TPTP Problem File: ITP137^1.p
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%------------------------------------------------------------------------------
% File : ITP137^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer Paraconsistency problem prob_407__3265932_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 : Paraconsistency/prob_407__3265932_1 [Des21]
% Status : Theorem
% Rating : 0.50 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0
% Syntax : Number of formulae : 499 ( 250 unt; 141 typ; 0 def)
% Number of atoms : 764 ( 473 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 2646 ( 122 ~; 5 |; 44 &;2233 @)
% ( 0 <=>; 242 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 24 ( 23 usr)
% Number of type conns : 971 ( 971 >; 0 *; 0 +; 0 <<)
% Number of symbols : 121 ( 118 usr; 4 con; 0-4 aty)
% Number of variables : 1205 ( 174 ^;1012 !; 19 ?;1205 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:36:27.301
%------------------------------------------------------------------------------
% Could-be-implicit typings (23)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J_J,type,
set_Pr1475944804lle_fm: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
produc1250255278lle_fm: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
set_Pr2012908090lle_tv: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
produc484385668lle_tv: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
set_Pr2061825550lle_tv: $tType ).
thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
produc1852595672lle_tv: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
set_Pr1723822845lle_tv: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
set_Pr2120184979lle_fm: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
produc1443694919lle_tv: $tType ).
thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
produc696645085lle_fm: $tType ).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_Eo_J_J,type,
set_Pr38785645e_tv_o: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
set_Pr2014382200lle_tv: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
set_Pr1019238018lle_fm: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
produc1647334210lle_tv: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
produc450659916lle_fm: $tType ).
thf(ty_n_t__Set__Oset_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
set_li72793489lle_tv: $tType ).
thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
set_Pa1764573435lle_tv: $tType ).
thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
set_Pa1499417344lle_fm: $tType ).
thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
paraco1605129243lle_tv: $tType ).
thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
paraco1604210848lle_fm: $tType ).
thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
list_char: $tType ).
thf(ty_n_t__Set__Oset_I_Eo_J,type,
set_o: $tType ).
thf(ty_n_t__Nat__Onat,type,
nat: $tType ).
% Explicit typings (118)
thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
the_Pr1724341910lle_fm: ( produc696645085lle_fm > $o ) > produc696645085lle_fm ).
thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
the_Pr304385787lle_tv: ( produc1647334210lle_tv > $o ) > produc1647334210lle_tv ).
thf(sy_c_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(sy_c_Order__Relation_OaboveS_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
order_1376767238lle_tv: set_Pr2014382200lle_tv > paraco1605129243lle_tv > set_Pa1764573435lle_tv ).
thf(sy_c_Order__Relation_Oabove_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
order_1434492699lle_tv: set_Pr2014382200lle_tv > paraco1605129243lle_tv > set_Pa1764573435lle_tv ).
thf(sy_c_Order__Relation_Orelation__of_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
order_1215526505lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv > set_Pr2014382200lle_tv ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
paraco367965286_Truth: paraco1604210848lle_fm ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_OIndet,type,
paraco793048302_Indet: nat > paraco1605129243lle_tv ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_Ocase__tv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
paraco327635598_valid: paraco1604210848lle_fm > $o ).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
produc1297923922lle_tv: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > produc1852595672lle_tv ).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).
thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm ).
thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv ).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm ).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
produc1537086518lle_tv: produc1647334210lle_tv > produc1647334210lle_tv > produc484385668lle_tv ).
thf(sy_c_Product__Type_OSigma_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
produc327378790lle_fm: set_li72793489lle_tv > ( ( list_char > paraco1605129243lle_tv ) > set_Pa1499417344lle_fm ) > set_Pr2120184979lle_fm ).
thf(sy_c_Product__Type_OSigma_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
produc559987792lle_tv: set_Pa1499417344lle_fm > ( paraco1604210848lle_fm > set_li72793489lle_tv ) > set_Pr1723822845lle_tv ).
thf(sy_c_Product__Type_OSigma_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
produc479904331lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > set_Pa1764573435lle_tv ) > set_Pr2014382200lle_tv ).
thf(sy_c_Product__Type_Obool_Ocase__bool_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
thf(sy_c_Product__Type_Ocurry_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_Eo,type,
produc1667860344e_tv_o: ( produc1852595672lle_tv > $o ) > ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > $o ).
thf(sy_c_Product__Type_Ocurry_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_Eo,type,
produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).
thf(sy_c_Product__Type_Ocurry_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
produc251170289lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
thf(sy_c_Product__Type_Ocurry_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_Eo,type,
produc298562633e_tv_o: ( produc1443694919lle_tv > $o ) > paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o ).
thf(sy_c_Product__Type_Ocurry_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
produc635060359lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm ).
thf(sy_c_Product__Type_Ocurry_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_Eo,type,
produc1339594628e_fm_o: ( produc450659916lle_fm > $o ) > paraco1604210848lle_fm > paraco1604210848lle_fm > $o ).
thf(sy_c_Product__Type_Ocurry_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_Eo_J,type,
produc2005494902e_tv_o: ( produc1647334210lle_tv > produc1647334210lle_tv > $o ) > paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o ).
thf(sy_c_Product__Type_Ocurry_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_Eo,type,
produc621423502e_tv_o: ( produc1647334210lle_tv > $o ) > paraco1605129243lle_tv > paraco1605129243lle_tv > $o ).
thf(sy_c_Product__Type_Ocurry_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
produc724036226lle_tv: ( produc1647334210lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(sy_c_Product__Type_Ocurry_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001_Eo,type,
produc408556266e_fm_o: ( produc1250255278lle_fm > $o ) > produc696645085lle_fm > produc696645085lle_fm > $o ).
thf(sy_c_Product__Type_Ocurry_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_Eo,type,
produc1113543188e_tv_o: ( produc484385668lle_tv > $o ) > produc1647334210lle_tv > produc1647334210lle_tv > $o ).
thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_Eo,type,
produc1504058474e_fm_o: ( ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ) > produc696645085lle_fm > $o ).
thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
produc144063912lle_fm: ( ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
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produc2008706836lle_fm: ( paraco1605129243lle_tv > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc1647334210lle_tv > produc696645085lle_fm ).
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produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
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produc1949847036lle_tv: ( ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
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produc427355858lle_fm: ( ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
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produc811245928lle_fm: ( paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm ) > produc1443694919lle_tv > produc696645085lle_fm ).
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produc1629543915lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm > list_char > paraco1605129243lle_tv ) > produc450659916lle_fm > list_char > paraco1605129243lle_tv ).
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produc182748835lle_fm: ( paraco1604210848lle_fm > paraco1604210848lle_fm > produc696645085lle_fm ) > produc450659916lle_fm > produc696645085lle_fm ).
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produc1370344801lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv > list_char > paraco1605129243lle_tv ) > produc1647334210lle_tv > list_char > paraco1605129243lle_tv ).
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produc25129173e_tv_o: ( paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o ) > produc1647334210lle_tv > produc1647334210lle_tv > $o ).
