39_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: produc629157763_pi_pi] :
( ( fresh_1335311330_pi_pi @ A @ ( produc1189045204_pi_pi @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_40_freshBoundDerivative_I2_J,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( ( Y != X )
=> ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% freshBoundDerivative(2)
thf(fact_41_prod_Oinject,axiom,
! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
( ( ( product_Pair_pi_pi @ X1 @ X2 )
= ( product_Pair_pi_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_42_prod_Oinject,axiom,
! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ X1 @ X2 )
= ( produc235456326_pi_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_43_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
( ( ( produc1505598906reeRes @ X1 @ X2 )
= ( produc1505598906reeRes @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_44_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
( ( ( produc540578151i_name @ X1 @ X2 )
= ( produc540578151i_name @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_45_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
( ( ( produc1820286517_pi_pi @ X1 @ X2 )
= ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_46_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
( ( ( produc1342893193ion_pi @ X1 @ X2 )
= ( produc1342893193ion_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_47_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: produc1141751126_pi_pi,Y1: name > noption_pi,Y2: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ X1 @ X2 )
= ( produc1275980869_pi_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_48_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: produc1834551554reeRes,Y1: name > noption_pi,Y2: produc1834551554reeRes] :
( ( ( produc703114481reeRes @ X1 @ X2 )
= ( produc703114481reeRes @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_49_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: produc405342261i_name,Y1: name > noption_pi,Y2: produc405342261i_name] :
( ( ( produc1024533510i_name @ X1 @ X2 )
= ( produc1024533510i_name @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_50_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: produc629157763_pi_pi,Y1: name > noption_pi,Y2: produc629157763_pi_pi] :
( ( ( produc1189045204_pi_pi @ X1 @ X2 )
= ( produc1189045204_pi_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_51_old_Oprod_Oinject,axiom,
! [A: pi,B: pi,A2: pi,B2: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_52_old_Oprod_Oinject,axiom,
! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_53_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
( ( ( produc1505598906reeRes @ A @ B )
= ( produc1505598906reeRes @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_54_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
( ( ( produc540578151i_name @ A @ B )
= ( produc540578151i_name @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_55_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
( ( ( produc1820286517_pi_pi @ A @ B )
= ( produc1820286517_pi_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_56_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
( ( ( produc1342893193ion_pi @ A @ B )
= ( produc1342893193ion_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_57_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ A @ B )
= ( produc1275980869_pi_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_58_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B: produc1834551554reeRes,A2: name > noption_pi,B2: produc1834551554reeRes] :
( ( ( produc703114481reeRes @ A @ B )
= ( produc703114481reeRes @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_59_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B: produc405342261i_name,A2: name > noption_pi,B2: produc405342261i_name] :
( ( ( produc1024533510i_name @ A @ B )
= ( produc1024533510i_name @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_60_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B: produc629157763_pi_pi,A2: name > noption_pi,B2: produc629157763_pi_pi] :
( ( ( produc1189045204_pi_pi @ A @ B )
= ( produc1189045204_pi_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_61_pi_Odistinct_I81_J,axiom,
! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(81)
thf(fact_62_freshResidual,axiom,
! [P: pi,Rs: late_residual,X: name] :
( ( late_transitions @ P @ Rs )
=> ( ( fresh_name_pi @ X @ P )
=> ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% freshResidual
thf(fact_63_old_Oprod_Oinducts,axiom,
! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_64_old_Oprod_Oinducts,axiom,
! [P: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_65_old_Oprod_Oinducts,axiom,
! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_66_old_Oprod_Oinducts,axiom,
! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_67_old_Oprod_Oinducts,axiom,
! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_68_old_Oprod_Oinducts,axiom,
! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_69_old_Oprod_Oinducts,axiom,
! [P: produc53907987_pi_pi > $o,Prod: produc53907987_pi_pi] :
( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_70_old_Oprod_Oinducts,axiom,
! [P: produc1961110975reeRes > $o,Prod: produc1961110975reeRes] :
( ! [A3: name > noption_pi,B3: produc1834551554reeRes] : ( P @ ( produc703114481reeRes @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_71_old_Oprod_Oinducts,axiom,
! [P: produc1443308494i_name > $o,Prod: produc1443308494i_name] :
( ! [A3: name > noption_pi,B3: produc405342261i_name] : ( P @ ( produc1024533510i_name @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_72_old_Oprod_Oinducts,axiom,
! [P: produc1559976732_pi_pi > $o,Prod: produc1559976732_pi_pi] :
( ! [A3: name > noption_pi,B3: produc629157763_pi_pi] : ( P @ ( produc1189045204_pi_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_73_old_Oprod_Oexhaust,axiom,
! [Y: product_prod_pi_pi] :
~ ! [A3: pi,B3: pi] :
( Y
!= ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_74_old_Oprod_Oexhaust,axiom,
! [Y: produc1141751126_pi_pi] :
~ ! [A3: name,B3: product_prod_pi_pi] :
( Y
!= ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_75_old_Oprod_Oexhaust,axiom,
! [Y: produc1834551554reeRes] :
~ ! [A3: name > noption_pi,B3: late_freeRes] :
( Y
!= ( produc1505598906reeRes @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_76_old_Oprod_Oexhaust,axiom,
! [Y: produc405342261i_name] :
~ ! [A3: name > noption_pi,B3: name] :
( Y
!= ( produc540578151i_name @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_77_old_Oprod_Oexhaust,axiom,
! [Y: produc629157763_pi_pi] :
~ ! [A3: name > noption_pi,B3: pi] :
( Y
!= ( produc1820286517_pi_pi @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_78_old_Oprod_Oexhaust,axiom,
! [Y: produc1462499409ion_pi] :
~ ! [A3: name > noption_pi,B3: name > noption_pi] :
( Y
!= ( produc1342893193ion_pi @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_79_old_Oprod_Oexhaust,axiom,
! [Y: produc53907987_pi_pi] :
~ ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] :
( Y
!= ( produc1275980869_pi_pi @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_80_old_Oprod_Oexhaust,axiom,
! [Y: produc1961110975reeRes] :
~ ! [A3: name > noption_pi,B3: produc1834551554reeRes] :
( Y
!= ( produc703114481reeRes @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_81_old_Oprod_Oexhaust,axiom,
! [Y: produc1443308494i_name] :
~ ! [A3: name > noption_pi,B3: produc405342261i_name] :
( Y
!= ( produc1024533510i_name @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_82_old_Oprod_Oexhaust,axiom,
! [Y: produc1559976732_pi_pi] :
~ ! [A3: name > noption_pi,B3: produc629157763_pi_pi] :
( Y
!= ( produc1189045204_pi_pi @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_83_Pair__inject,axiom,
! [A: pi,B: pi,A2: pi,B2: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_84_Pair__inject,axiom,
! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_85_Pair__inject,axiom,
! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
