TPTP Problem File: ITP182^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP182^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer Strong_Late_Sim_SC problem prob_279__3411076_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_279__3411076_1 [Des21]
% Status : Theorem
% Rating : 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% Syntax : Number of formulae : 557 ( 219 unt; 192 typ; 0 def)
% Number of atoms : 849 ( 387 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 3597 ( 111 ~; 1 |; 50 &;3097 @)
% ( 0 <=>; 338 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 47 ( 46 usr)
% Number of type conns : 371 ( 371 >; 0 *; 0 +; 0 <<)
% Number of symbols : 149 ( 146 usr; 15 con; 0-5 aty)
% Number of variables : 1211 ( 15 ^;1182 !; 14 ?;1211 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:30:40.333
%------------------------------------------------------------------------------
% Could-be-implicit typings (46)
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% Explicit typings (146)
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thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
perm_n1255502110_pi_pi: list_P227219501e_name > produc1141751126_pi_pi > produc1141751126_pi_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Oname_J,type,
perm_name_set_name: list_P227219501e_name > set_name > set_name ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi_J,type,
perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi____Rep_J,type,
perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__Osubject_J,type,
perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
thf(sy_c_Nominal_Oswap_001t__Agent__Oname,type,
swap_name: produc367475239e_name > name > name ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
ord_le793202855e_name: set_Pr443758855e_name > set_Pr443758855e_name > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).
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__Late____Semantics__OfreeRes,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
produc607574050ubject: name > late_subject > produc865358760ubject ).
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__Opi,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(sy_c_Product__Type_OPair_001t__Agent__Opi____Rep_001t__Agent__Opi____Rep,type,
produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep ).
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__Agent__Opi____Rep,type,
produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi____Rep,type,
produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).
thf(sy_c_Rel_Oeqvt_001t__Agent__Oname,type,
eqvt_name: set_Pr443758855e_name > $o ).
thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(sy_c_Rel_Oeqvt_001t__Agent__Opi____Rep,type,
eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).
thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__OfreeRes,type,
eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).
thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__Osubject,type,
eqvt_Late_subject: set_Pr806375235ubject > $o ).
thf(sy_c_Relation_OId_001t__Agent__Oname,type,
id_name: set_Pr443758855e_name ).
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__Agent__Oname,type,
member_name: name > set_name > $o ).
thf(sy_c_member_001t__Agent__Opi,type,
member_pi: pi > set_pi > $o ).
thf(sy_c_member_001t__Agent__Opi____Rep,type,
member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
thf(sy_c_member_001t__Late____Semantics__OfreeRes,type,
member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
thf(sy_c_member_001t__Late____Semantics__Osubject,type,
member_Late_subject: late_subject > set_Late_subject > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $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_c_member_001t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o ).
thf(sy_v_P,type,
p: pi ).
thf(sy_v_PQ____,type,
pq: pi ).
thf(sy_v_P_H____,type,
p2: 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_aa____,type,
aa: name ).
thf(sy_v_x,type,
x: name ).
thf(sy_v_y____,type,
y: name ).
% Relevant facts (353)
thf(fact_0_Id,axiom,
ord_le630093991_pi_pi @ id_pi @ rel ).
% Id
thf(fact_1_cOpen_Ohyps_I2_J,axiom,
aa != x ).
% cOpen.hyps(2)
thf(fact_2_cOpen_Ohyps_I3_J,axiom,
( a
= ( late_BoundOutputS @ aa ) ) ).
% cOpen.hyps(3)
thf(fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
y != x ).
% \<open>y \<noteq> x\<close>
thf(fact_4_Eqvt,axiom,
eqvt_pi @ rel ).
% Eqvt
thf(fact_5_perm__swap_I1_J,axiom,
! [A: name,B: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_6_perm__swap_I1_J,axiom,
! [A: name,B: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_7_perm__swap_I1_J,axiom,
! [A: name,B: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_8_perm__swap_I1_J,axiom,
! [A: name,B: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_9_perm__swap_I1_J,axiom,
! [A: name,B: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_10_name__id,axiom,
! [A: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_11_name__id,axiom,
! [A: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_12_name__id,axiom,
! [A: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_13_name__id,axiom,
! [A: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_14_name__id,axiom,
! [A: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_15_name__swap,axiom,
! [A: name,B: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_16_name__swap,axiom,
! [A: name,B: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_17_name__swap,axiom,
! [A: name,B: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_18_name__swap,axiom,
! [A: name,B: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_19_name__swap,axiom,
! [A: name,B: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_20_name__swap__bij,axiom,
! [A: name,B: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_21_name__swap__bij,axiom,
! [A: name,B: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_22_name__swap__bij,axiom,
! [A: name,B: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_23_name__swap__bij,axiom,
! [A: name,B: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_24_name__swap__bij,axiom,
! [A: name,B: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_25_pt__name1,axiom,
! [X: late_subject] :
( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_26_pt__name1,axiom,
! [X: late_freeRes] :
( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_27_pt__name1,axiom,
! [X: pi_Rep] :
( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_28_pt__name1,axiom,
! [X: name] :
( ( perm_name_name @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_29_pt__name1,axiom,
! [X: pi] :
( ( perm_name_pi @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_30_perm__swap_I2_J,axiom,
! [A: name,B: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_31_perm__swap_I2_J,axiom,
! [A: name,B: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_32_perm__swap_I2_J,axiom,
! [A: name,B: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_33_perm__swap_I2_J,axiom,
! [A: name,B: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_34_perm__swap_I2_J,axiom,
! [A: name,B: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_35_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_36_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_37__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062,axiom,
fresh_name_pi @ y @ p2 ).
% \<open>y \<sharp> P'\<close>
thf(fact_38_list_Oinject,axiom,
! [X21: produc367475239e_name,X22: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
( ( ( cons_P1213805021e_name @ X21 @ X22 )
= ( cons_P1213805021e_name @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_39_prod_Oinject,axiom,
! [X1: name,X2: name,Y1: name,Y2: name] :
( ( ( produc1570949143e_name @ X1 @ X2 )
= ( produc1570949143e_name @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_40_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_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_old_Oprod_Oinject,axiom,
! [A: name,B: name,A2: name,B2: name] :
( ( ( produc1570949143e_name @ A @ B )
= ( produc1570949143e_name @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_43_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_44_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_45_residual__perm__empty,axiom,
! [Residual_Rep: late_residual_Rep] :
( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
= Residual_Rep ) ).
% residual_perm_empty
thf(fact_46_subject__perm__empty,axiom,
! [Subject_Rep: late_subject_Rep] :
( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
= Subject_Rep ) ).
% subject_perm_empty
thf(fact_47_freeRes__perm__empty,axiom,
! [FreeRes_Rep: late_freeRes_Rep] :
( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
= FreeRes_Rep ) ).
% freeRes_perm_empty
thf(fact_48_pi__perm__empty,axiom,
! [Pi_Rep: pi_Rep] :
( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
= Pi_Rep ) ).
% pi_perm_empty
thf(fact_49_subject_Operm_I2_J,axiom,
! [Pi: list_P227219501e_name,X1: name] :
( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
= ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% subject.perm(2)
thf(fact_50_perm__fresh__fresh,axiom,
! [A: name,X: pi_Rep,B: name] :
( ( fresh_name_pi_Rep @ A @ X )
=> ( ( fresh_name_pi_Rep @ B @ X )
=> ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_51_perm__fresh__fresh,axiom,
! [A: name,X: late_subject,B: name] :
( ( fresh_717452603ubject @ A @ X )
=> ( ( fresh_717452603ubject @ B @ X )
=> ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_52_perm__fresh__fresh,axiom,
! [A: name,X: late_freeRes,B: name] :
( ( fresh_1641682979reeRes @ A @ X )
=> ( ( fresh_1641682979reeRes @ B @ X )
=> ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_53_perm__fresh__fresh,axiom,
! [A: name,X: produc1141751126_pi_pi,B: name] :
( ( fresh_1376661020_pi_pi @ A @ X )
=> ( ( fresh_1376661020_pi_pi @ B @ X )
=> ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_54_perm__fresh__fresh,axiom,
! [A: name,X: name,B: name] :
( ( fresh_name_name @ A @ X )
=> ( ( fresh_name_name @ B @ X )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_55_perm__fresh__fresh,axiom,
! [A: name,X: pi,B: name] :
( ( fresh_name_pi @ A @ X )
=> ( ( fresh_name_pi @ B @ X )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_56_name__fresh__fresh,axiom,
! [A: name,X: pi_Rep,B: name] :
( ( fresh_name_pi_Rep @ A @ X )
=> ( ( fresh_name_pi_Rep @ B @ X )
=> ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_57_name__fresh__fresh,axiom,
! [A: name,X: late_subject,B: name] :
( ( fresh_717452603ubject @ A @ X )
=> ( ( fresh_717452603ubject @ B @ X )
=> ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_58_name__fresh__fresh,axiom,
! [A: name,X: late_freeRes,B: name] :
( ( fresh_1641682979reeRes @ A @ X )
=> ( ( fresh_1641682979reeRes @ B @ X )
=> ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_59_name__fresh__fresh,axiom,
! [A: name,X: produc1141751126_pi_pi,B: name] :
( ( fresh_1376661020_pi_pi @ A @ X )
=> ( ( fresh_1376661020_pi_pi @ B @ X )
=> ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_60_name__fresh__fresh,axiom,
! [A: name,X: name,B: name] :
( ( fresh_name_name @ A @ X )
=> ( ( fresh_name_name @ B @ X )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_61_name__fresh__fresh,axiom,
! [A: name,X: pi,B: name] :
( ( fresh_name_pi @ A @ X )
=> ( ( fresh_name_pi @ B @ X )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_62_Bound_Ohyps_I4_J,axiom,
fresh_717452603ubject @ y @ a ).