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produc852673135e_tv_o: ( paraco1605129243lle_tv > paraco1605129243lle_tv > $o ) > produc1647334210lle_tv > $o ).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
produc1882560353lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > paraco1605129243lle_tv ).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
produc377990317lle_fm: ( paraco1605129243lle_tv > paraco1605129243lle_tv > produc696645085lle_fm ) > produc1647334210lle_tv > produc696645085lle_fm ).
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produc942307752lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
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produc1234307915e_fm_o: ( produc696645085lle_fm > produc696645085lle_fm > $o ) > produc1250255278lle_fm > $o ).
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produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).
thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
produc488585168lle_tv: produc1647334210lle_tv > paraco1605129243lle_tv ).
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produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).
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produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).
thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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produc1176291762lle_tv: produc1852595672lle_tv > produc1852595672lle_tv ).
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produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).
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produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).
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produc1426802342lle_fm: produc450659916lle_fm > produc450659916lle_fm ).
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produc1733045910lle_tv: produc484385668lle_tv > produc484385668lle_tv ).
thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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collec1102043437lle_tv: ( produc1852595672lle_tv > $o ) > set_Pr2061825550lle_tv ).
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collec1363950211lle_fm: ( produc1250255278lle_fm > $o ) > set_Pr1475944804lle_fm ).
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collec1900284505lle_tv: ( produc484385668lle_tv > $o ) > set_Pr2012908090lle_tv ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
image_305309148lle_tv: ( produc696645085lle_fm > list_char > paraco1605129243lle_tv ) > set_Pr2120184979lle_fm > set_li72793489lle_tv ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001_Eo,type,
image_1402739636e_fm_o: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm > set_o ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
image_1110913773lle_tv: ( produc696645085lle_fm > produc1647334210lle_tv ) > set_Pr2120184979lle_fm > set_Pr2014382200lle_tv ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
image_496052427lle_tv: ( produc450659916lle_fm > list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm > set_li72793489lle_tv ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
image_1662022595lle_fm: ( produc450659916lle_fm > produc696645085lle_fm ) > set_Pr1019238018lle_fm > set_Pr2120184979lle_fm ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
image_1070648001lle_tv: ( produc1647334210lle_tv > list_char > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv > set_li72793489lle_tv ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_Eo_J,type,
image_1015627317e_tv_o: ( produc1647334210lle_tv > produc1647334210lle_tv > $o ) > set_Pr2014382200lle_tv > set_Pr38785645e_tv_o ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
image_1263514817lle_tv: ( produc1647334210lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv > set_Pa1764573435lle_tv ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
image_937396045lle_fm: ( produc1647334210lle_tv > produc696645085lle_fm ) > set_Pr2014382200lle_tv > set_Pr2120184979lle_fm ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_001_Eo,type,
image_1610089293e_tv_o: ( produc484385668lle_tv > $o ) > set_Pr2012908090lle_tv > set_o ).
thf(sy_c_Wellfounded_Olex__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm ).
thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv ).
thf(sy_c_Wfrec_Osame__fst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
same_f1581085506lle_fm: ( ( list_char > paraco1605129243lle_tv ) > $o ) > ( ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm ) > set_Pr1475944804lle_fm ).
thf(sy_c_Wfrec_Osame__fst_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
same_f1119076903lle_tv: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > set_Pr2014382200lle_tv ) > set_Pr2012908090lle_tv ).
thf(sy_c_member_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
member894927066lle_tv: ( list_char > paraco1605129243lle_tv ) > set_li72793489lle_tv > $o ).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_Eo_J,type,
member1832524214e_tv_o: ( produc1647334210lle_tv > $o ) > set_Pr38785645e_tv_o > $o ).
thf(sy_c_member_001_Eo,type,
member_o: $o > set_o > $o ).
thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
member265982409lle_fm: paraco1604210848lle_fm > set_Pa1499417344lle_fm > $o ).
thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
member1074212123lle_tv: produc484385668lle_tv > set_Pr2012908090lle_tv > $o ).
thf(sy_v_p,type,
p: paraco1604210848lle_fm ).
% Relevant facts (354)
thf(fact_0_tv_Oinject_I1_J,axiom,
! [X1: $o,Y1: $o] :
( ( ( paraco1344940915le_Det @ X1 )
= ( paraco1344940915le_Det @ Y1 ) )
= ( X1 = Y1 ) ) ).
% tv.inject(1)
thf(fact_1_assms,axiom,
paraco327635598_valid @ ( paraco445776468le_Neg @ p ) ).
% assms
thf(fact_2_valid__def,axiom,
( paraco327635598_valid
= ( ^ [P: paraco1604210848lle_fm] :
! [I: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ I @ P )
= ( paraco1344940915le_Det @ $true ) ) ) ) ).
% valid_def
thf(fact_3_eval_Osimps_I2_J,axiom,
! [I2: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ I2 @ paraco367965286_Truth )
= ( paraco1344940915le_Det @ $true ) ) ).
% eval.simps(2)
thf(fact_4_eval_Osimps_I4_J,axiom,
! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1325918602e_eval @ I2 @ Q ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
= ( paraco1325918602e_eval @ I2 @ P2 ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1325918602e_eval @ I2 @ Q ) )
=> ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
= ( paraco1325918602e_eval @ I2 @ Q ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
= ( paraco1325918602e_eval @ I2 @ P2 ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ Q )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% eval.simps(4)
thf(fact_5_eval_Osimps_I5_J,axiom,
! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1325918602e_eval @ I2 @ Q ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1325918602e_eval @ I2 @ Q ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ).
% eval.simps(5)
thf(fact_6_eval__equality__simplify,axiom,
! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
= ( paraco1344940915le_Det
@ ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1325918602e_eval @ I2 @ Q ) ) ) ) ).
% eval_equality_simplify
thf(fact_7_eval__negation,axiom,
! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
= ( paraco1344940915le_Det @ $false ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
= ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ) ) ) ).
% eval_negation
thf(fact_8_tv_Osimps_I5_J,axiom,
! [F1: $o > paraco1605129243lle_tv,F2: nat > paraco1605129243lle_tv,X1: $o] :
( ( paraco2051596139lle_tv @ F1 @ F2 @ ( paraco1344940915le_Det @ X1 ) )
= ( F1 @ X1 ) ) ).
% tv.simps(5)
thf(fact_9_eval_Osimps_I1_J,axiom,
! [I2: list_char > paraco1605129243lle_tv,S: list_char] :
( ( paraco1325918602e_eval @ I2 @ ( paraco1480028776le_Pro @ S ) )
= ( I2 @ S ) ) ).
% eval.simps(1)
thf(fact_10_tv_Odistinct_I1_J,axiom,
! [X1: $o,X2: nat] :
( ( paraco1344940915le_Det @ X1 )
!= ( paraco793048302_Indet @ X2 ) ) ).
% tv.distinct(1)
thf(fact_11_tv_Oinduct,axiom,
! [P3: paraco1605129243lle_tv > $o,Tv: paraco1605129243lle_tv] :
( ! [X: $o] : ( P3 @ ( paraco1344940915le_Det @ X ) )
=> ( ! [X: nat] : ( P3 @ ( paraco793048302_Indet @ X ) )
=> ( P3 @ Tv ) ) ) ).