( ( ( produc1505598906reeRes @ A @ B )
= ( produc1505598906reeRes @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_86_Pair__inject,axiom,
! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
( ( ( produc540578151i_name @ A @ B )
= ( produc540578151i_name @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_87_Pair__inject,axiom,
! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
( ( ( produc1820286517_pi_pi @ A @ B )
= ( produc1820286517_pi_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_88_Pair__inject,axiom,
! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
( ( ( produc1342893193ion_pi @ A @ B )
= ( produc1342893193ion_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_89_Pair__inject,axiom,
! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ A @ B )
= ( produc1275980869_pi_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_90_Pair__inject,axiom,
! [A: name > noption_pi,B: produc1834551554reeRes,A2: name > noption_pi,B2: produc1834551554reeRes] :
( ( ( produc703114481reeRes @ A @ B )
= ( produc703114481reeRes @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_91_Pair__inject,axiom,
! [A: name > noption_pi,B: produc405342261i_name,A2: name > noption_pi,B2: produc405342261i_name] :
( ( ( produc1024533510i_name @ A @ B )
= ( produc1024533510i_name @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_92_Pair__inject,axiom,
! [A: name > noption_pi,B: produc629157763_pi_pi,A2: name > noption_pi,B2: produc629157763_pi_pi] :
( ( ( produc1189045204_pi_pi @ A @ B )
= ( produc1189045204_pi_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_93_prod__cases,axiom,
! [P: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_94_prod__cases,axiom,
! [P: produc1141751126_pi_pi > $o,P3: produc1141751126_pi_pi] :
( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_95_prod__cases,axiom,
! [P: produc1834551554reeRes > $o,P3: produc1834551554reeRes] :
( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_96_prod__cases,axiom,
! [P: produc405342261i_name > $o,P3: produc405342261i_name] :
( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_97_prod__cases,axiom,
! [P: produc629157763_pi_pi > $o,P3: produc629157763_pi_pi] :
( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_98_prod__cases,axiom,
! [P: produc1462499409ion_pi > $o,P3: produc1462499409ion_pi] :
( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_99_prod__cases,axiom,
! [P: produc53907987_pi_pi > $o,P3: produc53907987_pi_pi] :
( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_100_prod__cases,axiom,
! [P: produc1961110975reeRes > $o,P3: produc1961110975reeRes] :
( ! [A3: name > noption_pi,B3: produc1834551554reeRes] : ( P @ ( produc703114481reeRes @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_101_prod__cases,axiom,
! [P: produc1443308494i_name > $o,P3: produc1443308494i_name] :
( ! [A3: name > noption_pi,B3: produc405342261i_name] : ( P @ ( produc1024533510i_name @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_102_prod__cases,axiom,
! [P: produc1559976732_pi_pi > $o,P3: produc1559976732_pi_pi] :
( ! [A3: name > noption_pi,B3: produc629157763_pi_pi] : ( P @ ( produc1189045204_pi_pi @ A3 @ B3 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_103_surj__pair,axiom,
! [P3: produc1217648014ion_pi] :
? [X3: name > noption_pi,Y3: produc1462499409ion_pi] :
( P3
= ( produc674047040ion_pi @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_104_surj__pair,axiom,
! [P3: produc1141751126_pi_pi] :
? [X3: name,Y3: product_prod_pi_pi] :
( P3
= ( produc235456326_pi_pi @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_105_surj__pair,axiom,
! [P3: product_prod_pi_pi] :
? [X3: pi,Y3: pi] :
( P3
= ( product_Pair_pi_pi @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_106_surj__pair,axiom,
! [P3: produc1834551554reeRes] :
? [X3: name > noption_pi,Y3: late_freeRes] :
( P3
= ( produc1505598906reeRes @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_107_surj__pair,axiom,
! [P3: produc53907987_pi_pi] :
? [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
( P3
= ( produc1275980869_pi_pi @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_108_surj__pair,axiom,
! [P3: produc405342261i_name] :
? [X3: name > noption_pi,Y3: name] :
( P3
= ( produc540578151i_name @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_109_surj__pair,axiom,
! [P3: produc629157763_pi_pi] :
? [X3: name > noption_pi,Y3: pi] :
( P3
= ( produc1820286517_pi_pi @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_110_surj__pair,axiom,
! [P3: produc1462499409ion_pi] :
? [X3: name > noption_pi,Y3: name > noption_pi] :
( P3
= ( produc1342893193ion_pi @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_111_name__exists__fresh,axiom,
! [X: late_freeRes] :
~ ! [C: name] :
~ ( fresh_1641682979reeRes @ C @ X ) ).
% name_exists_fresh
thf(fact_112_name__exists__fresh,axiom,
! [X: produc1141751126_pi_pi] :
~ ! [C: name] :
~ ( fresh_1376661020_pi_pi @ C @ X ) ).
% name_exists_fresh
thf(fact_113_name__exists__fresh,axiom,
! [X: name] :
~ ! [C: name] :
~ ( fresh_name_name @ C @ X ) ).
% name_exists_fresh
thf(fact_114_name__exists__fresh,axiom,
! [X: pi] :
~ ! [C: name] :
~ ( fresh_name_pi @ C @ X ) ).
% name_exists_fresh
thf(fact_115_pi_Oinject_I6_J,axiom,
! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
( ( ( sum @ X2 @ X1 )
= ( sum @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(6)
thf(fact_116_prod__induct4,axiom,
! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
( ! [A3: name > noption_pi,B3: name,C: pi,D: pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C @ D ) ) ) )
=> ( P @ X ) ) ).
% prod_induct4
thf(fact_117_prod__induct3,axiom,
! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
( ! [A3: name,B3: pi,C: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_118_prod__induct3,axiom,
! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
( ! [A3: name > noption_pi,B3: name,C: product_prod_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_119_prod__cases4,axiom,
! [Y: produc53907987_pi_pi] :
~ ! [A3: name > noption_pi,B3: name,C: pi,D: pi] :
( Y
!= ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C @ D ) ) ) ) ).
% prod_cases4
thf(fact_120_prod__cases3,axiom,
! [Y: produc1141751126_pi_pi] :
~ ! [A3: name,B3: pi,C: pi] :
( Y
!= ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) ) ).
% prod_cases3
thf(fact_121_prod__cases3,axiom,
! [Y: produc53907987_pi_pi] :
~ ! [A3: name > noption_pi,B3: name,C: product_prod_pi_pi] :
( Y
!= ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C ) ) ) ).
% prod_cases3
thf(fact_122_freshRes,axiom,
! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% freshRes
thf(fact_123_Sum2,axiom,
! [Q: pi,Rs: late_residual,P: pi] :
( ( late_transitions @ Q @ Rs )
=> ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% Sum2
thf(fact_124_Sum1,axiom,
! [P: pi,Rs: late_residual,Q: pi] :
( ( late_transitions @ P @ Rs )
=> ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% Sum1
thf(fact_125_sumCases_H,axiom,
! [P: pi,Q: pi,Rs: late_residual] :
( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
=> ( ~ ( late_transitions @ P @ Rs )
=> ( late_transitions @ Q @ Rs ) ) ) ).
% sumCases'
thf(fact_126_sumCases,axiom,
! [P: pi,Q: pi,Rs: late_residual] :
( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
=> ( ~ ( late_transitions @ P @ Rs )
=> ( late_transitions @ Q @ Rs ) ) ) ).
% sumCases
thf(fact_127_Id,axiom,
ord_le630093991_pi_pi @ id_pi @ rel ).
% Id
thf(fact_128_transitions_OPar2B,axiom,
! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_717452603ubject @ X @ A )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% transitions.Par2B
thf(fact_129_transitions_OPar1B,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_717452603ubject @ X @ A )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% transitions.Par1B
thf(fact_130_mem__Collect__eq,axiom,
! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_131_Collect__mem__eq,axiom,
! [A4: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
= A4 ) ).