% Bound.hyps(4)
thf(fact_63_subseteq__eqvt,axiom,
! [Pi: list_P227219501e_name,X3: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
( ( perm_name_o @ Pi @ ( ord_le630093991_pi_pi @ X3 @ Y ) )
= ( ord_le630093991_pi_pi @ ( perm_n675238095_pi_pi @ Pi @ X3 ) @ ( perm_n675238095_pi_pi @ Pi @ Y ) ) ) ).
% subseteq_eqvt
thf(fact_64_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_name_pi_Rep @ A @ X )
=> ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_65_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: late_subject] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_717452603ubject @ A @ X )
=> ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_66_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_1641682979reeRes @ A @ X )
=> ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_67_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: produc1141751126_pi_pi] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_1376661020_pi_pi @ A @ X )
=> ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_68_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: name] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_name_name @ A @ X )
=> ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_69_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: pi] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_name_pi @ A @ X )
=> ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_70_name__exists__fresh,axiom,
! [X: late_subject] :
~ ! [C: name] :
~ ( fresh_717452603ubject @ C @ X ) ).
% name_exists_fresh
thf(fact_71_name__exists__fresh,axiom,
! [X: late_freeRes] :
~ ! [C: name] :
~ ( fresh_1641682979reeRes @ C @ X ) ).
% name_exists_fresh
thf(fact_72_name__exists__fresh,axiom,
! [X: produc1141751126_pi_pi] :
~ ! [C: name] :
~ ( fresh_1376661020_pi_pi @ C @ X ) ).
% name_exists_fresh
thf(fact_73_name__exists__fresh,axiom,
! [X: name] :
~ ! [C: name] :
~ ( fresh_name_name @ C @ X ) ).
% name_exists_fresh
thf(fact_74_name__exists__fresh,axiom,
! [X: pi] :
~ ! [C: name] :
~ ( fresh_name_pi @ C @ X ) ).
% name_exists_fresh
thf(fact_75_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
= ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_76_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: late_subject] :
( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
= ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_77_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
= ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_78_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
( ( perm_name_o @ Pi @ ( fresh_1376661020_pi_pi @ A @ X ) )
= ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_79_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: name] :
( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
= ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_80_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: pi] :
( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
= ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_81_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
= ( fresh_name_pi_Rep @ A @ X ) ) ).
% fresh_bij
thf(fact_82_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: late_subject] :
( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
= ( fresh_717452603ubject @ A @ X ) ) ).
% fresh_bij
thf(fact_83_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
= ( fresh_1641682979reeRes @ A @ X ) ) ).
% fresh_bij
thf(fact_84_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) )
= ( fresh_1376661020_pi_pi @ A @ X ) ) ).
% fresh_bij
thf(fact_85_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: name] :
( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
= ( fresh_name_name @ A @ X ) ) ).
% fresh_bij
thf(fact_86_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: pi] :
( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
= ( fresh_name_pi @ A @ X ) ) ).
% fresh_bij
thf(fact_87_name__calc_I2_J,axiom,
! [X: name] :
( ( perm_name_name @ nil_Pr743626285e_name @ X )
= X ) ).
% name_calc(2)
thf(fact_88_successively_Ocases,axiom,
! [X: produc1872410278e_name] :
( ! [P: produc367475239e_name > produc367475239e_name > $o] :
( X
!= ( produc1069608854e_name @ P @ nil_Pr743626285e_name ) )
=> ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name] :
( X
!= ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) ) )
=> ~ ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
( X
!= ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) ) ) ).
% successively.cases
thf(fact_89_sorted__wrt_Ocases,axiom,
! [X: produc1872410278e_name] :
( ! [P: produc367475239e_name > produc367475239e_name > $o] :
( X
!= ( produc1069608854e_name @ P @ nil_Pr743626285e_name ) )
=> ~ ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Ys: list_P227219501e_name] :
( X
!= ( produc1069608854e_name @ P @ ( cons_P1213805021e_name @ X4 @ Ys ) ) ) ) ).
% sorted_wrt.cases
thf(fact_90_shuffles_Ocases,axiom,
! [X: produc890461031e_name] :
( ! [Ys: list_P227219501e_name] :
( X
!= ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
=> ( ! [Xs: list_P227219501e_name] :
( X
!= ( produc208131031e_name @ Xs @ nil_Pr743626285e_name ) )
=> ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
( X
!= ( produc208131031e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) ) ) ).
% shuffles.cases
thf(fact_91_splice_Ocases,axiom,
! [X: produc890461031e_name] :
( ! [Ys: list_P227219501e_name] :
( X
!= ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
=> ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Ys: list_P227219501e_name] :
( X
!= ( produc208131031e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys ) ) ) ).
% splice.cases
thf(fact_92_swap__simps_I1_J,axiom,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
= B ) ).
% swap_simps(1)
thf(fact_93_swap__simps_I2_J,axiom,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
= A ) ).
% swap_simps(2)
thf(fact_94_swap__simps_I3_J,axiom,
! [A: name,C2: name,B: name] :
( ( A != C2 )
=> ( ( B != C2 )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C2 )
= C2 ) ) ) ).
% swap_simps(3)
thf(fact_95_fresh__aux,axiom,
! [C2: name,A: name,X: pi_Rep,B: name] :
( ( C2 != A )
=> ( ( fresh_name_pi_Rep @ A @ X )
=> ( ( fresh_name_pi_Rep @ C2 @ X )
=> ( fresh_name_pi_Rep @ C2 @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_96_fresh__aux,axiom,
! [C2: name,A: name,X: late_subject,B: name] :
( ( C2 != A )
=> ( ( fresh_717452603ubject @ A @ X )
=> ( ( fresh_717452603ubject @ C2 @ X )
=> ( fresh_717452603ubject @ C2 @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_97_fresh__aux,axiom,
! [C2: name,A: name,X: late_freeRes,B: name] :
( ( C2 != A )
=> ( ( fresh_1641682979reeRes @ A @ X )
=> ( ( fresh_1641682979reeRes @ C2 @ X )
=> ( fresh_1641682979reeRes @ C2 @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_98_fresh__aux,axiom,
! [C2: name,A: name,X: produc1141751126_pi_pi,B: name] :
( ( C2 != A )
=> ( ( fresh_1376661020_pi_pi @ A @ X )
=> ( ( fresh_1376661020_pi_pi @ C2 @ X )
=> ( fresh_1376661020_pi_pi @ C2 @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_99_fresh__aux,axiom,
! [C2: name,A: name,X: name,B: name] :
( ( C2 != A )
=> ( ( fresh_name_name @ A @ X )
=> ( ( fresh_name_name @ C2 @ X )
=> ( fresh_name_name @ C2 @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_100_fresh__aux,axiom,
! [C2: name,A: name,X: pi,B: name] :
( ( C2 != A )
=> ( ( fresh_name_pi @ A @ X )
=> ( ( fresh_name_pi @ C2 @ X )
=> ( fresh_name_pi @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_101_old_Oprod_Oinducts,axiom,
! [P2: produc367475239e_name > $o,Prod: produc367475239e_name] :
( ! [A3: name,B3: name] : ( P2 @ ( produc1570949143e_name @ A3 @ B3 ) )
=> ( P2 @ Prod ) ) ).
% old.prod.inducts
thf(fact_102_old_Oprod_Oinducts,axiom,
! [P2: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
( ! [A3: name,B3: product_prod_pi_pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ B3 ) )
=> ( P2 @ Prod ) ) ).
% old.prod.inducts
thf(fact_103_old_Oprod_Oinducts,axiom,
! [P2: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P2 @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P2 @ Prod ) ) ).
% old.prod.inducts
thf(fact_104_old_Oprod_Oexhaust,axiom,
! [Y4: produc367475239e_name] :
~ ! [A3: name,B3: name] :
( Y4
!= ( produc1570949143e_name @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_105_old_Oprod_Oexhaust,axiom,
! [Y4: produc1141751126_pi_pi] :
~ ! [A3: name,B3: product_prod_pi_pi] :
( Y4
!= ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_106_old_Oprod_Oexhaust,axiom,
! [Y4: product_prod_pi_pi] :
~ ! [A3: pi,B3: pi] :
( Y4
!= ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_107_mem__Collect__eq,axiom,
! [A: product_prod_pi_pi,P2: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P2 ) )
= ( P2 @ A ) ) ).