% tv.induct
thf(fact_12_tv_Oexhaust,axiom,
! [Y: paraco1605129243lle_tv] :
( ! [X12: $o] :
( Y
!= ( paraco1344940915le_Det @ X12 ) )
=> ~ ! [X22: nat] :
( Y
!= ( paraco793048302_Indet @ X22 ) ) ) ).
% tv.exhaust
thf(fact_13_fm_Oinject_I2_J,axiom,
! [X3: paraco1604210848lle_fm,Y3: paraco1604210848lle_fm] :
( ( ( paraco445776468le_Neg @ X3 )
= ( paraco445776468le_Neg @ Y3 ) )
= ( X3 = Y3 ) ) ).
% fm.inject(2)
thf(fact_14_tv_Oinject_I2_J,axiom,
! [X2: nat,Y2: nat] :
( ( ( paraco793048302_Indet @ X2 )
= ( paraco793048302_Indet @ Y2 ) )
= ( X2 = Y2 ) ) ).
% tv.inject(2)
thf(fact_15_fm_Oinject_I4_J,axiom,
! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
( ( ( paraco1389086619le_Eql @ X51 @ X52 )
= ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
= ( ( X51 = Y51 )
& ( X52 = Y52 ) ) ) ).
% fm.inject(4)
thf(fact_16_fm_Oinject_I1_J,axiom,
! [X1: list_char,Y1: list_char] :
( ( ( paraco1480028776le_Pro @ X1 )
= ( paraco1480028776le_Pro @ Y1 ) )
= ( X1 = Y1 ) ) ).
% fm.inject(1)
thf(fact_17_fm_Oinject_I3_J,axiom,
! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
( ( ( paraco69239110le_Con @ X41 @ X42 )
= ( paraco69239110le_Con @ Y41 @ Y42 ) )
= ( ( X41 = Y41 )
& ( X42 = Y42 ) ) ) ).
% fm.inject(3)
thf(fact_18_tv_Osimps_I6_J,axiom,
! [F1: $o > paraco1605129243lle_tv,F2: nat > paraco1605129243lle_tv,X2: nat] :
( ( paraco2051596139lle_tv @ F1 @ F2 @ ( paraco793048302_Indet @ X2 ) )
= ( F2 @ X2 ) ) ).
% tv.simps(6)
thf(fact_19_fm_Odistinct_I25_J,axiom,
! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ X41 @ X42 )
!= ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% fm.distinct(25)
thf(fact_20_fm_Odistinct_I21_J,axiom,
! [X3: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ X3 )
!= ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% fm.distinct(21)
thf(fact_21_fm_Odistinct_I19_J,axiom,
! [X3: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ X3 )
!= ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% fm.distinct(19)
thf(fact_22_fm_Odistinct_I15_J,axiom,
! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% fm.distinct(15)
thf(fact_23_fm_Odistinct_I13_J,axiom,
! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% fm.distinct(13)
thf(fact_24_fm_Odistinct_I11_J,axiom,
! [X3: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco445776468le_Neg @ X3 ) ) ).
% fm.distinct(11)
thf(fact_25_fm_Odistinct_I7_J,axiom,
! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ X1 )
!= ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% fm.distinct(7)
thf(fact_26_fm_Odistinct_I5_J,axiom,
! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ X1 )
!= ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% fm.distinct(5)
thf(fact_27_fm_Odistinct_I3_J,axiom,
! [X1: list_char,X3: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ X1 )
!= ( paraco445776468le_Neg @ X3 ) ) ).
% fm.distinct(3)
thf(fact_28_fm_Odistinct_I1_J,axiom,
! [X1: list_char] :
( ( paraco1480028776le_Pro @ X1 )
!= paraco367965286_Truth ) ).
% fm.distinct(1)
thf(fact_29_double__negation,axiom,
( paraco1325918602e_eval
= ( ^ [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P ) ) ) ) ) ).
% double_negation
thf(fact_30_string__tv_Oinduct,axiom,
! [P3: paraco1605129243lle_tv > $o,A0: paraco1605129243lle_tv] :
( ( P3 @ ( paraco1344940915le_Det @ $true ) )
=> ( ( P3 @ ( paraco1344940915le_Det @ $false ) )
=> ( ! [N: nat] : ( P3 @ ( paraco793048302_Indet @ N ) )
=> ( P3 @ A0 ) ) ) ) ).
% string_tv.induct
thf(fact_31_string__tv_Ocases,axiom,
! [X4: paraco1605129243lle_tv] :
( ( X4
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( X4
!= ( paraco1344940915le_Det @ $false ) )
=> ~ ! [N: nat] :
( X4
!= ( paraco793048302_Indet @ N ) ) ) ) ).
% string_tv.cases
thf(fact_32_fm_Oinduct,axiom,
! [P3: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
( ! [X: list_char] : ( P3 @ ( paraco1480028776le_Pro @ X ) )
=> ( ( P3 @ paraco367965286_Truth )
=> ( ! [X: paraco1604210848lle_fm] :
( ( P3 @ X )
=> ( P3 @ ( paraco445776468le_Neg @ X ) ) )
=> ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
( ( P3 @ X1a )
=> ( ( P3 @ X22 )
=> ( P3 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
=> ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
( ( P3 @ X1a )
=> ( ( P3 @ X22 )
=> ( P3 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
=> ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
( ( P3 @ X1a )
=> ( ( P3 @ X22 )
=> ( P3 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
=> ( P3 @ Fm ) ) ) ) ) ) ) ).
% fm.induct
thf(fact_33_fm_Oexhaust,axiom,
! [Y: paraco1604210848lle_fm] :
( ! [X12: list_char] :
( Y
!= ( paraco1480028776le_Pro @ X12 ) )
=> ( ( Y != paraco367965286_Truth )
=> ( ! [X32: paraco1604210848lle_fm] :
( Y
!= ( paraco445776468le_Neg @ X32 ) )
=> ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
( Y
!= ( paraco69239110le_Con @ X412 @ X422 ) )
=> ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
( Y
!= ( paraco1389086619le_Eql @ X512 @ X522 ) )
=> ~ ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
( Y
!= ( paraco1745535428le_Eql @ X61 @ X62 ) ) ) ) ) ) ) ).
% fm.exhaust
thf(fact_34_eval_Osimps_I3_J,axiom,
! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
= ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ).
% eval.simps(3)
thf(fact_35_eval__equality,axiom,
! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1325918602e_eval @ I2 @ Q ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1325918602e_eval @ I2 @ Q ) )
=> ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
= ( paraco1325918602e_eval @ I2 @ Q ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
= ( paraco1325918602e_eval @ I2 @ P2 ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ Q )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
= ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ Q ) ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
= ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ Q )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% eval_equality
thf(fact_36_eval_Ocases,axiom,
! [X4: produc696645085lle_fm] :
( ! [I3: list_char > paraco1605129243lle_tv,S2: list_char] :
( X4
!= ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S2 ) ) )
=> ( ! [I3: list_char > paraco1605129243lle_tv] :
( X4
!= ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
=> ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
( X4
!= ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
=> ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
( X4
!= ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q2 ) ) )
=> ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
( X4
!= ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q2 ) ) )
=> ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q2: paraco1604210848lle_fm] :
( X4
!= ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q2 ) ) ) ) ) ) ) ) ).