% Collect_mem_eq
thf(fact_132_parCasesB_H,axiom,
! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
=> ( ! [P4: pi,A3: late_subject,X3: name,P5: pi,Q3: pi] :
( ( ( par @ P @ Q )
= ( par @ P4 @ Q3 ) )
=> ( ( ( late_BoundR @ B @ Y @ P2 )
= ( late_BoundR @ A3 @ X3 @ ( par @ P5 @ Q3 ) ) )
=> ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
=> ( ( fresh_name_pi @ X3 @ P4 )
=> ( ( fresh_name_pi @ X3 @ Q3 )
=> ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) )
=> ~ ! [Q3: pi,A3: late_subject,X3: name,Q4: pi,P4: pi] :
( ( ( par @ P @ Q )
= ( par @ P4 @ Q3 ) )
=> ( ( ( late_BoundR @ B @ Y @ P2 )
= ( late_BoundR @ A3 @ X3 @ ( par @ P4 @ Q4 ) ) )
=> ( ( late_transitions @ Q3 @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
=> ( ( fresh_name_pi @ X3 @ P4 )
=> ( ( fresh_name_pi @ X3 @ Q3 )
=> ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ).
% parCasesB'
thf(fact_133_inputIneqTrans,axiom,
! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
=> ~ ( fresh_717452603ubject @ A @ B ) ) ).
% inputIneqTrans
thf(fact_134_resTauBoundTrans,axiom,
! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% resTauBoundTrans
thf(fact_135_residual_Ostrong__inducts,axiom,
! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_freeRes] :
( ( fresh_1641682979reeRes @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_136_residual_Ostrong__inducts,axiom,
! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_137_residual_Ostrong__inducts,axiom,
! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: name] :
( ( fresh_name_name @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_138_residual_Ostrong__inducts,axiom,
! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: pi] :
( ( fresh_name_pi @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_139_residual_Ostrong__induct,axiom,
! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_freeRes] :
( ( fresh_1641682979reeRes @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_140_residual_Ostrong__induct,axiom,
! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_141_residual_Ostrong__induct,axiom,
! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: name] :
( ( fresh_name_name @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_142_residual_Ostrong__induct,axiom,
! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: pi] :
( ( fresh_name_pi @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_143_pi_Ofresh_I8_J,axiom,
! [A: name,X2: pi,X1: pi] :
( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
= ( ( fresh_name_pi @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(8)
thf(fact_144_pi_Ofresh_I3_J,axiom,
! [A: name,X1: pi] :
( ( fresh_name_pi @ A @ ( tau @ X1 ) )
= ( fresh_name_pi @ A @ X1 ) ) ).
% pi.fresh(3)
thf(fact_145_residual_Ofresh_I2_J,axiom,
! [A: name,X2: late_freeRes,X1: pi] :
( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
= ( ( fresh_1641682979reeRes @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% residual.fresh(2)
thf(fact_146_residual_Oinject_I2_J,axiom,
! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
( ( ( late_FreeR @ X2 @ X1 )
= ( late_FreeR @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% residual.inject(2)
thf(fact_147_pi_Odistinct_I35_J,axiom,
! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
( ( tau @ Pi4 )
!= ( input @ Name1 @ Name22 @ Pi ) ) ).
% pi.distinct(35)
thf(fact_148_pi_Odistinct_I43_J,axiom,
! [Pi4: pi,Pi12: pi,Pi22: pi] :
( ( tau @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(43)
thf(fact_149_pi_Odistinct_I55_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(55)
thf(fact_150_pi_Oinject_I2_J,axiom,
! [X1: pi,Y1: pi] :
( ( ( tau @ X1 )
= ( tau @ Y1 ) )
= ( X1 = Y1 ) ) ).
% pi.inject(2)
thf(fact_151_pi_Oinject_I7_J,axiom,
! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
( ( ( par @ X2 @ X1 )
= ( par @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(7)
thf(fact_152_Par2F,axiom,
! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% Par2F
thf(fact_153_Par1F,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% Par1F
thf(fact_154_inputFreeTrans,axiom,
! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% inputFreeTrans
thf(fact_155_resInputFreeTrans,axiom,
! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% resInputFreeTrans
thf(fact_156_pi_Odistinct_I85_J,axiom,
! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(85)
thf(fact_157_pi_Odistinct_I79_J,axiom,
! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(79)
thf(fact_158_residual_Odistinct_I1_J,axiom,
! [Subject2: late_subject,Name3: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
( ( late_BoundR @ Subject2 @ Name3 @ Pi4 )
!= ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% residual.distinct(1)
thf(fact_159_residual_Oinducts,axiom,
! [P: late_residual > $o,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Residual ) ) ) ).
% residual.inducts
thf(fact_160_pi_Odistinct_I57_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(57)
thf(fact_161_pi_Odistinct_I45_J,axiom,
! [Pi4: pi,Name: name,Pi: pi] :
( ( tau @ Pi4 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(45)
thf(fact_162_pi_Odistinct_I53_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(53)
thf(fact_163_pi_Odistinct_I41_J,axiom,
! [Pi4: pi,Pi12: pi,Pi22: pi] :
( ( tau @ Pi4 )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(41)
thf(fact_164_resCasesF,axiom,
! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
=> ( ! [P5: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha )
=> ( F @ ( res @ X @ P5 ) ) ) )
=> ( F @ XP ) ) ) ).
% resCasesF
thf(fact_165_resCasesF_H,axiom,
! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
=> ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
( ( ( res @ X @ P )
= ( res @ Y3 @ P4 ) )
=> ( ( ( late_FreeR @ Alpha @ P2 )
= ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
=> ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
=> ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% resCasesF'
thf(fact_166_ResF,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( fresh_1641682979reeRes @ Y @ Alpha )
=> ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% ResF
thf(fact_167_freshFreeDerivative_I2_J,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_name_pi @ Y @ P2 ) ) ) ).
% freshFreeDerivative(2)
thf(fact_168_freshFreeDerivative_I1_J,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% freshFreeDerivative(1)
thf(fact_169_resTrans_I2_J,axiom,
! [X: name,Y: name,P: pi,Rs: late_residual] :
~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% resTrans(2)
thf(fact_170_tauBoundTrans,axiom,
! [P: pi,A: late_subject,X: name,P2: pi] :
~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% tauBoundTrans
thf(fact_171_Late__Semantics_OPar1B,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_name_pi @ X @ Q )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% Late_Semantics.Par1B
thf(fact_172_Late__Semantics_OPar2B,axiom,
! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% Late_Semantics.Par2B
thf(fact_173_parCasesB,axiom,
! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ! [P5: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
=> ( Prop @ ( par @ P5 @ Q ) ) )
=> ( ! [Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q4 ) )
=> ( Prop @ ( par @ P @ Q4 ) ) )
=> ( Prop @ PQ ) ) ) ) ) ) ).
% parCasesB
thf(fact_174_IdI,axiom,
! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% IdI
thf(fact_175_IdI,axiom,
! [A: name > noption_pi] : ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ A ) @ id_name_noption_pi ) ).
% IdI
thf(fact_176_pair__in__Id__conv,axiom,
! [A: pi,B: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
= ( A = B ) ) ).
% pair_in_Id_conv
thf(fact_177_pair__in__Id__conv,axiom,
! [A: name > noption_pi,B: name > noption_pi] :
( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
= ( A = B ) ) ).
% pair_in_Id_conv
thf(fact_178_subsetI,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
( ! [X3: product_prod_pi_pi] :
( ( member558706512_pi_pi @ X3 @ A4 )
=> ( member558706512_pi_pi @ X3 @ B4 ) )
=> ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% subsetI
thf(fact_179_subset__antisym,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ( ( ord_le630093991_pi_pi @ B4 @ A4 )
=> ( A4 = B4 ) ) ) ).