% mem_Collect_eq
thf(fact_108_Collect__mem__eq,axiom,
! [A4: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [X5: product_prod_pi_pi] : ( member558706512_pi_pi @ X5 @ A4 ) )
= A4 ) ).
% Collect_mem_eq
thf(fact_109_prod__induct3,axiom,
! [P2: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
( ! [A3: name,B3: pi,C: pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) )
=> ( P2 @ X ) ) ).
% prod_induct3
thf(fact_110_prod__cases3,axiom,
! [Y4: produc1141751126_pi_pi] :
~ ! [A3: name,B3: pi,C: pi] :
( Y4
!= ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) ) ).
% prod_cases3
thf(fact_111_Pair__inject,axiom,
! [A: name,B: name,A2: name,B2: name] :
( ( ( produc1570949143e_name @ A @ B )
= ( produc1570949143e_name @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_112_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_113_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_114_prod__cases,axiom,
! [P2: produc367475239e_name > $o,P3: produc367475239e_name] :
( ! [A3: name,B3: name] : ( P2 @ ( produc1570949143e_name @ A3 @ B3 ) )
=> ( P2 @ P3 ) ) ).
% prod_cases
thf(fact_115_prod__cases,axiom,
! [P2: produc1141751126_pi_pi > $o,P3: produc1141751126_pi_pi] :
( ! [A3: name,B3: product_prod_pi_pi] : ( P2 @ ( produc235456326_pi_pi @ A3 @ B3 ) )
=> ( P2 @ P3 ) ) ).
% prod_cases
thf(fact_116_prod__cases,axiom,
! [P2: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P2 @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P2 @ P3 ) ) ).
% prod_cases
thf(fact_117_surj__pair,axiom,
! [P3: produc367475239e_name] :
? [X4: name,Y3: name] :
( P3
= ( produc1570949143e_name @ X4 @ Y3 ) ) ).
% surj_pair
thf(fact_118_surj__pair,axiom,
! [P3: produc1141751126_pi_pi] :
? [X4: name,Y3: product_prod_pi_pi] :
( P3
= ( produc235456326_pi_pi @ X4 @ Y3 ) ) ).
% surj_pair
thf(fact_119_surj__pair,axiom,
! [P3: product_prod_pi_pi] :
? [X4: pi,Y3: pi] :
( P3
= ( product_Pair_pi_pi @ X4 @ Y3 ) ) ).
% surj_pair
thf(fact_120_not__Cons__self2,axiom,
! [X: produc367475239e_name,Xs2: list_P227219501e_name] :
( ( cons_P1213805021e_name @ X @ Xs2 )
!= Xs2 ) ).
% not_Cons_self2
thf(fact_121_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_122_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_123_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_124_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_125_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_126_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_127_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_128_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_129_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_130_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_131_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_132_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_133_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_134_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_135_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_136_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
( ( ( perm_n1559866809ubject @ Pi @ X )
= ( perm_n1559866809ubject @ Pi @ Y4 ) )
= ( X = Y4 ) ) ).
% perm_bij
thf(fact_137_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
( ( ( perm_n336613537reeRes @ Pi @ X )
= ( perm_n336613537reeRes @ Pi @ Y4 ) )
= ( X = Y4 ) ) ).
% perm_bij
thf(fact_138_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
( ( ( perm_name_pi_Rep @ Pi @ X )
= ( perm_name_pi_Rep @ Pi @ Y4 ) )
= ( X = Y4 ) ) ).
% perm_bij
thf(fact_139_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: name,Y4: name] :
( ( ( perm_name_name @ Pi @ X )
= ( perm_name_name @ Pi @ Y4 ) )
= ( X = Y4 ) ) ).
% perm_bij
thf(fact_140_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: pi,Y4: pi] :
( ( ( perm_name_pi @ Pi @ X )
= ( perm_name_pi @ Pi @ Y4 ) )
= ( X = Y4 ) ) ).
% perm_bij
thf(fact_141_perm__app,axiom,
! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% perm_app
thf(fact_142_perm__app,axiom,
! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% perm_app
thf(fact_143_perm__app,axiom,
! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% perm_app
thf(fact_144_perm__app,axiom,
! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% perm_app
thf(fact_145_perm__app,axiom,
! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% perm_app
thf(fact_146_perm__app,axiom,
! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% perm_app
thf(fact_147_perm__app,axiom,
! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% perm_app
thf(fact_148_perm__app,axiom,
! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% perm_app
thf(fact_149_perm__app,axiom,
! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% perm_app
thf(fact_150_perm__app,axiom,
! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% perm_app
thf(fact_151_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X3: set_Pr1834926343_pi_pi] :
( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X3 ) )
= ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X3 ) ) ) ).
% in_eqvt
thf(fact_152_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_subject,X3: set_Late_subject] :
( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X3 ) )
= ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X3 ) ) ) ).
% in_eqvt
thf(fact_153_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,X3: set_Late_freeRes] :
( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X3 ) )
= ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X3 ) ) ) ).
% in_eqvt
thf(fact_154_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi_Rep,X3: set_pi_Rep] :
( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X3 ) )
= ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X3 ) ) ) ).
% in_eqvt
thf(fact_155_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: name,X3: set_name] :
( ( perm_name_o @ Pi @ ( member_name @ X @ X3 ) )
= ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X3 ) ) ) ).
% in_eqvt
thf(fact_156_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi,X3: set_pi] :
( ( perm_name_o @ Pi @ ( member_pi @ X @ X3 ) )
= ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X3 ) ) ) ).
% in_eqvt
thf(fact_157_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
( ( perm_name_o @ Pi @ ( X = Y4 ) )
= ( ( perm_n1559866809ubject @ Pi @ X )
= ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% eq_eqvt
thf(fact_158_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
( ( perm_name_o @ Pi @ ( X = Y4 ) )
= ( ( perm_n336613537reeRes @ Pi @ X )
= ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% eq_eqvt
thf(fact_159_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
( ( perm_name_o @ Pi @ ( X = Y4 ) )
= ( ( perm_name_pi_Rep @ Pi @ X )
= ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% eq_eqvt
thf(fact_160_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: name,Y4: name] :
( ( perm_name_o @ Pi @ ( X = Y4 ) )
= ( ( perm_name_name @ Pi @ X )
= ( perm_name_name @ Pi @ Y4 ) ) ) ).
% eq_eqvt
thf(fact_161_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi,Y4: pi] :
( ( perm_name_o @ Pi @ ( X = Y4 ) )
= ( ( perm_name_pi @ Pi @ X )
= ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% eq_eqvt
thf(fact_162_map__tailrec__rev_Oinduct,axiom,
! [P2: ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name,A1: list_P227219501e_name,A22: list_P227219501e_name] :
( ! [F2: produc367475239e_name > produc367475239e_name,X_1: list_P227219501e_name] : ( P2 @ F2 @ nil_Pr743626285e_name @ X_1 )
=> ( ! [F2: produc367475239e_name > produc367475239e_name,A3: produc367475239e_name,As: list_P227219501e_name,Bs: list_P227219501e_name] :
( ( P2 @ F2 @ As @ ( cons_P1213805021e_name @ ( F2 @ A3 ) @ Bs ) )
=> ( P2 @ F2 @ ( cons_P1213805021e_name @ A3 @ As ) @ Bs ) )
=> ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_163_list__nonempty__induct,axiom,
! [Xs2: list_P227219501e_name,P2: list_P227219501e_name > $o] :
( ( Xs2 != nil_Pr743626285e_name )
=> ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
=> ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name] :
( ( Xs != nil_Pr743626285e_name )
=> ( ( P2 @ Xs )
=> ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) ) ) )
=> ( P2 @ Xs2 ) ) ) ) ).
% list_nonempty_induct
thf(fact_164_successively_Oinduct,axiom,
! [P2: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
( ! [P: produc367475239e_name > produc367475239e_name > $o] : ( P2 @ P @ nil_Pr743626285e_name )
=> ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name] : ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
=> ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
( ( P2 @ P @ ( cons_P1213805021e_name @ Y3 @ Xs ) )
=> ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) )
=> ( P2 @ A0 @ A1 ) ) ) ) ).
% successively.induct
thf(fact_165_remdups__adj_Oinduct,axiom,
! [P2: list_P227219501e_name > $o,A0: list_P227219501e_name] :
( ( P2 @ nil_Pr743626285e_name )
=> ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
=> ( ! [X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
( ( ( X4 = Y3 )
=> ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) ) )
=> ( ( ( X4 != Y3 )
=> ( P2 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) )
=> ( P2 @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) )
=> ( P2 @ A0 ) ) ) ) ).