% eval.cases
thf(fact_37_fm_Odistinct_I17_J,axiom,
! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% fm.distinct(17)
thf(fact_38_mem__Collect__eq,axiom,
! [A: produc1250255278lle_fm,P3: produc1250255278lle_fm > $o] :
( ( member1592865093lle_fm @ A @ ( collec1363950211lle_fm @ P3 ) )
= ( P3 @ A ) ) ).
% mem_Collect_eq
thf(fact_39_mem__Collect__eq,axiom,
! [A: produc696645085lle_fm,P3: produc696645085lle_fm > $o] :
( ( member1474794996lle_fm @ A @ ( collec835549234lle_fm @ P3 ) )
= ( P3 @ A ) ) ).
% mem_Collect_eq
thf(fact_40_mem__Collect__eq,axiom,
! [A: produc1852595672lle_tv,P3: produc1852595672lle_tv > $o] :
( ( member146333935lle_tv @ A @ ( collec1102043437lle_tv @ P3 ) )
= ( P3 @ A ) ) ).
% mem_Collect_eq
thf(fact_41_mem__Collect__eq,axiom,
! [A: list_char > paraco1605129243lle_tv,P3: ( list_char > paraco1605129243lle_tv ) > $o] :
( ( member894927066lle_tv @ A @ ( collec1351702300lle_tv @ P3 ) )
= ( P3 @ A ) ) ).
% mem_Collect_eq
thf(fact_42_mem__Collect__eq,axiom,
! [A: produc484385668lle_tv,P3: produc484385668lle_tv > $o] :
( ( member1074212123lle_tv @ A @ ( collec1900284505lle_tv @ P3 ) )
= ( P3 @ A ) ) ).
% mem_Collect_eq
thf(fact_43_mem__Collect__eq,axiom,
! [A: produc1647334210lle_tv,P3: produc1647334210lle_tv > $o] :
( ( member1531318361lle_tv @ A @ ( collec15260823lle_tv @ P3 ) )
= ( P3 @ A ) ) ).
% mem_Collect_eq
thf(fact_44_mem__Collect__eq,axiom,
! [A: paraco1605129243lle_tv,P3: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ P3 ) )
= ( P3 @ A ) ) ).
% mem_Collect_eq
thf(fact_45_Collect__mem__eq,axiom,
! [A2: set_Pr1475944804lle_fm] :
( ( collec1363950211lle_fm
@ ^ [X5: produc1250255278lle_fm] : ( member1592865093lle_fm @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_46_Collect__mem__eq,axiom,
! [A2: set_Pr2120184979lle_fm] :
( ( collec835549234lle_fm
@ ^ [X5: produc696645085lle_fm] : ( member1474794996lle_fm @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_47_Collect__mem__eq,axiom,
! [A2: set_Pr2061825550lle_tv] :
( ( collec1102043437lle_tv
@ ^ [X5: produc1852595672lle_tv] : ( member146333935lle_tv @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_48_Collect__mem__eq,axiom,
! [A2: set_li72793489lle_tv] :
( ( collec1351702300lle_tv
@ ^ [X5: list_char > paraco1605129243lle_tv] : ( member894927066lle_tv @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_49_Collect__mem__eq,axiom,
! [A2: set_Pr2012908090lle_tv] :
( ( collec1900284505lle_tv
@ ^ [X5: produc484385668lle_tv] : ( member1074212123lle_tv @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_50_Collect__mem__eq,axiom,
! [A2: set_Pr2014382200lle_tv] :
( ( collec15260823lle_tv
@ ^ [X5: produc1647334210lle_tv] : ( member1531318361lle_tv @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_51_Collect__mem__eq,axiom,
! [A2: set_Pa1764573435lle_tv] :
( ( collec1111687558lle_tv
@ ^ [X5: paraco1605129243lle_tv] : ( member266900804lle_tv @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_52_Collect__cong,axiom,
! [P3: produc484385668lle_tv > $o,Q3: produc484385668lle_tv > $o] :
( ! [X: produc484385668lle_tv] :
( ( P3 @ X )
= ( Q3 @ X ) )
=> ( ( collec1900284505lle_tv @ P3 )
= ( collec1900284505lle_tv @ Q3 ) ) ) ).
% Collect_cong
thf(fact_53_Collect__cong,axiom,
! [P3: produc1647334210lle_tv > $o,Q3: produc1647334210lle_tv > $o] :
( ! [X: produc1647334210lle_tv] :
( ( P3 @ X )
= ( Q3 @ X ) )
=> ( ( collec15260823lle_tv @ P3 )
= ( collec15260823lle_tv @ Q3 ) ) ) ).
% Collect_cong
thf(fact_54_Collect__cong,axiom,
! [P3: paraco1605129243lle_tv > $o,Q3: paraco1605129243lle_tv > $o] :
( ! [X: paraco1605129243lle_tv] :
( ( P3 @ X )
= ( Q3 @ X ) )
=> ( ( collec1111687558lle_tv @ P3 )
= ( collec1111687558lle_tv @ Q3 ) ) ) ).
% Collect_cong
thf(fact_55_fm_Oinject_I5_J,axiom,
! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
( ( ( paraco1745535428le_Eql @ X612 @ X622 )
= ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
= ( ( X612 = Y61 )
& ( X622 = Y62 ) ) ) ).
% fm.inject(5)
thf(fact_56_fm_Odistinct_I23_J,axiom,
! [X3: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ X3 )
!= ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% fm.distinct(23)
thf(fact_57_fm_Odistinct_I29_J,axiom,
! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
( ( paraco1389086619le_Eql @ X51 @ X52 )
!= ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% fm.distinct(29)
thf(fact_58_fm_Odistinct_I9_J,axiom,
! [X1: list_char,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ X1 )
!= ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% fm.distinct(9)
thf(fact_59_fm_Odistinct_I27_J,axiom,
! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ X41 @ X42 )
!= ( paraco1745535428le_Eql @ X612 @ X622 ) ) ).