% subset_antisym
thf(fact_180_order__refl,axiom,
! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% order_refl
thf(fact_181_IdE,axiom,
! [P3: product_prod_pi_pi] :
( ( member558706512_pi_pi @ P3 @ id_pi )
=> ~ ! [X3: pi] :
( P3
!= ( product_Pair_pi_pi @ X3 @ X3 ) ) ) ).
% IdE
thf(fact_182_IdE,axiom,
! [P3: produc1462499409ion_pi] :
( ( member1632198138ion_pi @ P3 @ id_name_noption_pi )
=> ~ ! [X3: name > noption_pi] :
( P3
!= ( produc1342893193ion_pi @ X3 @ X3 ) ) ) ).
% IdE
thf(fact_183_IdD,axiom,
! [A: pi,B: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
=> ( A = B ) ) ).
% IdD
thf(fact_184_IdD,axiom,
! [A: name > noption_pi,B: name > noption_pi] :
( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
=> ( A = B ) ) ).
% IdD
thf(fact_185_subrelI,axiom,
! [R: set_Pr1654044726_pi_pi,S: set_Pr1654044726_pi_pi] :
( ! [X3: name,Y3: product_prod_pi_pi] :
( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X3 @ Y3 ) @ R )
=> ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X3 @ Y3 ) @ S ) )
=> ( ord_le797229014_pi_pi @ R @ S ) ) ).
% subrelI
thf(fact_186_subrelI,axiom,
! [R: set_Pr305743074reeRes,S: set_Pr305743074reeRes] :
( ! [X3: name > noption_pi,Y3: late_freeRes] :
( ( member2081207979reeRes @ ( produc1505598906reeRes @ X3 @ Y3 ) @ R )
=> ( member2081207979reeRes @ ( produc1505598906reeRes @ X3 @ Y3 ) @ S ) )
=> ( ord_le1762471042reeRes @ R @ S ) ) ).
% subrelI
thf(fact_187_subrelI,axiom,
! [R: set_Pr100209225_pi_pi,S: set_Pr100209225_pi_pi] :
( ! [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
( ( member695660714_pi_pi @ ( produc1275980869_pi_pi @ X3 @ Y3 ) @ R )
=> ( member695660714_pi_pi @ ( produc1275980869_pi_pi @ X3 @ Y3 ) @ S ) )
=> ( ord_le211833513_pi_pi @ R @ S ) ) ).
% subrelI
thf(fact_188_subrelI,axiom,
! [R: set_Pr1294453099i_name,S: set_Pr1294453099i_name] :
( ! [X3: name > noption_pi,Y3: name] :
( ( member1353687244i_name @ ( produc540578151i_name @ X3 @ Y3 ) @ R )
=> ( member1353687244i_name @ ( produc540578151i_name @ X3 @ Y3 ) @ S ) )
=> ( ord_le2082425291i_name @ R @ S ) ) ).
% subrelI
thf(fact_189_subrelI,axiom,
! [R: set_Pr1694908217_pi_pi,S: set_Pr1694908217_pi_pi] :
( ! [X3: name > noption_pi,Y3: pi] :
( ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X3 @ Y3 ) @ R )
=> ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X3 @ Y3 ) @ S ) )
=> ( ord_le1854926745_pi_pi @ R @ S ) ) ).
% subrelI
thf(fact_190_subrelI,axiom,
! [R: set_Pr1569510577ion_pi,S: set_Pr1569510577ion_pi] :
( ! [X3: name > noption_pi,Y3: name > noption_pi] :
( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X3 @ Y3 ) @ R )
=> ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X3 @ Y3 ) @ S ) )
=> ( ord_le1032043601ion_pi @ R @ S ) ) ).
% subrelI
thf(fact_191_subrelI,axiom,
! [R: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
( ! [X3: pi,Y3: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X3 @ Y3 ) @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X3 @ Y3 ) @ S ) )
=> ( ord_le630093991_pi_pi @ R @ S ) ) ).
% subrelI
thf(fact_192_dual__order_Oantisym,axiom,
! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ B @ A )
=> ( ( ord_le630093991_pi_pi @ A @ B )
=> ( A = B ) ) ) ).
% dual_order.antisym
thf(fact_193_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : Y4 = Z3 )
= ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ B5 @ A5 )
& ( ord_le630093991_pi_pi @ A5 @ B5 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_194_dual__order_Otrans,axiom,
! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ B @ A )
=> ( ( ord_le630093991_pi_pi @ C2 @ B )
=> ( ord_le630093991_pi_pi @ C2 @ A ) ) ) ).
% dual_order.trans
thf(fact_195_dual__order_Orefl,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% dual_order.refl
thf(fact_196_order__trans,axiom,
! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X @ Y )
=> ( ( ord_le630093991_pi_pi @ Y @ Z )
=> ( ord_le630093991_pi_pi @ X @ Z ) ) ) ).
% order_trans
thf(fact_197_order__class_Oorder_Oantisym,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ) ).
% order_class.order.antisym
thf(fact_198_ord__le__eq__trans,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( B = C2 )
=> ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% ord_le_eq_trans
thf(fact_199_ord__eq__le__trans,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ( ord_le630093991_pi_pi @ B @ C2 )
=> ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% ord_eq_le_trans
thf(fact_200_order__class_Oorder_Oeq__iff,axiom,
( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : Y4 = Z3 )
= ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A5 @ B5 )
& ( ord_le630093991_pi_pi @ B5 @ A5 ) ) ) ) ).
% order_class.order.eq_iff
thf(fact_201_antisym__conv,axiom,
! [Y: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ Y @ X )
=> ( ( ord_le630093991_pi_pi @ X @ Y )
= ( X = Y ) ) ) ).
% antisym_conv
thf(fact_202_order_Otrans,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C2 )
=> ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% order.trans
thf(fact_203_eq__refl,axiom,
! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
( ( X = Y )
=> ( ord_le630093991_pi_pi @ X @ Y ) ) ).
% eq_refl
thf(fact_204_antisym,axiom,
! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X @ Y )
=> ( ( ord_le630093991_pi_pi @ Y @ X )
=> ( X = Y ) ) ) ).
% antisym
thf(fact_205_eq__iff,axiom,
( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : Y4 = Z3 )
= ( ^ [X4: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X4 @ Y5 )
& ( ord_le630093991_pi_pi @ Y5 @ X4 ) ) ) ) ).
% eq_iff
thf(fact_206_ord__le__eq__subst,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ( F2 @ B )
= C2 )
=> ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X3 @ Y3 )
=> ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
=> ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_207_ord__eq__le__subst,axiom,
! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( A
= ( F2 @ B ) )
=> ( ( ord_le630093991_pi_pi @ B @ C2 )
=> ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X3 @ Y3 )
=> ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_208_order__subst2,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ ( F2 @ B ) @ C2 )
=> ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X3 @ Y3 )
=> ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
=> ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_209_order__subst1,axiom,
! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ ( F2 @ B ) )
=> ( ( ord_le630093991_pi_pi @ B @ C2 )
=> ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X3 @ Y3 )
=> ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_210_Collect__mono__iff,axiom,
! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
( ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) )
= ( ! [X4: product_prod_pi_pi] :
( ( P @ X4 )
=> ( Q @ X4 ) ) ) ) ).