% remdups_adj.induct
thf(fact_166_sorted__wrt_Oinduct,axiom,
! [P2: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
( ! [P: produc367475239e_name > produc367475239e_name > $o] : ( P2 @ P @ nil_Pr743626285e_name )
=> ( ! [P: produc367475239e_name > produc367475239e_name > $o,X4: produc367475239e_name,Ys: list_P227219501e_name] :
( ( P2 @ P @ Ys )
=> ( P2 @ P @ ( cons_P1213805021e_name @ X4 @ Ys ) ) )
=> ( P2 @ A0 @ A1 ) ) ) ).
% sorted_wrt.induct
thf(fact_167_remdups__adj_Ocases,axiom,
! [X: list_P227219501e_name] :
( ( X != nil_Pr743626285e_name )
=> ( ! [X4: produc367475239e_name] :
( X
!= ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
=> ~ ! [X4: produc367475239e_name,Y3: produc367475239e_name,Xs: list_P227219501e_name] :
( X
!= ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Xs ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_168_transpose_Ocases,axiom,
! [X: list_l1406151091e_name] :
( ( X != nil_li29751603e_name )
=> ( ! [Xss: list_l1406151091e_name] :
( X
!= ( cons_l798145763e_name @ nil_Pr743626285e_name @ Xss ) )
=> ~ ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Xss: list_l1406151091e_name] :
( X
!= ( cons_l798145763e_name @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_169_shuffles_Oinduct,axiom,
! [P2: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
( ! [X_1: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ X_1 )
=> ( ! [Xs: list_P227219501e_name] : ( P2 @ Xs @ nil_Pr743626285e_name )
=> ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
( ( P2 @ Xs @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
=> ( ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys )
=> ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) )
=> ( P2 @ A0 @ A1 ) ) ) ) ).
% shuffles.induct
thf(fact_170_induct__list012,axiom,
! [P2: list_P227219501e_name > $o,Xs2: list_P227219501e_name] :
( ( P2 @ nil_Pr743626285e_name )
=> ( ! [X4: produc367475239e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ nil_Pr743626285e_name ) )
=> ( ! [X4: produc367475239e_name,Y3: produc367475239e_name,Zs: list_P227219501e_name] :
( ( P2 @ Zs )
=> ( ( P2 @ ( cons_P1213805021e_name @ Y3 @ Zs ) )
=> ( P2 @ ( cons_P1213805021e_name @ X4 @ ( cons_P1213805021e_name @ Y3 @ Zs ) ) ) ) )
=> ( P2 @ Xs2 ) ) ) ) ).
% induct_list012
thf(fact_171_splice_Oinduct,axiom,
! [P2: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
( ! [X_1: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ X_1 )
=> ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Ys: list_P227219501e_name] :
( ( P2 @ Ys @ Xs )
=> ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ Ys ) )
=> ( P2 @ A0 @ A1 ) ) ) ).
% splice.induct
thf(fact_172_list__induct2_H,axiom,
! [P2: list_P227219501e_name > list_P227219501e_name > $o,Xs2: list_P227219501e_name,Ys2: list_P227219501e_name] :
( ( P2 @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
=> ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name] : ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ nil_Pr743626285e_name )
=> ( ! [Y3: produc367475239e_name,Ys: list_P227219501e_name] : ( P2 @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
=> ( ! [X4: produc367475239e_name,Xs: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
( ( P2 @ Xs @ Ys )
=> ( P2 @ ( cons_P1213805021e_name @ X4 @ Xs ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) )
=> ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_173_neq__Nil__conv,axiom,
! [Xs2: list_P227219501e_name] :
( ( Xs2 != nil_Pr743626285e_name )
= ( ? [Y5: produc367475239e_name,Ys3: list_P227219501e_name] :
( Xs2
= ( cons_P1213805021e_name @ Y5 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_174_list_Oinducts,axiom,
! [P2: list_P227219501e_name > $o,List: list_P227219501e_name] :
( ( P2 @ nil_Pr743626285e_name )
=> ( ! [X12: produc367475239e_name,X23: list_P227219501e_name] :
( ( P2 @ X23 )
=> ( P2 @ ( cons_P1213805021e_name @ X12 @ X23 ) ) )
=> ( P2 @ List ) ) ) ).
% list.inducts
thf(fact_175_list_Oexhaust,axiom,
! [Y4: list_P227219501e_name] :
( ( Y4 != nil_Pr743626285e_name )
=> ~ ! [X212: produc367475239e_name,X222: list_P227219501e_name] :
( Y4
!= ( cons_P1213805021e_name @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_176_list_OdiscI,axiom,
! [List: list_P227219501e_name,X21: produc367475239e_name,X22: list_P227219501e_name] :
( ( List
= ( cons_P1213805021e_name @ X21 @ X22 ) )
=> ( List != nil_Pr743626285e_name ) ) ).
% list.discI
thf(fact_177_list_Odistinct_I1_J,axiom,
! [X21: produc367475239e_name,X22: list_P227219501e_name] :
( nil_Pr743626285e_name
!= ( cons_P1213805021e_name @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_178__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
fresh_name_pi @ y @ q ).
% \<open>y \<sharp> Q\<close>
thf(fact_179_pair__in__Id__conv,axiom,
! [A: name,B: name] :
( ( member695284560e_name @ ( produc1570949143e_name @ A @ B ) @ id_name )
= ( A = B ) ) ).
% pair_in_Id_conv
thf(fact_180_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_181_IdI,axiom,
! [A: name] : ( member695284560e_name @ ( produc1570949143e_name @ A @ A ) @ id_name ) ).
% IdI
thf(fact_182_IdI,axiom,
! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% IdI
thf(fact_183_fresh__prod,axiom,
! [A: name,X: late_subject,Y4: late_subject] :
( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y4 ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_184_fresh__prod,axiom,
! [A: name,X: late_subject,Y4: late_freeRes] :
( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y4 ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_185_fresh__prod,axiom,
! [A: name,X: late_subject,Y4: name] :
( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y4 ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_name_name @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_186_fresh__prod,axiom,
! [A: name,X: late_subject,Y4: pi] :
( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y4 ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_name_pi @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_187_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y4: late_subject] :
( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y4 ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_188_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y4: late_freeRes] :
( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y4 ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_189_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y4: name] :
( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y4 ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_name_name @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_190_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y4: pi] :
( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y4 ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_name_pi @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_191_fresh__prod,axiom,
! [A: name,X: name,Y4: late_subject] :
( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y4 ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_717452603ubject @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_192_fresh__prod,axiom,
! [A: name,X: name,Y4: late_freeRes] :
( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y4 ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y4 ) ) ) ).
% fresh_prod
thf(fact_193__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
fresh_name_pi @ y @ p ).
% \<open>y \<sharp> P\<close>
thf(fact_194_derivativeReflexive,axiom,
! [Rel: set_Pr1834926343_pi_pi,P2: pi,A: late_subject,X: name] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong2129052853vative @ P2 @ P2 @ A @ X @ Rel ) ) ).
% derivativeReflexive
thf(fact_195_derivativeEqvtI,axiom,
! [P2: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
( ( strong2129052853vative @ P2 @ Q @ A @ X @ Rel )
=> ( ( eqvt_pi @ Rel )
=> ( strong2129052853vative @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% derivativeEqvtI
thf(fact_196_derivativeEqvtI2,axiom,
! [P2: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
( ( strong2129052853vative @ P2 @ Q @ A @ X @ Rel )
=> ( ( eqvt_pi @ Rel )
=> ( strong2129052853vative @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% derivativeEqvtI2
thf(fact_197_eqvtRelI,axiom,
! [Rel: set_Pr806375235ubject,P2: late_subject,Q: late_subject,Perm: list_P227219501e_name] :
( ( eqvt_Late_subject @ Rel )
=> ( ( member1586545036ubject @ ( produc1465345179ubject @ P2 @ Q ) @ Rel )
=> ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P2 ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_198_eqvtRelI,axiom,
! [Rel: set_Pr1780909331reeRes,P2: late_freeRes,Q: late_freeRes,Perm: list_P227219501e_name] :
( ( eqvt_Late_freeRes @ Rel )
=> ( ( member1584979804reeRes @ ( produc1244821099reeRes @ P2 @ Q ) @ Rel )
=> ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P2 ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_199_eqvtRelI,axiom,
! [Rel: set_Pr1131282415pi_Rep,P2: pi_Rep,Q: pi_Rep,Perm: list_P227219501e_name] :
( ( eqvt_pi_Rep @ Rel )
=> ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P2 @ Q ) @ Rel )
=> ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P2 ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_200_eqvtRelI,axiom,
! [Rel: set_Pr443758855e_name,P2: name,Q: name,Perm: list_P227219501e_name] :
( ( eqvt_name @ Rel )
=> ( ( member695284560e_name @ ( produc1570949143e_name @ P2 @ Q ) @ Rel )
=> ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P2 ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_201_eqvtRelI,axiom,
! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,Perm: list_P227219501e_name] :
( ( eqvt_pi @ Rel )
=> ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_202_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_203_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_204_name__bij,axiom,
! [Pi: list_P227219501e_name,X: name,Y4: name] :
( ( ( perm_name_name @ Pi @ X )
= ( perm_name_name @ Pi @ Y4 ) )
= ( X = Y4 ) ) ).