% fm.distinct(27)
thf(fact_60_old_Oprod_Oinject,axiom,
! [A: paraco1604210848lle_fm,B: list_char > paraco1605129243lle_tv,A3: paraco1604210848lle_fm,B2: list_char > paraco1605129243lle_tv] :
( ( ( produc1943344577lle_tv @ A @ B )
= ( produc1943344577lle_tv @ A3 @ B2 ) )
= ( ( A = A3 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_61_old_Oprod_Oinject,axiom,
! [A: produc1647334210lle_tv,B: produc1647334210lle_tv,A3: produc1647334210lle_tv,B2: produc1647334210lle_tv] :
( ( ( produc1537086518lle_tv @ A @ B )
= ( produc1537086518lle_tv @ A3 @ B2 ) )
= ( ( A = A3 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_62_old_Oprod_Oinject,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,A3: paraco1604210848lle_fm,B2: paraco1604210848lle_fm] :
( ( ( produc1126104134lle_fm @ A @ B )
= ( produc1126104134lle_fm @ A3 @ B2 ) )
= ( ( A = A3 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_63_old_Oprod_Oinject,axiom,
! [A: produc696645085lle_fm,B: produc696645085lle_fm,A3: produc696645085lle_fm,B2: produc696645085lle_fm] :
( ( ( produc407632608lle_fm @ A @ B )
= ( produc407632608lle_fm @ A3 @ B2 ) )
= ( ( A = A3 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_64_old_Oprod_Oinject,axiom,
! [A: list_char > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,A3: list_char > paraco1605129243lle_tv,B2: list_char > paraco1605129243lle_tv] :
( ( ( produc1297923922lle_tv @ A @ B )
= ( produc1297923922lle_tv @ A3 @ B2 ) )
= ( ( A = A3 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_65_old_Oprod_Oinject,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ A @ B )
= ( produc1710735575lle_fm @ A3 @ B2 ) )
= ( ( A = A3 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_66_old_Oprod_Oinject,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A3: paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
( ( ( produc2058540732lle_tv @ A @ B )
= ( produc2058540732lle_tv @ A3 @ B2 ) )
= ( ( A = A3 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_67_prod_Oinject,axiom,
! [X1: paraco1604210848lle_fm,X2: list_char > paraco1605129243lle_tv,Y1: paraco1604210848lle_fm,Y2: list_char > paraco1605129243lle_tv] :
( ( ( produc1943344577lle_tv @ X1 @ X2 )
= ( produc1943344577lle_tv @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_68_prod_Oinject,axiom,
! [X1: produc1647334210lle_tv,X2: produc1647334210lle_tv,Y1: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
( ( ( produc1537086518lle_tv @ X1 @ X2 )
= ( produc1537086518lle_tv @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_69_prod_Oinject,axiom,
! [X1: paraco1604210848lle_fm,X2: paraco1604210848lle_fm,Y1: paraco1604210848lle_fm,Y2: paraco1604210848lle_fm] :
( ( ( produc1126104134lle_fm @ X1 @ X2 )
= ( produc1126104134lle_fm @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_70_prod_Oinject,axiom,
! [X1: produc696645085lle_fm,X2: produc696645085lle_fm,Y1: produc696645085lle_fm,Y2: produc696645085lle_fm] :
( ( ( produc407632608lle_fm @ X1 @ X2 )
= ( produc407632608lle_fm @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_71_prod_Oinject,axiom,
! [X1: list_char > paraco1605129243lle_tv,X2: list_char > paraco1605129243lle_tv,Y1: list_char > paraco1605129243lle_tv,Y2: list_char > paraco1605129243lle_tv] :
( ( ( produc1297923922lle_tv @ X1 @ X2 )
= ( produc1297923922lle_tv @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_72_prod_Oinject,axiom,
! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm,Y1: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ X1 @ X2 )
= ( produc1710735575lle_fm @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_73_prod_Oinject,axiom,
! [X1: paraco1605129243lle_tv,X2: paraco1605129243lle_tv,Y1: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
( ( ( produc2058540732lle_tv @ X1 @ X2 )
= ( produc2058540732lle_tv @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_74_bool_Osplit__sel__asm,axiom,
! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
( ( P3 @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
= ( ~ ( ( Bool
& ~ ( P3 @ F1 ) )
| ( ~ Bool
& ~ ( P3 @ F2 ) ) ) ) ) ).
% bool.split_sel_asm
thf(fact_75_bool_Ocase__distrib,axiom,
! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
( ( H @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
= ( produc234482697lle_tv @ ( H @ F1 ) @ ( H @ F2 ) @ Bool ) ) ).
% bool.case_distrib
thf(fact_76_bool_Ocase__eq__if,axiom,
( produc234482697lle_tv
= ( ^ [F12: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool2: $o] : ( if_Par1134130401lle_tv @ Bool2 @ F12 @ F22 ) ) ) ).
% bool.case_eq_if
thf(fact_77_bool_Osplit__sel,axiom,
! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
( ( P3 @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
= ( ( Bool
=> ( P3 @ F1 ) )
& ( ~ Bool
=> ( P3 @ F2 ) ) ) ) ).
% bool.split_sel
thf(fact_78_old_Obool_Osimps_I3_J,axiom,
! [F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv] :
( ( produc234482697lle_tv @ F1 @ F2 @ $true )
= F1 ) ).
% old.bool.simps(3)
thf(fact_79_old_Obool_Osimps_I4_J,axiom,
! [F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv] :
( ( produc234482697lle_tv @ F1 @ F2 @ $false )
= F2 ) ).
% old.bool.simps(4)
thf(fact_80_surj__pair,axiom,
! [P2: produc1443694919lle_tv] :
? [X: paraco1604210848lle_fm,Y4: list_char > paraco1605129243lle_tv] :
( P2
= ( produc1943344577lle_tv @ X @ Y4 ) ) ).
% surj_pair
thf(fact_81_surj__pair,axiom,
! [P2: produc484385668lle_tv] :
? [X: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
( P2
= ( produc1537086518lle_tv @ X @ Y4 ) ) ).
% surj_pair
thf(fact_82_surj__pair,axiom,
! [P2: produc450659916lle_fm] :
? [X: paraco1604210848lle_fm,Y4: paraco1604210848lle_fm] :
( P2
= ( produc1126104134lle_fm @ X @ Y4 ) ) ).
% surj_pair
thf(fact_83_surj__pair,axiom,
! [P2: produc1250255278lle_fm] :
? [X: produc696645085lle_fm,Y4: produc696645085lle_fm] :
( P2
= ( produc407632608lle_fm @ X @ Y4 ) ) ).
% surj_pair
thf(fact_84_surj__pair,axiom,
! [P2: produc1852595672lle_tv] :
? [X: list_char > paraco1605129243lle_tv,Y4: list_char > paraco1605129243lle_tv] :
( P2
= ( produc1297923922lle_tv @ X @ Y4 ) ) ).
% surj_pair
thf(fact_85_surj__pair,axiom,
! [P2: produc696645085lle_fm] :
? [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( P2
= ( produc1710735575lle_fm @ X @ Y4 ) ) ).
% surj_pair
thf(fact_86_surj__pair,axiom,
! [P2: produc1647334210lle_tv] :
? [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( P2
= ( produc2058540732lle_tv @ X @ Y4 ) ) ).
% surj_pair
thf(fact_87_prod__cases,axiom,
! [P3: produc1443694919lle_tv > $o,P2: produc1443694919lle_tv] :
( ! [A4: paraco1604210848lle_fm,B3: list_char > paraco1605129243lle_tv] : ( P3 @ ( produc1943344577lle_tv @ A4 @ B3 ) )
=> ( P3 @ P2 ) ) ).