% Collect_mono_iff
thf(fact_211_set__eq__subset,axiom,
( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : Y4 = Z3 )
= ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A6 @ B6 )
& ( ord_le630093991_pi_pi @ B6 @ A6 ) ) ) ) ).
% set_eq_subset
thf(fact_212_subset__trans,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,C3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ( ( ord_le630093991_pi_pi @ B4 @ C3 )
=> ( ord_le630093991_pi_pi @ A4 @ C3 ) ) ) ).
% subset_trans
thf(fact_213_Collect__mono,axiom,
! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
( ! [X3: product_prod_pi_pi] :
( ( P @ X3 )
=> ( Q @ X3 ) )
=> ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) ) ) ).
% Collect_mono
thf(fact_214_subset__refl,axiom,
! [A4: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A4 @ A4 ) ).
% subset_refl
thf(fact_215_subset__iff,axiom,
( ord_le630093991_pi_pi
= ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
! [T: product_prod_pi_pi] :
( ( member558706512_pi_pi @ T @ A6 )
=> ( member558706512_pi_pi @ T @ B6 ) ) ) ) ).
% subset_iff
thf(fact_216_equalityD2,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
( ( A4 = B4 )
=> ( ord_le630093991_pi_pi @ B4 @ A4 ) ) ).
% equalityD2
thf(fact_217_equalityD1,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
( ( A4 = B4 )
=> ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% equalityD1
thf(fact_218_subset__eq,axiom,
( ord_le630093991_pi_pi
= ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
! [X4: product_prod_pi_pi] :
( ( member558706512_pi_pi @ X4 @ A6 )
=> ( member558706512_pi_pi @ X4 @ B6 ) ) ) ) ).
% subset_eq
thf(fact_219_equalityE,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
( ( A4 = B4 )
=> ~ ( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ~ ( ord_le630093991_pi_pi @ B4 @ A4 ) ) ) ).
% equalityE
thf(fact_220_subsetD,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,C2: product_prod_pi_pi] :
( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ( ( member558706512_pi_pi @ C2 @ A4 )
=> ( member558706512_pi_pi @ C2 @ B4 ) ) ) ).
% subsetD
thf(fact_221_in__mono,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,X: product_prod_pi_pi] :
( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ( ( member558706512_pi_pi @ X @ A4 )
=> ( member558706512_pi_pi @ X @ B4 ) ) ) ).
% in_mono
thf(fact_222_resInputBoundOutputTrans,axiom,
! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% resInputBoundOutputTrans
thf(fact_223_resTauOutputTrans,axiom,
! [X: name,P: pi,A: name,B: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% resTauOutputTrans
thf(fact_224_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
( ( eqvt_pi @ Rel )
=> ( ! [A3: late_subject,X3: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
=> ( ( fresh_name_pi @ X3 @ P )
=> ( ( fresh_name_pi @ X3 @ Q )
=> ( ( fresh_717452603ubject @ X3 @ A3 )
=> ( ( fresh_1641682979reeRes @ X3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_225_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
( ( eqvt_pi @ Rel )
=> ( ! [A3: late_subject,X3: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
=> ( ( fresh_name_pi @ X3 @ P )
=> ( ( fresh_name_pi @ X3 @ Q )
=> ( ( fresh_717452603ubject @ X3 @ A3 )
=> ( ( fresh_1376661020_pi_pi @ X3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_226_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
( ( eqvt_pi @ Rel )
=> ( ! [A3: late_subject,X3: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
=> ( ( fresh_name_pi @ X3 @ P )
=> ( ( fresh_name_pi @ X3 @ Q )
=> ( ( fresh_717452603ubject @ X3 @ A3 )
=> ( ( fresh_name_name @ X3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_227_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
( ( eqvt_pi @ Rel )
=> ( ! [A3: late_subject,X3: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
=> ( ( fresh_name_pi @ X3 @ P )
=> ( ( fresh_name_pi @ X3 @ Q )
=> ( ( fresh_717452603ubject @ X3 @ A3 )
=> ( ( fresh_name_pi @ X3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_228_residual_Ofresh_I1_J,axiom,
! [A: name,X32: late_subject,X1: name,X2: pi] :
( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
= ( ( fresh_717452603ubject @ A @ X32 )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% residual.fresh(1)
thf(fact_229_resCases_H,axiom,
! [X: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( res @ X @ P ) @ Rs )
=> ( ! [P4: pi,A3: name,B3: name] :
( ( ( res @ X @ P )
= ( res @ B3 @ P4 ) )
=> ! [P5: pi] :
( ( Rs
= ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
=> ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
=> ( A3 = B3 ) ) ) )
=> ( ! [P4: pi,A3: late_subject,X3: name,P5: pi,Y3: name] :
( ( ( res @ X @ P )
= ( res @ Y3 @ P4 ) )
=> ( ( Rs
= ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P5 ) ) )
=> ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
=> ( ( fresh_717452603ubject @ Y3 @ A3 )
=> ( ( Y3 != X3 )
=> ( ( fresh_name_pi @ X3 @ P4 )
=> ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) )
=> ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
( ( ( res @ X @ P )
= ( res @ Y3 @ P4 ) )
=> ( ( Rs
= ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
=> ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
=> ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% resCases'
thf(fact_230_Late__Semantics_OfreeRes_Oinject,axiom,
! [X2: name,X1: name,Y2: name,Y1: name] :
( ( ( late_OutputR @ X2 @ X1 )
= ( late_OutputR @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% Late_Semantics.freeRes.inject
thf(fact_231_Late__Semantics_Osubject_Oinject_I2_J,axiom,
! [X1: name,Y1: name] :
( ( ( late_BoundOutputS @ X1 )
= ( late_BoundOutputS @ Y1 ) )
= ( X1 = Y1 ) ) ).
% Late_Semantics.subject.inject(2)
thf(fact_232_subject_Ofresh_I2_J,axiom,
! [A: name,X1: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
= ( fresh_name_name @ A @ X1 ) ) ).
% subject.fresh(2)
thf(fact_233_freeRes_Ofresh_I1_J,axiom,
! [A: name,X2: name,X1: name] :
( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
= ( ( fresh_name_name @ A @ X2 )
& ( fresh_name_name @ A @ X1 ) ) ) ).
% freeRes.fresh(1)
thf(fact_234_pi_Ofresh_I9_J,axiom,
! [A: name,X1: name,X2: pi] :
( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
= ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% pi.fresh(9)
thf(fact_235_pi_Ofresh_I4_J,axiom,
! [A: name,X32: name,X1: name,X2: pi] :
( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
= ( ( fresh_name_name @ A @ X32 )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% pi.fresh(4)
thf(fact_236_monotonic,axiom,
! [P: pi,A4: set_Pr1834926343_pi_pi,P2: pi,B4: set_Pr1834926343_pi_pi] :
( ( strong743114133lation @ P @ A4 @ P2 )
=> ( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ( strong743114133lation @ P @ B4 @ P2 ) ) ) ).
% monotonic
thf(fact_237_abs__fun__eq1,axiom,
! [A: name,X: pi,Y: pi] :
( ( ( abs_fun_name_pi @ A @ X )
= ( abs_fun_name_pi @ A @ Y ) )
= ( X = Y ) ) ).
% abs_fun_eq1
thf(fact_238_derivativeMonotonic,axiom,
! [P: pi,Q: pi,A: late_subject,X: name,A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
( ( strong2129052853vative @ P @ Q @ A @ X @ A4 )
=> ( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ( strong2129052853vative @ P @ Q @ A @ X @ B4 ) ) ) ).