% name_bij
thf(fact_205_allE__Nil,axiom,
! [P2: list_P227219501e_name > $o] :
( ! [X_1: list_P227219501e_name] : ( P2 @ X_1 )
=> ( P2 @ nil_Pr743626285e_name ) ) ).
% allE_Nil
thf(fact_206_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
= ( perm_n1559866809ubject @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
= ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_207_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
= ( perm_n336613537reeRes @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
= ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_208_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
= ( perm_name_pi_Rep @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
= ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_209_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
= ( perm_name_name @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
= ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_210_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
= ( perm_name_pi @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
= ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_211_pt__bij3,axiom,
! [X: late_subject,Y4: late_subject,Pi: list_P227219501e_name] :
( ( X = Y4 )
=> ( ( perm_n1559866809ubject @ Pi @ X )
= ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% pt_bij3
thf(fact_212_pt__bij3,axiom,
! [X: late_freeRes,Y4: late_freeRes,Pi: list_P227219501e_name] :
( ( X = Y4 )
=> ( ( perm_n336613537reeRes @ Pi @ X )
= ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% pt_bij3
thf(fact_213_pt__bij3,axiom,
! [X: pi_Rep,Y4: pi_Rep,Pi: list_P227219501e_name] :
( ( X = Y4 )
=> ( ( perm_name_pi_Rep @ Pi @ X )
= ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% pt_bij3
thf(fact_214_pt__bij3,axiom,
! [X: name,Y4: name,Pi: list_P227219501e_name] :
( ( X = Y4 )
=> ( ( perm_name_name @ Pi @ X )
= ( perm_name_name @ Pi @ Y4 ) ) ) ).
% pt_bij3
thf(fact_215_pt__bij3,axiom,
! [X: pi,Y4: pi,Pi: list_P227219501e_name] :
( ( X = Y4 )
=> ( ( perm_name_pi @ Pi @ X )
= ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% pt_bij3
thf(fact_216_abs__fun__if,axiom,
! [C2: $o,Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
( ( C2
=> ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y4 ) )
= ( perm_n1559866809ubject @ Pi @ X ) ) )
& ( ~ C2
=> ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y4 ) )
= ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ) ).
% abs_fun_if
thf(fact_217_abs__fun__if,axiom,
! [C2: $o,Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
( ( C2
=> ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y4 ) )
= ( perm_n336613537reeRes @ Pi @ X ) ) )
& ( ~ C2
=> ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y4 ) )
= ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ) ).
% abs_fun_if
thf(fact_218_abs__fun__if,axiom,
! [C2: $o,Pi: list_P227219501e_name,X: pi_Rep,Y4: pi_Rep] :
( ( C2
=> ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y4 ) )
= ( perm_name_pi_Rep @ Pi @ X ) ) )
& ( ~ C2
=> ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y4 ) )
= ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ) ).
% abs_fun_if
thf(fact_219_abs__fun__if,axiom,
! [C2: $o,Pi: list_P227219501e_name,X: name,Y4: name] :
( ( C2
=> ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y4 ) )
= ( perm_name_name @ Pi @ X ) ) )
& ( ~ C2
=> ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y4 ) )
= ( perm_name_name @ Pi @ Y4 ) ) ) ) ).
% abs_fun_if
thf(fact_220_abs__fun__if,axiom,
! [C2: $o,Pi: list_P227219501e_name,X: pi,Y4: pi] :
( ( C2
=> ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y4 ) )
= ( perm_name_pi @ Pi @ X ) ) )
& ( ~ C2
=> ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y4 ) )
= ( perm_name_pi @ Pi @ Y4 ) ) ) ) ).
% abs_fun_if
thf(fact_221_eqvt__def,axiom,
( eqvt_pi
= ( ^ [Rel2: set_Pr1834926343_pi_pi] :
! [X5: product_prod_pi_pi,Perm2: list_P227219501e_name] :
( ( member558706512_pi_pi @ X5 @ Rel2 )
=> ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Perm2 @ X5 ) @ Rel2 ) ) ) ) ).
% eqvt_def
thf(fact_222_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y4: late_subject] :
( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y4 ) )
= ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_223_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y4: late_freeRes] :
( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y4 ) )
= ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_224_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y4: pi_Rep] :
( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y4 ) )
= ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_225_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y4: name] :
( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y4 ) )
= ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_226_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y4: pi] :
( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y4 ) )
= ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_227_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_subject] :
( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y4 ) )
= ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_228_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y4: late_freeRes] :
( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y4 ) )
= ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_229_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y4: pi_Rep] :
( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y4 ) )
= ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_230_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y4: name] :
( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y4 ) )
= ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_231_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y4: pi] :
( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y4 ) )
= ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y4 ) ) ) ).
% perm_prod.simps
thf(fact_232_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Xs2: list_Late_subject] :
( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs2 ) )
= ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs2 ) ) ) ).
% cons_eqvt
thf(fact_233_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Xs2: list_Late_freeRes] :
( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs2 ) )
= ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs2 ) ) ) ).
% cons_eqvt
thf(fact_234_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi_Rep,Xs2: list_pi_Rep] :
( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs2 ) )
= ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs2 ) ) ) ).
% cons_eqvt
thf(fact_235_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: name,Xs2: list_name] :
( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs2 ) )
= ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs2 ) ) ) ).
% cons_eqvt
thf(fact_236_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi,Xs2: list_pi] :
( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs2 ) )
= ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs2 ) ) ) ).
% cons_eqvt
thf(fact_237_fresh__prodD_I1_J,axiom,
! [A: name,X: name,Y4: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y4 ) )
=> ( fresh_name_name @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_238_fresh__prodD_I1_J,axiom,
! [A: name,X: name,Y4: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y4 ) )
=> ( fresh_name_name @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_239_fresh__prodD_I1_J,axiom,
! [A: name,X: pi,Y4: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y4 ) )
=> ( fresh_name_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_240_fresh__prodD_I2_J,axiom,
! [A: name,X: name,Y4: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y4 ) )
=> ( fresh_name_name @ A @ Y4 ) ) ).
% fresh_prodD(2)
thf(fact_241_fresh__prodD_I2_J,axiom,
! [A: name,X: name,Y4: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y4 ) )
=> ( fresh_1627595501_pi_pi @ A @ Y4 ) ) ).
% fresh_prodD(2)
thf(fact_242_fresh__prodD_I2_J,axiom,
! [A: name,X: pi,Y4: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y4 ) )
=> ( fresh_name_pi @ A @ Y4 ) ) ).
% fresh_prodD(2)
thf(fact_243_fresh__list__cons,axiom,
! [A: name,X: late_subject,Xs2: list_Late_subject] :
( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ X @ Xs2 ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_838462539ubject @ A @ Xs2 ) ) ) ).
% fresh_list_cons
thf(fact_244_fresh__list__cons,axiom,
! [A: name,X: late_freeRes,Xs2: list_Late_freeRes] :
( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ X @ Xs2 ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_1981651763reeRes @ A @ Xs2 ) ) ) ).
% fresh_list_cons
thf(fact_245_fresh__list__cons,axiom,
! [A: name,X: produc1141751126_pi_pi,Xs2: list_P431515740_pi_pi] :
( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ X @ Xs2 ) )
= ( ( fresh_1376661020_pi_pi @ A @ X )
& ( fresh_1958133282_pi_pi @ A @ Xs2 ) ) ) ).
% fresh_list_cons
thf(fact_246_fresh__list__cons,axiom,
! [A: name,X: name,Xs2: list_name] :
( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs2 ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_name_list_name @ A @ Xs2 ) ) ) ).
% fresh_list_cons
thf(fact_247_fresh__list__cons,axiom,
! [A: name,X: pi,Xs2: list_pi] :
( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs2 ) )
= ( ( fresh_name_pi @ A @ X )
& ( fresh_name_list_pi @ A @ Xs2 ) ) ) ).
% fresh_list_cons
thf(fact_248_subrelI,axiom,
! [R: set_Pr443758855e_name,S: set_Pr443758855e_name] :
( ! [X4: name,Y3: name] :
( ( member695284560e_name @ ( produc1570949143e_name @ X4 @ Y3 ) @ R )
=> ( member695284560e_name @ ( produc1570949143e_name @ X4 @ Y3 ) @ S ) )
=> ( ord_le793202855e_name @ R @ S ) ) ).
% subrelI
thf(fact_249_subrelI,axiom,
! [R: set_Pr1654044726_pi_pi,S: set_Pr1654044726_pi_pi] :
( ! [X4: name,Y3: product_prod_pi_pi] :
( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X4 @ Y3 ) @ R )
=> ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X4 @ Y3 ) @ S ) )
=> ( ord_le797229014_pi_pi @ R @ S ) ) ).