% prod_cases
thf(fact_88_prod__cases,axiom,
! [P3: produc484385668lle_tv > $o,P2: produc484385668lle_tv] :
( ! [A4: produc1647334210lle_tv,B3: produc1647334210lle_tv] : ( P3 @ ( produc1537086518lle_tv @ A4 @ B3 ) )
=> ( P3 @ P2 ) ) ).
% prod_cases
thf(fact_89_prod__cases,axiom,
! [P3: produc450659916lle_fm > $o,P2: produc450659916lle_fm] :
( ! [A4: paraco1604210848lle_fm,B3: paraco1604210848lle_fm] : ( P3 @ ( produc1126104134lle_fm @ A4 @ B3 ) )
=> ( P3 @ P2 ) ) ).
% prod_cases
thf(fact_90_prod__cases,axiom,
! [P3: produc1250255278lle_fm > $o,P2: produc1250255278lle_fm] :
( ! [A4: produc696645085lle_fm,B3: produc696645085lle_fm] : ( P3 @ ( produc407632608lle_fm @ A4 @ B3 ) )
=> ( P3 @ P2 ) ) ).
% prod_cases
thf(fact_91_prod__cases,axiom,
! [P3: produc1852595672lle_tv > $o,P2: produc1852595672lle_tv] :
( ! [A4: list_char > paraco1605129243lle_tv,B3: list_char > paraco1605129243lle_tv] : ( P3 @ ( produc1297923922lle_tv @ A4 @ B3 ) )
=> ( P3 @ P2 ) ) ).
% prod_cases
thf(fact_92_prod__cases,axiom,
! [P3: produc696645085lle_fm > $o,P2: produc696645085lle_fm] :
( ! [A4: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A4 @ B3 ) )
=> ( P3 @ P2 ) ) ).
% prod_cases
thf(fact_93_prod__cases,axiom,
! [P3: produc1647334210lle_tv > $o,P2: produc1647334210lle_tv] :
( ! [A4: paraco1605129243lle_tv,B3: paraco1605129243lle_tv] : ( P3 @ ( produc2058540732lle_tv @ A4 @ B3 ) )
=> ( P3 @ P2 ) ) ).
% prod_cases
thf(fact_94_Pair__inject,axiom,
! [A: paraco1604210848lle_fm,B: list_char > paraco1605129243lle_tv,A3: paraco1604210848lle_fm,B2: list_char > paraco1605129243lle_tv] :
( ( ( produc1943344577lle_tv @ A @ B )
= ( produc1943344577lle_tv @ A3 @ B2 ) )
=> ~ ( ( A = A3 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_95_Pair__inject,axiom,
! [A: produc1647334210lle_tv,B: produc1647334210lle_tv,A3: produc1647334210lle_tv,B2: produc1647334210lle_tv] :
( ( ( produc1537086518lle_tv @ A @ B )
= ( produc1537086518lle_tv @ A3 @ B2 ) )
=> ~ ( ( A = A3 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_96_Pair__inject,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,A3: paraco1604210848lle_fm,B2: paraco1604210848lle_fm] :
( ( ( produc1126104134lle_fm @ A @ B )
= ( produc1126104134lle_fm @ A3 @ B2 ) )
=> ~ ( ( A = A3 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_97_Pair__inject,axiom,
! [A: produc696645085lle_fm,B: produc696645085lle_fm,A3: produc696645085lle_fm,B2: produc696645085lle_fm] :
( ( ( produc407632608lle_fm @ A @ B )
= ( produc407632608lle_fm @ A3 @ B2 ) )
=> ~ ( ( A = A3 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_98_Pair__inject,axiom,
! [A: list_char > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,A3: list_char > paraco1605129243lle_tv,B2: list_char > paraco1605129243lle_tv] :
( ( ( produc1297923922lle_tv @ A @ B )
= ( produc1297923922lle_tv @ A3 @ B2 ) )
=> ~ ( ( A = A3 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_99_Pair__inject,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ A @ B )
= ( produc1710735575lle_fm @ A3 @ B2 ) )
=> ~ ( ( A = A3 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_100_Pair__inject,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A3: paraco1605129243lle_tv,B2: paraco1605129243lle_tv] :
( ( ( produc2058540732lle_tv @ A @ B )
= ( produc2058540732lle_tv @ A3 @ B2 ) )
=> ~ ( ( A = A3 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_101_prod__cases3,axiom,
! [Y: produc484385668lle_tv] :
~ ! [A4: produc1647334210lle_tv,B3: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( Y
!= ( produc1537086518lle_tv @ A4 @ ( produc2058540732lle_tv @ B3 @ C ) ) ) ).
% prod_cases3
thf(fact_102_prod__cases3,axiom,
! [Y: produc1250255278lle_fm] :
~ ! [A4: produc696645085lle_fm,B3: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( Y
!= ( produc407632608lle_fm @ A4 @ ( produc1710735575lle_fm @ B3 @ C ) ) ) ).
% prod_cases3
thf(fact_103_prod__induct3,axiom,
! [P3: produc484385668lle_tv > $o,X4: produc484385668lle_tv] :
( ! [A4: produc1647334210lle_tv,B3: paraco1605129243lle_tv,C: paraco1605129243lle_tv] : ( P3 @ ( produc1537086518lle_tv @ A4 @ ( produc2058540732lle_tv @ B3 @ C ) ) )
=> ( P3 @ X4 ) ) ).
% prod_induct3
thf(fact_104_prod__induct3,axiom,
! [P3: produc1250255278lle_fm > $o,X4: produc1250255278lle_fm] :
( ! [A4: produc696645085lle_fm,B3: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] : ( P3 @ ( produc407632608lle_fm @ A4 @ ( produc1710735575lle_fm @ B3 @ C ) ) )
=> ( P3 @ X4 ) ) ).
% prod_induct3
thf(fact_105_old_Oprod_Oexhaust,axiom,
! [Y: produc1443694919lle_tv] :
~ ! [A4: paraco1604210848lle_fm,B3: list_char > paraco1605129243lle_tv] :
( Y
!= ( produc1943344577lle_tv @ A4 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_106_old_Oprod_Oexhaust,axiom,
! [Y: produc484385668lle_tv] :
~ ! [A4: produc1647334210lle_tv,B3: produc1647334210lle_tv] :
( Y
!= ( produc1537086518lle_tv @ A4 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_107_old_Oprod_Oexhaust,axiom,
! [Y: produc450659916lle_fm] :
~ ! [A4: paraco1604210848lle_fm,B3: paraco1604210848lle_fm] :
( Y
!= ( produc1126104134lle_fm @ A4 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_108_old_Oprod_Oexhaust,axiom,
! [Y: produc1250255278lle_fm] :
~ ! [A4: produc696645085lle_fm,B3: produc696645085lle_fm] :
( Y
!= ( produc407632608lle_fm @ A4 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_109_old_Oprod_Oexhaust,axiom,
! [Y: produc1852595672lle_tv] :
~ ! [A4: list_char > paraco1605129243lle_tv,B3: list_char > paraco1605129243lle_tv] :
( Y
!= ( produc1297923922lle_tv @ A4 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_110_old_Oprod_Oexhaust,axiom,
! [Y: produc696645085lle_fm] :
~ ! [A4: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
( Y
!= ( produc1710735575lle_fm @ A4 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_111_old_Oprod_Oexhaust,axiom,
! [Y: produc1647334210lle_tv] :
~ ! [A4: paraco1605129243lle_tv,B3: paraco1605129243lle_tv] :
( Y
!= ( produc2058540732lle_tv @ A4 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_112_old_Oprod_Oinducts,axiom,
! [P3: produc1443694919lle_tv > $o,Prod: produc1443694919lle_tv] :
( ! [A4: paraco1604210848lle_fm,B3: list_char > paraco1605129243lle_tv] : ( P3 @ ( produc1943344577lle_tv @ A4 @ B3 ) )
=> ( P3 @ Prod ) ) ).