% derivativeMonotonic
thf(fact_239_pi_Oinject_I8_J,axiom,
! [X1: name,X2: pi,Y1: name,Y2: pi] :
( ( ( res @ X1 @ X2 )
= ( res @ Y1 @ Y2 ) )
= ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% pi.inject(8)
thf(fact_240_residual_Oinject_I1_J,axiom,
! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
( ( ( late_BoundR @ X32 @ X1 @ X2 )
= ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
= ( ( X32 = Y32 )
& ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% residual.inject(1)
thf(fact_241_abs__fresh_I1_J,axiom,
! [B: name,A: name,X: late_freeRes] :
( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
= ( ( B = A )
| ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% abs_fresh(1)
thf(fact_242_abs__fresh_I1_J,axiom,
! [B: name,A: name,X: produc1141751126_pi_pi] :
( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
= ( ( B = A )
| ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% abs_fresh(1)
thf(fact_243_abs__fresh_I1_J,axiom,
! [B: name,A: name,X: name] :
( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
= ( ( B = A )
| ( fresh_name_name @ B @ X ) ) ) ).
% abs_fresh(1)
thf(fact_244_abs__fresh_I1_J,axiom,
! [B: name,A: name,X: pi] :
( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
= ( ( B = A )
| ( fresh_name_pi @ B @ X ) ) ) ).
% abs_fresh(1)
thf(fact_245_name__fresh__abs,axiom,
! [B: name,A: name,X: late_freeRes] :
( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
= ( ( B = A )
| ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% name_fresh_abs
thf(fact_246_name__fresh__abs,axiom,
! [B: name,A: name,X: produc1141751126_pi_pi] :
( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
= ( ( B = A )
| ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% name_fresh_abs
thf(fact_247_name__fresh__abs,axiom,
! [B: name,A: name,X: name] :
( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
= ( ( B = A )
| ( fresh_name_name @ B @ X ) ) ) ).
% name_fresh_abs
thf(fact_248_name__fresh__abs,axiom,
! [B: name,A: name,X: pi] :
( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
= ( ( B = A )
| ( fresh_name_pi @ B @ X ) ) ) ).
% name_fresh_abs
thf(fact_249_pi_Oinject_I3_J,axiom,
! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
( ( ( input @ X32 @ X1 @ X2 )
= ( input @ Y32 @ Y1 @ Y2 ) )
= ( ( X32 = Y32 )
& ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% pi.inject(3)
thf(fact_250_simE_I1_J,axiom,
! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
( ( strong743114133lation @ P @ Rel @ Q )
=> ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ? [P5: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
& ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% simE(1)
thf(fact_251_Strong__Late__Sim_Oreflexive,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ P @ Rel @ P ) ) ).
% Strong_Late_Sim.reflexive
thf(fact_252_Open,axiom,
! [P: pi,A: name,B: name,P2: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
=> ( ( A != B )
=> ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% Open
thf(fact_253_derivativeReflexive,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi,A: late_subject,X: name] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong2129052853vative @ P @ P @ A @ X @ Rel ) ) ).
% derivativeReflexive
thf(fact_254_simE_I2_J,axiom,
! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
( ( strong743114133lation @ P @ Rel @ Q )
=> ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
=> ? [P5: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% simE(2)
thf(fact_255_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
( ( eqvt_pi @ Rel )
=> ( ! [Q4: pi,A3: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
=> ( ( A3 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
=> ( ! [Q4: pi,A3: late_subject,Y3: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_717452603ubject @ X @ A3 )
=> ( ( X != Y3 )
=> ( ( fresh_1641682979reeRes @ Y3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
=> ( ! [Q4: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_256_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
( ( eqvt_pi @ Rel )
=> ( ! [Q4: pi,A3: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
=> ( ( A3 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
=> ( ! [Q4: pi,A3: late_subject,Y3: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_717452603ubject @ X @ A3 )
=> ( ( X != Y3 )
=> ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
=> ( ! [Q4: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_257_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
( ( eqvt_pi @ Rel )
=> ( ! [Q4: pi,A3: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
=> ( ( A3 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
=> ( ! [Q4: pi,A3: late_subject,Y3: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_717452603ubject @ X @ A3 )
=> ( ( X != Y3 )
=> ( ( fresh_name_name @ Y3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
=> ( ! [Q4: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_258_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
( ( eqvt_pi @ Rel )
=> ( ! [Q4: pi,A3: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
=> ( ( A3 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
=> ( ! [Q4: pi,A3: late_subject,Y3: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_717452603ubject @ X @ A3 )
=> ( ( X != Y3 )
=> ( ( fresh_name_pi @ Y3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
=> ( ! [Q4: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_259_simCases,axiom,
! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
( ! [A3: late_subject,Y3: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_name_pi @ Y3 @ P )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ Y3 @ Rel ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% simCases
thf(fact_260_simulation__def,axiom,
( strong743114133lation
= ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
( ! [A5: late_subject,X4: name,Q6: pi] :
( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
& ( fresh_name_pi @ X4 @ P7 ) )
=> ? [P8: pi] :
( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X4 @ P8 ) )
& ( strong2129052853vative @ P8 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
& ! [Alpha3: late_freeRes,Q6: pi] :
( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
=> ? [P8: pi] :
( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% simulation_def
thf(fact_261_resCasesB_H,axiom,
! [X5: name,P: pi,A: late_subject,Y6: name,P2: pi] :
( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y6 @ P2 ) )
=> ( ! [P4: pi,A3: name,B3: name] :
( ( ( res @ X5 @ P )
= ( res @ B3 @ P4 ) )
=> ! [P5: pi] :
( ( ( late_BoundR @ A @ Y6 @ P2 )
= ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
=> ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
=> ( A3 = B3 ) ) ) )
=> ~ ! [P4: pi,A3: late_subject,X3: name,P5: pi,Y3: name] :
( ( ( res @ X5 @ P )
= ( res @ Y3 @ P4 ) )
=> ( ( ( late_BoundR @ A @ Y6 @ P2 )
= ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P5 ) ) )
=> ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
=> ( ( fresh_717452603ubject @ Y3 @ A3 )
=> ( ( Y3 != X3 )
=> ( ( fresh_name_pi @ X3 @ P4 )
=> ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ) ).
% resCasesB'
thf(fact_262_tauOutputTrans,axiom,
! [P: pi,A: name,B: name,P2: pi] :
~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% tauOutputTrans
thf(fact_263_inputBoundOutputTrans,axiom,
! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% inputBoundOutputTrans
thf(fact_264_sumIdempRight,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% sumIdempRight
thf(fact_265_sumAssocRight,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R2: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R2 ) ) ) ).
% sumAssocRight
thf(fact_266_sumIdempLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% sumIdempLeft
thf(fact_267_sumAssocLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R2: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R2 ) @ Rel @ ( sum @ P @ ( sum @ Q @ R2 ) ) ) ) ).
% sumAssocLeft
thf(fact_268_sumSym,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% sumSym
thf(fact_269_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
! [X2: name,Y2: name] :
( ( ( late_BoundOutputS @ X2 )
= ( late_BoundOutputS @ Y2 ) )
= ( X2 = Y2 ) ) ).
% Late_Semantics1.subject.inject(2)
thf(fact_270_Late__Semantics1_OfreeRes_Oinject,axiom,
! [X11: name,X12: name,Y11: name,Y12: name] :
( ( ( late_OutputR @ X11 @ X12 )
= ( late_OutputR @ Y11 @ Y12 ) )
= ( ( X11 = Y11 )
& ( X12 = Y12 ) ) ) ).