% subrelI
thf(fact_250_subrelI,axiom,
! [R: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
( ! [X4: pi,Y3: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X4 @ Y3 ) @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X4 @ Y3 ) @ S ) )
=> ( ord_le630093991_pi_pi @ R @ S ) ) ).
% subrelI
thf(fact_251_IdE,axiom,
! [P3: produc367475239e_name] :
( ( member695284560e_name @ P3 @ id_name )
=> ~ ! [X4: name] :
( P3
!= ( produc1570949143e_name @ X4 @ X4 ) ) ) ).
% IdE
thf(fact_252_IdE,axiom,
! [P3: product_prod_pi_pi] :
( ( member558706512_pi_pi @ P3 @ id_pi )
=> ~ ! [X4: pi] :
( P3
!= ( product_Pair_pi_pi @ X4 @ X4 ) ) ) ).
% IdE
thf(fact_253_derivativeMonotonic,axiom,
! [P2: pi,Q: pi,A: late_subject,X: name,A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
( ( strong2129052853vative @ P2 @ Q @ A @ X @ A4 )
=> ( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ( strong2129052853vative @ P2 @ Q @ A @ X @ B4 ) ) ) ).
% derivativeMonotonic
thf(fact_254_eqvtRelE,axiom,
! [Rel: set_Pr806375235ubject,Perm: list_P227219501e_name,P2: late_subject,Q: late_subject] :
( ( eqvt_Late_subject @ Rel )
=> ( ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P2 ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel )
=> ( member1586545036ubject @ ( produc1465345179ubject @ P2 @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_255_eqvtRelE,axiom,
! [Rel: set_Pr1780909331reeRes,Perm: list_P227219501e_name,P2: late_freeRes,Q: late_freeRes] :
( ( eqvt_Late_freeRes @ Rel )
=> ( ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P2 ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel )
=> ( member1584979804reeRes @ ( produc1244821099reeRes @ P2 @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_256_eqvtRelE,axiom,
! [Rel: set_Pr1131282415pi_Rep,Perm: list_P227219501e_name,P2: pi_Rep,Q: pi_Rep] :
( ( eqvt_pi_Rep @ Rel )
=> ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P2 ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel )
=> ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P2 @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_257_eqvtRelE,axiom,
! [Rel: set_Pr443758855e_name,Perm: list_P227219501e_name,P2: name,Q: name] :
( ( eqvt_name @ Rel )
=> ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P2 ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel )
=> ( member695284560e_name @ ( produc1570949143e_name @ P2 @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_258_eqvtRelE,axiom,
! [Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name,P2: pi,Q: pi] :
( ( eqvt_pi @ Rel )
=> ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P2 ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_259_Bound_Ohyps_I3_J,axiom,
fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% Bound.hyps(3)
thf(fact_260_Bound_Ohyps_I2_J,axiom,
fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% Bound.hyps(2)
thf(fact_261_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_262_subsetI,axiom,
! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
( ! [X4: product_prod_pi_pi] :
( ( member558706512_pi_pi @ X4 @ A4 )
=> ( member558706512_pi_pi @ X4 @ B4 ) )
=> ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% subsetI
thf(fact_263_order__refl,axiom,
! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% order_refl
thf(fact_264_name__fresh,axiom,
( fresh_name_name
= ( ^ [A5: name,B5: name] : A5 != B5 ) ) ).
% name_fresh
thf(fact_265_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_266_pi_Operm_I7_J,axiom,
! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
( ( perm_name_pi @ Pi @ ( sum @ X2 @ X1 ) )
= ( sum @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% pi.perm(7)
thf(fact_267_pi_Operm_I9_J,axiom,
! [Pi: list_P227219501e_name,X1: name,X2: pi] :
( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
= ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% pi.perm(9)
thf(fact_268_pi_Odistinct_I81_J,axiom,
! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi3 ) ) ).
% pi.distinct(81)
thf(fact_269_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_270_freshRes,axiom,
! [A: name,P2: pi] : ( fresh_name_pi @ A @ ( res @ A @ P2 ) ) ).
% freshRes
thf(fact_271_order__subst1,axiom,
! [A: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ ( F @ B ) )
=> ( ( ord_le630093991_pi_pi @ B @ C2 )
=> ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X4 @ Y3 )
=> ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_272_order__subst2,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ ( F @ B ) @ C2 )
=> ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X4 @ Y3 )
=> ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_le630093991_pi_pi @ ( F @ A ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_273_ord__eq__le__subst,axiom,
! [A: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( A
= ( F @ B ) )
=> ( ( ord_le630093991_pi_pi @ B @ C2 )
=> ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X4 @ Y3 )
=> ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_274_ord__le__eq__subst,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X4: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X4 @ Y3 )
=> ( ord_le630093991_pi_pi @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_le630093991_pi_pi @ ( F @ A ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_275_eq__iff,axiom,
( ( ^ [Y6: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] : Y6 = Z )
= ( ^ [X5: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X5 @ Y5 )
& ( ord_le630093991_pi_pi @ Y5 @ X5 ) ) ) ) ).
% eq_iff
thf(fact_276_antisym,axiom,
! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X @ Y4 )
=> ( ( ord_le630093991_pi_pi @ Y4 @ X )
=> ( X = Y4 ) ) ) ).
% antisym
thf(fact_277_eq__refl,axiom,
! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi] :
( ( X = Y4 )
=> ( ord_le630093991_pi_pi @ X @ Y4 ) ) ).
% eq_refl
thf(fact_278_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_279_antisym__conv,axiom,
! [Y4: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ Y4 @ X )
=> ( ( ord_le630093991_pi_pi @ X @ Y4 )
= ( X = Y4 ) ) ) ).
% antisym_conv
thf(fact_280_order__class_Oorder_Oeq__iff,axiom,
( ( ^ [Y6: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] : Y6 = Z )
= ( ^ [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_281_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_282_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_283_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_284_order__trans,axiom,
! [X: set_Pr1834926343_pi_pi,Y4: set_Pr1834926343_pi_pi,Z2: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ X @ Y4 )
=> ( ( ord_le630093991_pi_pi @ Y4 @ Z2 )
=> ( ord_le630093991_pi_pi @ X @ Z2 ) ) ) ).
% order_trans
thf(fact_285_dual__order_Orefl,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% dual_order.refl
thf(fact_286_alphaRes,axiom,
! [C2: name,P2: pi,A: name] :
( ( fresh_name_pi @ C2 @ P2 )
=> ( ( res @ A @ P2 )
= ( res @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C2 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% alphaRes
thf(fact_287_calculation,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) ) ).
% calculation
thf(fact_288_Bound_Ohyps_I1_J,axiom,
late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% Bound.hyps(1)
thf(fact_289__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ) ).
% \<open><\<nu>x>(P \<oplus> Q) \<longmapsto> a<\<nu>x> \<prec> P'\<close>
thf(fact_290_sumResLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,X: name,P2: pi,Q: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( ( eqvt_pi @ Rel )
=> ( strong743114133lation @ ( sum @ ( res @ X @ P2 ) @ ( res @ X @ Q ) ) @ Rel @ ( res @ X @ ( sum @ P2 @ Q ) ) ) ) ) ).
% sumResLeft
thf(fact_291_cSum1_Ohyps,axiom,
late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ) ).
% cSum1.hyps
thf(fact_292_residual_Operm_I1_J,axiom,
! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
= ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% residual.perm(1)
thf(fact_293_freshBoundDerivative_I1_J,axiom,
! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
=> ( ( fresh_name_pi @ Y4 @ P2 )
=> ( fresh_717452603ubject @ Y4 @ A ) ) ) ).
% freshBoundDerivative(1)
thf(fact_294_Late__Semantics_OResB,axiom,
! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
=> ( ( fresh_717452603ubject @ Y4 @ A )
=> ( ( Y4 != X )
=> ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ ( res @ Y4 @ P4 ) ) ) ) ) ) ).
% Late_Semantics.ResB
thf(fact_295_freshBoundDerivative_I2_J,axiom,
! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
=> ( ( fresh_name_pi @ Y4 @ P2 )
=> ( ( Y4 != X )
=> ( fresh_name_pi @ Y4 @ P4 ) ) ) ) ).
% freshBoundDerivative(2)
thf(fact_296_simE_I1_J,axiom,
! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
( ( strong743114133lation @ P2 @ Rel @ Q )
=> ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P2 )
=> ? [P5: pi] :
( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P5 ) )
& ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% simE(1)
thf(fact_297_Sum2,axiom,
! [Q: pi,Rs: late_residual,P2: pi] :
( ( late_transitions @ Q @ Rs )
=> ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% Sum2
thf(fact_298_Sum1,axiom,
! [P2: pi,Rs: late_residual,Q: pi] :
( ( late_transitions @ P2 @ Rs )
=> ( late_transitions @ ( sum @ P2 @ Q ) @ Rs ) ) ).