% old.prod.inducts
thf(fact_113_old_Oprod_Oinducts,axiom,
! [P3: produc484385668lle_tv > $o,Prod: produc484385668lle_tv] :
( ! [A4: produc1647334210lle_tv,B3: produc1647334210lle_tv] : ( P3 @ ( produc1537086518lle_tv @ A4 @ B3 ) )
=> ( P3 @ Prod ) ) ).
% old.prod.inducts
thf(fact_114_old_Oprod_Oinducts,axiom,
! [P3: produc450659916lle_fm > $o,Prod: produc450659916lle_fm] :
( ! [A4: paraco1604210848lle_fm,B3: paraco1604210848lle_fm] : ( P3 @ ( produc1126104134lle_fm @ A4 @ B3 ) )
=> ( P3 @ Prod ) ) ).
% old.prod.inducts
thf(fact_115_old_Oprod_Oinducts,axiom,
! [P3: produc1250255278lle_fm > $o,Prod: produc1250255278lle_fm] :
( ! [A4: produc696645085lle_fm,B3: produc696645085lle_fm] : ( P3 @ ( produc407632608lle_fm @ A4 @ B3 ) )
=> ( P3 @ Prod ) ) ).
% old.prod.inducts
thf(fact_116_old_Oprod_Oinducts,axiom,
! [P3: produc1852595672lle_tv > $o,Prod: produc1852595672lle_tv] :
( ! [A4: list_char > paraco1605129243lle_tv,B3: list_char > paraco1605129243lle_tv] : ( P3 @ ( produc1297923922lle_tv @ A4 @ B3 ) )
=> ( P3 @ Prod ) ) ).
% old.prod.inducts
thf(fact_117_old_Oprod_Oinducts,axiom,
! [P3: produc696645085lle_fm > $o,Prod: produc696645085lle_fm] :
( ! [A4: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A4 @ B3 ) )
=> ( P3 @ Prod ) ) ).
% old.prod.inducts
thf(fact_118_old_Oprod_Oinducts,axiom,
! [P3: produc1647334210lle_tv > $o,Prod: produc1647334210lle_tv] :
( ! [A4: paraco1605129243lle_tv,B3: paraco1605129243lle_tv] : ( P3 @ ( produc2058540732lle_tv @ A4 @ B3 ) )
=> ( P3 @ Prod ) ) ).
% old.prod.inducts
thf(fact_119_internal__case__prod__conv,axiom,
! [C2: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc192124683lle_tv @ C2 @ ( produc2058540732lle_tv @ A @ B ) )
= ( C2 @ A @ B ) ) ).
% internal_case_prod_conv
thf(fact_120_ssubst__Pair__rhs,axiom,
! [R: paraco1604210848lle_fm,S: list_char > paraco1605129243lle_tv,R2: set_Pr1723822845lle_tv,S3: list_char > paraco1605129243lle_tv] :
( ( member74361182lle_tv @ ( produc1943344577lle_tv @ R @ S ) @ R2 )
=> ( ( S3 = S )
=> ( member74361182lle_tv @ ( produc1943344577lle_tv @ R @ S3 ) @ R2 ) ) ) ).
% ssubst_Pair_rhs
thf(fact_121_ssubst__Pair__rhs,axiom,
! [R: produc1647334210lle_tv,S: produc1647334210lle_tv,R2: set_Pr2012908090lle_tv,S3: produc1647334210lle_tv] :
( ( member1074212123lle_tv @ ( produc1537086518lle_tv @ R @ S ) @ R2 )
=> ( ( S3 = S )
=> ( member1074212123lle_tv @ ( produc1537086518lle_tv @ R @ S3 ) @ R2 ) ) ) ).
% ssubst_Pair_rhs
thf(fact_122_ssubst__Pair__rhs,axiom,
! [R: paraco1604210848lle_fm,S: paraco1604210848lle_fm,R2: set_Pr1019238018lle_fm,S3: paraco1604210848lle_fm] :
( ( member334644067lle_fm @ ( produc1126104134lle_fm @ R @ S ) @ R2 )
=> ( ( S3 = S )
=> ( member334644067lle_fm @ ( produc1126104134lle_fm @ R @ S3 ) @ R2 ) ) ) ).
% ssubst_Pair_rhs
thf(fact_123_ssubst__Pair__rhs,axiom,
! [R: produc696645085lle_fm,S: produc696645085lle_fm,R2: set_Pr1475944804lle_fm,S3: produc696645085lle_fm] :
( ( member1592865093lle_fm @ ( produc407632608lle_fm @ R @ S ) @ R2 )
=> ( ( S3 = S )
=> ( member1592865093lle_fm @ ( produc407632608lle_fm @ R @ S3 ) @ R2 ) ) ) ).
% ssubst_Pair_rhs
thf(fact_124_ssubst__Pair__rhs,axiom,
! [R: list_char > paraco1605129243lle_tv,S: list_char > paraco1605129243lle_tv,R2: set_Pr2061825550lle_tv,S3: list_char > paraco1605129243lle_tv] :
( ( member146333935lle_tv @ ( produc1297923922lle_tv @ R @ S ) @ R2 )
=> ( ( S3 = S )
=> ( member146333935lle_tv @ ( produc1297923922lle_tv @ R @ S3 ) @ R2 ) ) ) ).
% ssubst_Pair_rhs
thf(fact_125_ssubst__Pair__rhs,axiom,
! [R: list_char > paraco1605129243lle_tv,S: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,S3: paraco1604210848lle_fm] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S ) @ R2 )
=> ( ( S3 = S )
=> ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S3 ) @ R2 ) ) ) ).
% ssubst_Pair_rhs
thf(fact_126_ssubst__Pair__rhs,axiom,
! [R: paraco1605129243lle_tv,S: paraco1605129243lle_tv,R2: set_Pr2014382200lle_tv,S3: paraco1605129243lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ R @ S ) @ R2 )
=> ( ( S3 = S )
=> ( member1531318361lle_tv @ ( produc2058540732lle_tv @ R @ S3 ) @ R2 ) ) ) ).