% Late_Semantics1.freeRes.inject
thf(fact_271_sumZeroRight,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% sumZeroRight
thf(fact_272_sumZeroLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% sumZeroLeft
thf(fact_273_name__fresh,axiom,
( fresh_name_name
= ( ^ [A5: name,B5: name] : A5 != B5 ) ) ).
% name_fresh
thf(fact_274_pi_Ofresh_I1_J,axiom,
! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% pi.fresh(1)
thf(fact_275_zeroTrans,axiom,
! [Rs: late_residual] :
~ ( late_transitions @ piNil @ Rs ) ).
% zeroTrans
thf(fact_276_nilCases_H,axiom,
! [Rs: late_residual] :
~ ( late_transitions @ piNil @ Rs ) ).
% nilCases'
thf(fact_277_pi_Odistinct_I15_J,axiom,
! [Name: name,Pi: pi] :
( piNil
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(15)
thf(fact_278_pi_Odistinct_I13_J,axiom,
! [Pi12: pi,Pi22: pi] :
( piNil
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(13)
thf(fact_279_pi_Odistinct_I11_J,axiom,
! [Pi12: pi,Pi22: pi] :
( piNil
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(11)
thf(fact_280_pi_Odistinct_I5_J,axiom,
! [Name1: name,Name22: name,Pi: pi] :
( piNil
!= ( input @ Name1 @ Name22 @ Pi ) ) ).
% pi.distinct(5)
thf(fact_281_pi_Odistinct_I3_J,axiom,
! [Pi: pi] :
( piNil
!= ( tau @ Pi ) ) ).
% pi.distinct(3)
thf(fact_282_nilSimRight,axiom,
! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% nilSimRight
thf(fact_283_resZeroTrans,axiom,
! [X: name,Rs: late_residual] :
~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% resZeroTrans
thf(fact_284_nilSim_I2_J,axiom,
! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% nilSim(2)
thf(fact_285_nilSim_I1_J,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% nilSim(1)
thf(fact_286_inputCases_H,axiom,
! [A: name,B: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
=> ~ ! [X3: name,A3: name,P4: pi] :
( ( ( A = A3 )
& ( ( abs_fun_name_pi @ B @ P )
= ( abs_fun_name_pi @ X3 @ P4 ) ) )
=> ( ( Rs
= ( late_BoundR @ ( late_InputS @ A3 ) @ X3 @ P4 ) )
=> ( X3 = A3 ) ) ) ) ).
% inputCases'
thf(fact_287_subject_Ofresh_I1_J,axiom,
! [A: name,X1: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
= ( fresh_name_name @ A @ X1 ) ) ).
% subject.fresh(1)
thf(fact_288_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
! [X1: name,X2: name] :
( ( late_InputS @ X1 )
!= ( late_BoundOutputS @ X2 ) ) ).
% Late_Semantics1.subject.distinct(1)
thf(fact_289_subject_Oexhaust,axiom,
! [Y: late_subject] :
( ! [X13: name] :
( Y
!= ( late_InputS @ X13 ) )
=> ~ ! [X22: name] :
( Y
!= ( late_BoundOutputS @ X22 ) ) ) ).
% subject.exhaust
thf(fact_290_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
! [Name3: name,Name: name] :
( ( late_InputS @ Name3 )
!= ( late_BoundOutputS @ Name ) ) ).
% Late_Semantics.subject.distinct(1)
thf(fact_291_subject_Oinducts,axiom,
! [P: late_subject > $o,Subject2: late_subject] :
( ! [Name2: name] : ( P @ ( late_InputS @ Name2 ) )
=> ( ! [Name2: name] : ( P @ ( late_BoundOutputS @ Name2 ) )
=> ( P @ Subject2 ) ) ) ).
% subject.inducts
thf(fact_292_Late__Semantics_OInput,axiom,
! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% Late_Semantics.Input
thf(fact_293_transitions_OInput,axiom,
! [X: name,A: name,P: pi] :
( ( X != A )
=> ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% transitions.Input
thf(fact_294_resOutputInputTrans,axiom,
! [X: name,A: name,B: name,P: pi,C2: name,Y: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y @ P2 ) ) ).
% resOutputInputTrans
thf(fact_295_resOutputOutputTrans,axiom,
! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% resOutputOutputTrans
thf(fact_296_Late__Semantics_OClose1,axiom,
! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% Late_Semantics.Close1
thf(fact_297_subst__identity,axiom,
! [P: pi,A: name] :
( ( subs @ P @ A @ A )
= P ) ).
% subst_identity
thf(fact_298_simps_I9_J,axiom,
! [X: name,C2: name,D2: name,P: pi] :
( ( X != C2 )
=> ( ( X != D2 )
=> ( ( subs @ ( res @ X @ P ) @ C2 @ D2 )
= ( res @ X @ ( subs @ P @ C2 @ D2 ) ) ) ) ) ).
% simps(9)
thf(fact_299_simps_I8_J,axiom,
! [P: pi,Q: pi,C2: name,D2: name] :
( ( subs @ ( par @ P @ Q ) @ C2 @ D2 )
= ( par @ ( subs @ P @ C2 @ D2 ) @ ( subs @ Q @ C2 @ D2 ) ) ) ).
% simps(8)
thf(fact_300_substTrans,axiom,
! [B: name,P: pi,A: name,C2: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( subs @ P @ A @ B ) @ B @ C2 )
= ( subs @ P @ A @ C2 ) ) ) ).
% substTrans
thf(fact_301_simps_I7_J,axiom,
! [P: pi,Q: pi,C2: name,D2: name] :
( ( subs @ ( sum @ P @ Q ) @ C2 @ D2 )
= ( sum @ ( subs @ P @ C2 @ D2 ) @ ( subs @ Q @ C2 @ D2 ) ) ) ).
% simps(7)
thf(fact_302_simps_I2_J,axiom,
! [P: pi,C2: name,D2: name] :
( ( subs @ ( tau @ P ) @ C2 @ D2 )
= ( tau @ ( subs @ P @ C2 @ D2 ) ) ) ).
% simps(2)
thf(fact_303_simps_I1_J,axiom,
! [C2: name,D2: name] :
( ( subs @ piNil @ C2 @ D2 )
= piNil ) ).
% simps(1)
thf(fact_304_freeRes_Ofresh_I2_J,axiom,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% freeRes.fresh(2)
thf(fact_305_pi_Ofresh_I2_J,axiom,
! [A: name,X32: name,X2: name,X1: pi] :
( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
= ( ( fresh_name_name @ A @ X32 )
& ( fresh_name_name @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(2)
thf(fact_306_resOutputTauTrans,axiom,
! [X: name,A: name,B: name,P: pi,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% resOutputTauTrans
thf(fact_307_outputTauTrans,axiom,
! [A: name,B: name,P: pi,P2: pi] :
~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% outputTauTrans
thf(fact_308_pi_Odistinct_I31_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(31)
thf(fact_309_pi_Odistinct_I29_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(29)
thf(fact_310_pi_Odistinct_I27_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(27)
thf(fact_311_pi_Oinject_I1_J,axiom,
! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
( ( ( output @ X32 @ X2 @ X1 )
= ( output @ Y32 @ Y2 @ Y1 ) )
= ( ( X32 = Y32 )
& ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(1)
thf(fact_312_freeRes_Oinducts,axiom,
! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
( ! [Name13: name,Name24: name] : ( P @ ( late_OutputR @ Name13 @ Name24 ) )
=> ( ( P @ late_TauR )
=> ( P @ FreeRes3 ) ) ) ).