% Sum1
thf(fact_299_sumCases_H,axiom,
! [P2: pi,Q: pi,Rs: late_residual] :
( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
=> ( ~ ( late_transitions @ P2 @ Rs )
=> ( late_transitions @ Q @ Rs ) ) ) ).
% sumCases'
thf(fact_300_sumCases,axiom,
! [P2: pi,Q: pi,Rs: late_residual] :
( ( late_transitions @ ( sum @ P2 @ Q ) @ Rs )
=> ( ~ ( late_transitions @ P2 @ Rs )
=> ( late_transitions @ Q @ Rs ) ) ) ).
% sumCases
thf(fact_301_freshResidual,axiom,
! [P2: pi,Rs: late_residual,X: name] :
( ( late_transitions @ P2 @ Rs )
=> ( ( fresh_name_pi @ X @ P2 )
=> ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% freshResidual
thf(fact_302_eqvt,axiom,
! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
( ( late_transitions @ X1 @ X2 )
=> ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% eqvt
thf(fact_303_transitions_OResB,axiom,
! [P2: pi,A: late_subject,X: name,P4: pi,Y4: name] :
( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P4 ) )
=> ( ( fresh_717452603ubject @ Y4 @ A )
=> ( ( Y4 != X )
=> ( ( fresh_name_pi @ X @ P2 )
=> ( ( fresh_717452603ubject @ X @ A )
=> ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ ( res @ Y4 @ P4 ) ) ) ) ) ) ) ) ).
% transitions.ResB
thf(fact_304_monotonic,axiom,
! [P2: pi,A4: set_Pr1834926343_pi_pi,P4: pi,B4: set_Pr1834926343_pi_pi] :
( ( strong743114133lation @ P2 @ A4 @ P4 )
=> ( ( ord_le630093991_pi_pi @ A4 @ B4 )
=> ( strong743114133lation @ P2 @ B4 @ P4 ) ) ) ).
% monotonic
thf(fact_305_Strong__Late__Sim_Oreflexive,axiom,
! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ P2 @ Rel @ P2 ) ) ).
% Strong_Late_Sim.reflexive
thf(fact_306_sumIdempRight,axiom,
! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ P2 @ P2 ) @ Rel @ P2 ) ) ).
% sumIdempRight
thf(fact_307_sumAssocRight,axiom,
! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,R2: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) ) ) ).
% sumAssocRight
thf(fact_308_sumIdempLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,P2: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ P2 @ Rel @ ( sum @ P2 @ P2 ) ) ) ).
% sumIdempLeft
thf(fact_309_sumAssocLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi,R2: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ ( sum @ P2 @ Q ) @ R2 ) @ Rel @ ( sum @ P2 @ ( sum @ Q @ R2 ) ) ) ) ).
% sumAssocLeft
thf(fact_310_sumSym,axiom,
! [Rel: set_Pr1834926343_pi_pi,P2: pi,Q: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ Rel )
=> ( strong743114133lation @ ( sum @ P2 @ Q ) @ Rel @ ( sum @ Q @ P2 ) ) ) ).
% sumSym
thf(fact_311_eqvtI,axiom,
! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Rel3: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
( ( strong743114133lation @ P2 @ Rel @ Q )
=> ( ( ord_le630093991_pi_pi @ Rel @ Rel3 )
=> ( ( eqvt_pi @ Rel3 )
=> ( strong743114133lation @ ( perm_name_pi @ Perm @ P2 ) @ Rel3 @ ( perm_name_pi @ Perm @ Q ) ) ) ) ) ).
% eqvtI
thf(fact_312_alphaBoundResidual,axiom,
! [X6: name,P2: pi,A: late_subject,X: name] :
( ( fresh_name_pi @ X6 @ P2 )
=> ( ( late_BoundR @ A @ X @ P2 )
= ( late_BoundR @ A @ X6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X6 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% alphaBoundResidual
thf(fact_313_cOpen_Ohyps_I1_J,axiom,
late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% cOpen.hyps(1)
thf(fact_314__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062,axiom,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ) ).
% \<open>P \<oplus> Q \<longmapsto> a[x] \<prec> P'\<close>
thf(fact_315_Late__Semantics1_OfreeRes_Oinject,axiom,
! [X11: name,X122: name,Y11: name,Y12: name] :
( ( ( late_OutputR @ X11 @ X122 )
= ( late_OutputR @ Y11 @ Y12 ) )
= ( ( X11 = Y11 )
& ( X122 = Y12 ) ) ) ).
% Late_Semantics1.freeRes.inject
thf(fact_316_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_317_freeRes_Operm_I1_J,axiom,
! [Pi: list_P227219501e_name,X2: name,X1: name] :
( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
= ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% freeRes.perm(1)
thf(fact_318_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_319_residual_Operm_I2_J,axiom,
! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
= ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% residual.perm(2)
thf(fact_320_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_321_residual_Odistinct_I1_J,axiom,
! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
( ( late_BoundR @ Subject @ Name2 @ Pi )
!= ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% residual.distinct(1)
thf(fact_322_residual_Oinducts,axiom,
! [P2: late_residual > $o,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P2 @ Residual ) ) ) ).
% residual.inducts
thf(fact_323_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_324_ResF,axiom,
! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
=> ( ( fresh_1641682979reeRes @ Y4 @ Alpha )
=> ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_FreeR @ Alpha @ ( res @ Y4 @ P4 ) ) ) ) ) ).
% ResF
thf(fact_325_resCasesF_H,axiom,
! [X: name,P2: pi,Alpha: late_freeRes,P4: pi] :
( ( late_transitions @ ( res @ X @ P2 ) @ ( late_FreeR @ Alpha @ P4 ) )
=> ~ ! [P: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
( ( ( res @ X @ P2 )
= ( res @ Y3 @ P ) )
=> ( ( ( late_FreeR @ Alpha @ P4 )
= ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
=> ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
=> ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% resCasesF'
thf(fact_326_resCasesF,axiom,
! [X: name,P2: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
( ( late_transitions @ ( res @ X @ P2 ) @ ( late_FreeR @ Alpha @ XP ) )
=> ( ! [P5: pi] :
( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P5 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha )
=> ( F3 @ ( res @ X @ P5 ) ) ) )
=> ( F3 @ XP ) ) ) ).
% resCasesF
thf(fact_327_freshFreeDerivative_I2_J,axiom,
! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
=> ( ( fresh_name_pi @ Y4 @ P2 )
=> ( fresh_name_pi @ Y4 @ P4 ) ) ) ).
% freshFreeDerivative(2)
thf(fact_328_freshFreeDerivative_I1_J,axiom,
! [P2: pi,Alpha: late_freeRes,P4: pi,Y4: name] :
( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P4 ) )
=> ( ( fresh_name_pi @ Y4 @ P2 )
=> ( fresh_1641682979reeRes @ Y4 @ Alpha ) ) ) ).
% freshFreeDerivative(1)
thf(fact_329_Open,axiom,
! [P2: pi,A: name,B: name,P4: pi] :
( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P4 ) )
=> ( ( A != B )
=> ( late_transitions @ ( res @ B @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P4 ) ) ) ) ).
% Open
thf(fact_330_simE_I2_J,axiom,
! [P2: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
( ( strong743114133lation @ P2 @ Rel @ Q )
=> ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
=> ? [P5: pi] :
( ( late_transitions @ P2 @ ( late_FreeR @ Alpha @ P5 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% simE(2)
thf(fact_331_resCasesB_H,axiom,
! [X6: name,P2: pi,A: late_subject,Y7: name,P4: pi] :
( ( late_transitions @ ( res @ X6 @ P2 ) @ ( late_BoundR @ A @ Y7 @ P4 ) )
=> ( ! [P: pi,A3: name,B3: name] :
( ( ( res @ X6 @ P2 )
= ( res @ B3 @ P ) )
=> ! [P5: pi] :
( ( ( late_BoundR @ A @ Y7 @ P4 )
= ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
=> ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
=> ( A3 = B3 ) ) ) )
=> ~ ! [P: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
( ( ( res @ X6 @ P2 )
= ( res @ Y3 @ P ) )
=> ( ( ( late_BoundR @ A @ Y7 @ P4 )
= ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
=> ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P5 ) )
=> ( ( fresh_717452603ubject @ Y3 @ A3 )
=> ( ( Y3 != X4 )
=> ( ( fresh_name_pi @ X4 @ P )
=> ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).