% freeRes.inducts
thf(fact_313_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
! [Name12: name,Name23: name] :
( ( late_OutputR @ Name12 @ Name23 )
!= late_TauR ) ).
% Late_Semantics.freeRes.distinct(1)
thf(fact_314_pi_Odistinct_I19_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( tau @ Pi ) ) ).
% pi.distinct(19)
thf(fact_315_pi_Odistinct_I21_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( input @ Name1 @ Name22 @ Pi ) ) ).
% pi.distinct(21)
thf(fact_316_pi_Odistinct_I1_J,axiom,
! [Name1: name,Name22: name,Pi: pi] :
( piNil
!= ( output @ Name1 @ Name22 @ Pi ) ) ).
% pi.distinct(1)
thf(fact_317_fresh__fact2,axiom,
! [A: name,B: name,P: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% fresh_fact2
thf(fact_318_fresh__fact1,axiom,
! [A: name,P: pi,C2: name,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( A != C2 )
=> ( fresh_name_pi @ A @ ( subs @ P @ B @ C2 ) ) ) ) ).
% fresh_fact1
thf(fact_319_forget,axiom,
! [A: name,P: pi,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( subs @ P @ A @ B )
= P ) ) ).
% forget
thf(fact_320_freeRes_Oexhaust,axiom,
! [Y: late_freeRes] :
( ! [X112: name,X122: name] :
( Y
!= ( late_OutputR @ X112 @ X122 ) )
=> ( Y = late_TauR ) ) ).
% freeRes.exhaust
thf(fact_321_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
! [X11: name,X12: name] :
( ( late_OutputR @ X11 @ X12 )
!= late_TauR ) ).
% Late_Semantics1.freeRes.distinct(1)
thf(fact_322_substRes3,axiom,
! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( res @ A @ P ) @ A @ B )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% substRes3
thf(fact_323_substRes2,axiom,
! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( res @ A @ P )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% substRes2
thf(fact_324_resTrans_I1_J,axiom,
! [X: name,B: name,P: pi,Rs: late_residual] :
~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% resTrans(1)
thf(fact_325_outputBoundTrans,axiom,
! [A: name,B: name,P: pi,C2: late_subject,X: name,P2: pi] :
~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C2 @ X @ P2 ) ) ).
% outputBoundTrans
thf(fact_326_nilSim_I3_J,axiom,
! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% nilSim(3)
thf(fact_327_Late__Semantics_OComm2,axiom,
! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% Late_Semantics.Comm2
thf(fact_328_Late__Semantics_OComm1,axiom,
! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% Late_Semantics.Comm1
thf(fact_329_Output,axiom,
! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% Output
thf(fact_330_outputIneqTrans,axiom,
! [A: name,B: name,P: pi,C2: name,D2: name,P2: pi] :
( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D2 ) @ P2 ) )
=> ~ ( ( A != C2 )
| ( B != D2 ) ) ) ).
% outputIneqTrans
thf(fact_331_outputCases_H,axiom,
! [A: name,B: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
=> ~ ! [A3: name,B3: name,P4: pi] :
( ( ( A = A3 )
& ( B = B3 )
& ( P = P4 ) )
=> ( Rs
!= ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) ) ) ) ).
% outputCases'
thf(fact_332_outputCases,axiom,
! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( ( Alpha
= ( late_OutputR @ A @ B ) )
=> ( ( P = P2 )
=> ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
=> ( Prop @ Alpha @ P2 ) ) ) ).
% outputCases
thf(fact_333_outputFreshTrans,axiom,
! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
=> ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
| ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% outputFreshTrans
thf(fact_334_transitions_OComm2,axiom,
! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( X != A )
=> ( ( X != B )
=> ( ( fresh_name_pi @ X @ P2 )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Comm2
thf(fact_335_transitions_OComm1,axiom,
! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( X != A )
=> ( ( X != B )
=> ( ( fresh_name_pi @ X @ Q2 )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% transitions.Comm1
thf(fact_336_Tau,axiom,
! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% Tau
thf(fact_337_tauCases_H,axiom,
! [P: pi,Rs: late_residual] :
( ( late_transitions @ ( tau @ P ) @ Rs )
=> ~ ! [P4: pi] :
( ( ( tau @ P )
= ( tau @ P4 ) )
=> ( Rs
!= ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% tauCases'
thf(fact_338_tauCases,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( ( Alpha = late_TauR )
=> ( ( P = P2 )
=> ( Prop @ late_TauR @ P ) ) )
=> ( Prop @ Alpha @ P2 ) ) ) ).
% tauCases
thf(fact_339_transitions_OClose2,axiom,
! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_name_pi @ Y @ P )
=> ( ( fresh_name_pi @ Y @ Q )
=> ( ( X != A )
=> ( ( fresh_name_pi @ X @ P2 )
=> ( ( Y != A )
=> ( ( fresh_name_pi @ Y @ Q2 )
=> ( ( X != Y )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Close2
thf(fact_340_transitions_OClose1,axiom,
! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_name_pi @ Y @ P )
=> ( ( fresh_name_pi @ Y @ Q )
=> ( ( X != A )
=> ( ( fresh_name_pi @ X @ Q2 )
=> ( ( Y != A )
=> ( ( fresh_name_pi @ Y @ P2 )
=> ( ( X != Y )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Close1
thf(fact_341_Late__Semantics_OClose2,axiom,
! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( ( fresh_name_pi @ Y @ Q )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% Late_Semantics.Close2
thf(fact_342_mismatchIdRight,axiom,
! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( ( A != B )
=> ( strong743114133lation @ P @ Rel @ ( mismatch @ A @ B @ P ) ) ) ) ).
% mismatchIdRight
thf(fact_343_mismatchIdLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( ( A != B )
=> ( strong743114133lation @ ( mismatch @ A @ B @ P ) @ Rel @ P ) ) ) ).
% mismatchIdLeft
thf(fact_344_pi_Ofresh_I6_J,axiom,
! [A: name,X32: name,X2: name,X1: pi] :
( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
= ( ( fresh_name_name @ A @ X32 )
& ( fresh_name_name @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(6)
thf(fact_345_pi_Odistinct_I25_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% pi.distinct(25)
thf(fact_346_pi_Odistinct_I9_J,axiom,
! [Name1: name,Name22: name,Pi: pi] :
( piNil
!= ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% pi.distinct(9)
thf(fact_347_pi_Odistinct_I71_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( mismatch @ Name12 @ Name23 @ Pi4 )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(71)
thf(fact_348_pi_Odistinct_I51_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% pi.distinct(51)
thf(fact_349_pi_Odistinct_I39_J,axiom,
! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
( ( tau @ Pi4 )
!= ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% pi.distinct(39)
thf(fact_350_pi_Oinject_I5_J,axiom,
! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
( ( ( mismatch @ X32 @ X2 @ X1 )
= ( mismatch @ Y32 @ Y2 @ Y1 ) )
= ( ( X32 = Y32 )
& ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(5)
thf(fact_351_pi_Odistinct_I73_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( mismatch @ Name12 @ Name23 @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(73)
% Conjectures (1)
thf(conj_0,conjecture,
y != x ).
%------------------------------------------------------------------------------