% resCasesB'
thf(fact_332_resCases_H,axiom,
! [X: name,P2: pi,Rs: late_residual] :
( ( late_transitions @ ( res @ X @ P2 ) @ Rs )
=> ( ! [P: pi,A3: name,B3: name] :
( ( ( res @ X @ P2 )
= ( res @ B3 @ P ) )
=> ! [P5: pi] :
( ( Rs
= ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
=> ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
=> ( A3 = B3 ) ) ) )
=> ( ! [P: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
( ( ( res @ X @ P2 )
= ( res @ Y3 @ P ) )
=> ( ( Rs
= ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
=> ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P5 ) )
=> ( ( fresh_717452603ubject @ Y3 @ A3 )
=> ( ( Y3 != X4 )
=> ( ( fresh_name_pi @ X4 @ P )
=> ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
=> ~ ! [P: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
( ( ( res @ X @ P2 )
= ( res @ Y3 @ P ) )
=> ( ( Rs
= ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
=> ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
=> ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% resCases'
thf(fact_333_resCasesB,axiom,
! [Y4: name,P2: pi,A: late_subject,X: name,YP: pi,F3: late_subject > pi > $o] :
( ( late_transitions @ ( res @ Y4 @ P2 ) @ ( late_BoundR @ A @ X @ YP ) )
=> ( ( X != Y4 )
=> ( ( fresh_name_pi @ X @ P2 )
=> ( ! [B3: name,P5: pi] :
( ( late_transitions @ P2 @ ( late_FreeR @ ( late_OutputR @ B3 @ Y4 ) @ P5 ) )
=> ( ( B3 != Y4 )
=> ( ( A
= ( late_BoundOutputS @ B3 ) )
=> ( F3 @ ( late_BoundOutputS @ B3 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P5 ) ) ) ) )
=> ( ! [P5: pi] :
( ( late_transitions @ P2 @ ( late_BoundR @ A @ X @ P5 ) )
=> ( ( fresh_717452603ubject @ Y4 @ A )
=> ( F3 @ A @ ( res @ Y4 @ P5 ) ) ) )
=> ( F3 @ A @ YP ) ) ) ) ) ) ).
% resCasesB
thf(fact_334_simulation__def,axiom,
( strong743114133lation
= ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q3: pi] :
( ! [A5: late_subject,X5: name,Q4: pi] :
( ( ( late_transitions @ Q3 @ ( late_BoundR @ A5 @ X5 @ Q4 ) )
& ( fresh_name_pi @ X5 @ P6 ) )
=> ? [P7: pi] :
( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X5 @ P7 ) )
& ( strong2129052853vative @ P7 @ Q4 @ A5 @ X5 @ Rel2 ) ) )
& ! [Alpha3: late_freeRes,Q4: pi] :
( ( late_transitions @ Q3 @ ( late_FreeR @ Alpha3 @ Q4 ) )
=> ? [P7: pi] :
( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q4 ) @ Rel2 ) ) ) ) ) ) ).
% simulation_def
thf(fact_335_simCases,axiom,
! [Q: pi,P2: pi,Rel: set_Pr1834926343_pi_pi] :
( ! [A3: late_subject,Y3: name,Q5: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q5 ) )
=> ( ( fresh_name_pi @ Y3 @ P2 )
=> ? [P8: pi] :
( ( late_transitions @ P2 @ ( late_BoundR @ A3 @ Y3 @ P8 ) )
& ( strong2129052853vative @ P8 @ Q5 @ A3 @ Y3 @ Rel ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q5: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q5 ) )
=> ? [P8: pi] :
( ( late_transitions @ P2 @ ( late_FreeR @ Alpha2 @ P8 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q5 ) @ Rel ) ) )
=> ( strong743114133lation @ P2 @ Rel @ Q ) ) ) ).
% simCases
thf(fact_336_residual__Rep_Oinject_I2_J,axiom,
! [X21: late_freeRes,X22: pi,Y21: late_freeRes,Y22: pi] :
( ( ( late_r347633188eR_Rep @ X21 @ X22 )
= ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% residual_Rep.inject(2)
thf(fact_337_alphaInput,axiom,
! [C2: name,P2: pi,A: name,X: name] :
( ( fresh_name_pi @ C2 @ P2 )
=> ( ( input @ A @ X @ P2 )
= ( input @ A @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C2 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) ) ).
% alphaInput
thf(fact_338_pi_Operm_I4_J,axiom,
! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
= ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% pi.perm(4)
thf(fact_339_resTrans_I2_J,axiom,
! [X: name,Y4: name,P2: pi,Rs: late_residual] :
~ ( late_transitions @ ( res @ X @ ( input @ X @ Y4 @ P2 ) ) @ Rs ) ).
% resTrans(2)
thf(fact_340_pi_Odistinct_I53_J,axiom,
! [Name1: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name1 @ Name22 @ Pi )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(53)
thf(fact_341_pi_Odistinct_I57_J,axiom,
! [Name1: name,Name22: name,Pi: pi,Name: name,Pi3: pi] :
( ( input @ Name1 @ Name22 @ Pi )
!= ( res @ Name @ Pi3 ) ) ).
% pi.distinct(57)
thf(fact_342_inputFreeTrans,axiom,
! [A: name,X: name,P2: pi,Alpha: late_freeRes,P4: pi] :
~ ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_FreeR @ Alpha @ P4 ) ) ).
% inputFreeTrans
thf(fact_343_resInputFreeTrans,axiom,
! [X: name,A: name,Y4: name,P2: pi,Alpha: late_freeRes,P4: pi] :
~ ( late_transitions @ ( res @ X @ ( input @ A @ Y4 @ P2 ) ) @ ( late_FreeR @ Alpha @ P4 ) ) ).
% resInputFreeTrans
thf(fact_344_inputBoundOutputTrans,axiom,
! [A: name,X: name,P2: pi,B: name,Y4: name,P4: pi] :
~ ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y4 @ P4 ) ) ).
% inputBoundOutputTrans
thf(fact_345_inputIneqTrans,axiom,
! [A: name,X: name,P2: pi,B: late_subject,Y4: name,P4: pi] :
( ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ B @ Y4 @ P4 ) )
=> ~ ( fresh_717452603ubject @ A @ B ) ) ).
% inputIneqTrans
thf(fact_346_resInputBoundOutputTrans,axiom,
! [X: name,A: name,Y4: name,P2: pi,B: name,Z2: name,P4: pi] :
~ ( late_transitions @ ( res @ X @ ( input @ A @ Y4 @ P2 ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z2 @ P4 ) ) ).
% resInputBoundOutputTrans
thf(fact_347_inputCases,axiom,
! [A: name,X: name,P2: pi,B: late_subject,Y4: name,YP: pi,Prop: late_subject > name > pi > $o] :
( ( late_transitions @ ( input @ A @ X @ P2 ) @ ( late_BoundR @ B @ Y4 @ YP ) )
=> ( ( Y4 != A )
=> ( ( Y4 != X )
=> ( ( fresh_name_pi @ Y4 @ P2 )
=> ( ( ( B
= ( late_InputS @ A ) )
=> ( ( YP
= ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P2 ) )
=> ( Prop @ ( late_InputS @ A ) @ Y4 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y4 ) @ nil_Pr743626285e_name ) @ P2 ) ) ) )
=> ( Prop @ B @ Y4 @ YP ) ) ) ) ) ) ).
% inputCases
thf(fact_348_name__calc_I1_J,axiom,
! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
= ( swap_name @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% name_calc(1)
thf(fact_349_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
! [X1: name,Y1: name] :
( ( ( late_InputS @ X1 )
= ( late_InputS @ Y1 ) )
= ( X1 = Y1 ) ) ).
% Late_Semantics1.subject.inject(1)
thf(fact_350_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_351_subject_Operm_I1_J,axiom,
! [Pi: list_P227219501e_name,X1: name] :
( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
= ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% subject.perm(1)
thf(fact_352_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
! [Name2: name,Name: name] :
( ( late_InputS @ Name2 )
!= ( late_BoundOutputS @ Name ) ) ).
% Late_Semantics.subject.distinct(1)
% Helper facts (11)
thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
! [X: pi,Y4: pi] :
( ( if_pi @ $false @ X @ Y4 )
= Y4 ) ).
thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
! [X: pi,Y4: pi] :
( ( if_pi @ $true @ X @ Y4 )
= X ) ).
thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
! [X: name,Y4: name] :
( ( if_name @ $false @ X @ Y4 )
= Y4 ) ).
thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
! [X: name,Y4: name] :
( ( if_name @ $true @ X @ Y4 )
= X ) ).
thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
! [X: pi_Rep,Y4: pi_Rep] :
( ( if_pi_Rep @ $false @ X @ Y4 )
= Y4 ) ).
thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
! [X: pi_Rep,Y4: pi_Rep] :
( ( if_pi_Rep @ $true @ X @ Y4 )
= X ) ).
thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
! [X: late_freeRes,Y4: late_freeRes] :
( ( if_Late_freeRes @ $false @ X @ Y4 )
= Y4 ) ).
thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
! [X: late_freeRes,Y4: late_freeRes] :
( ( if_Late_freeRes @ $true @ X @ Y4 )
= X ) ).
thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
! [P2: $o] :
( ( P2 = $true )
| ( P2 = $false ) ) ).
thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
! [X: late_subject,Y4: late_subject] :
( ( if_Late_subject @ $false @ X @ Y4 )
= Y4 ) ).
thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
! [X: late_subject,Y4: late_subject] :
( ( if_Late_subject @ $true @ X @ Y4 )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ).
%------------------------------------------------------------------------------