% ssubst_Pair_rhs
thf(fact_127_curry__conv,axiom,
( produc621423502e_tv_o
= ( ^ [F: produc1647334210lle_tv > $o,A5: paraco1605129243lle_tv,B4: paraco1605129243lle_tv] : ( F @ ( produc2058540732lle_tv @ A5 @ B4 ) ) ) ) ).
% curry_conv
thf(fact_128_curry__conv,axiom,
( produc275353523e_fm_o
= ( ^ [F: produc696645085lle_fm > $o,A5: list_char > paraco1605129243lle_tv,B4: paraco1604210848lle_fm] : ( F @ ( produc1710735575lle_fm @ A5 @ B4 ) ) ) ) ).
% curry_conv
thf(fact_129_curry__conv,axiom,
( produc724036226lle_tv
= ( ^ [F: produc1647334210lle_tv > paraco1605129243lle_tv,A5: paraco1605129243lle_tv,B4: paraco1605129243lle_tv] : ( F @ ( produc2058540732lle_tv @ A5 @ B4 ) ) ) ) ).
% curry_conv
thf(fact_130_curryI,axiom,
! [F3: produc1443694919lle_tv > $o,A: paraco1604210848lle_fm,B: list_char > paraco1605129243lle_tv] :
( ( F3 @ ( produc1943344577lle_tv @ A @ B ) )
=> ( produc298562633e_tv_o @ F3 @ A @ B ) ) ).
% curryI
thf(fact_131_curryI,axiom,
! [F3: produc484385668lle_tv > $o,A: produc1647334210lle_tv,B: produc1647334210lle_tv] :
( ( F3 @ ( produc1537086518lle_tv @ A @ B ) )
=> ( produc1113543188e_tv_o @ F3 @ A @ B ) ) ).
% curryI
thf(fact_132_curryI,axiom,
! [F3: produc450659916lle_fm > $o,A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( F3 @ ( produc1126104134lle_fm @ A @ B ) )
=> ( produc1339594628e_fm_o @ F3 @ A @ B ) ) ).
% curryI
thf(fact_133_curryI,axiom,
! [F3: produc1250255278lle_fm > $o,A: produc696645085lle_fm,B: produc696645085lle_fm] :
( ( F3 @ ( produc407632608lle_fm @ A @ B ) )
=> ( produc408556266e_fm_o @ F3 @ A @ B ) ) ).
% curryI
thf(fact_134_curryI,axiom,
! [F3: produc1852595672lle_tv > $o,A: list_char > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv] :
( ( F3 @ ( produc1297923922lle_tv @ A @ B ) )
=> ( produc1667860344e_tv_o @ F3 @ A @ B ) ) ).
% curryI
thf(fact_135_curryI,axiom,
! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( F3 @ ( produc1710735575lle_fm @ A @ B ) )
=> ( produc275353523e_fm_o @ F3 @ A @ B ) ) ).
% curryI
thf(fact_136_curryI,axiom,
! [F3: produc1647334210lle_tv > $o,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( F3 @ ( produc2058540732lle_tv @ A @ B ) )
=> ( produc621423502e_tv_o @ F3 @ A @ B ) ) ).
% curryI
thf(fact_137_swap__simp,axiom,
! [X4: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
( ( produc1733045910lle_tv @ ( produc1537086518lle_tv @ X4 @ Y ) )
= ( produc1537086518lle_tv @ Y @ X4 ) ) ).
% swap_simp
thf(fact_138_swap__simp,axiom,
! [X4: paraco1604210848lle_fm,Y: paraco1604210848lle_fm] :
( ( produc1426802342lle_fm @ ( produc1126104134lle_fm @ X4 @ Y ) )
= ( produc1126104134lle_fm @ Y @ X4 ) ) ).
% swap_simp
thf(fact_139_swap__simp,axiom,
! [X4: produc696645085lle_fm,Y: produc696645085lle_fm] :
( ( produc116249920lle_fm @ ( produc407632608lle_fm @ X4 @ Y ) )
= ( produc407632608lle_fm @ Y @ X4 ) ) ).
% swap_simp
thf(fact_140_swap__simp,axiom,
! [X4: list_char > paraco1605129243lle_tv,Y: list_char > paraco1605129243lle_tv] :
( ( produc1176291762lle_tv @ ( produc1297923922lle_tv @ X4 @ Y ) )
= ( produc1297923922lle_tv @ Y @ X4 ) ) ).
% swap_simp
thf(fact_141_swap__simp,axiom,
! [X4: paraco1604210848lle_fm,Y: list_char > paraco1605129243lle_tv] :
( ( produc1232814113lle_tv @ ( produc1943344577lle_tv @ X4 @ Y ) )
= ( produc1710735575lle_fm @ Y @ X4 ) ) ).
% swap_simp
thf(fact_142_swap__simp,axiom,
! [X4: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
( ( produc1000205111lle_fm @ ( produc1710735575lle_fm @ X4 @ Y ) )
= ( produc1943344577lle_tv @ Y @ X4 ) ) ).
% swap_simp
thf(fact_143_swap__simp,axiom,
! [X4: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
( ( produc211755292lle_tv @ ( produc2058540732lle_tv @ X4 @ Y ) )
= ( produc2058540732lle_tv @ Y @ X4 ) ) ).
% swap_simp
thf(fact_144_eval_Osimps_I6_J,axiom,
! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
= ( paraco1325918602e_eval @ I2 @ Q ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ I2 @ P2 )
!= ( paraco1325918602e_eval @ I2 @ Q ) )
=> ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
= ( produc1882560353lle_tv
@ ^ [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] :
( paraco2051596139lle_tv
@ ( produc234482697lle_tv @ ( paraco1325918602e_eval @ I2 @ Q )
@ ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1325918602e_eval @ I2 @ P2 ) @ ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I2 @ Q ) ) )
@ ^ [Nat: nat] : ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I2 @ Q ) )
@ Y5 ) )
@ ^ [Nat: nat] :
( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1325918602e_eval @ I2 @ P2 ) @ ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I2 @ P2 ) ) )
@ ^ [Nata: nat] : ( paraco1344940915le_Det @ $false )
@ Y5 )
@ X5 )
@ ( produc2058540732lle_tv @ ( paraco1325918602e_eval @ I2 @ P2 ) @ ( paraco1325918602e_eval @ I2 @ Q ) ) ) ) ) ) ).
% eval.simps(6)
thf(fact_145_swap__swap,axiom,
! [P2: produc1647334210lle_tv] :
( ( produc211755292lle_tv @ ( produc211755292lle_tv @ P2 ) )
= P2 ) ).
% swap_swap
thf(fact_146_swap__swap,axiom,
! [P2: produc1443694919lle_tv] :
( ( produc1000205111lle_fm @ ( produc1232814113lle_tv @ P2 ) )
= P2 ) ).
% swap_swap
thf(fact_147_swap__swap,axiom,
! [P2: produc696645085lle_fm] :
( ( produc1232814113lle_tv @ ( produc1000205111lle_fm @ P2 ) )
= P2 ) ).
% swap_swap
thf(fact_148_case__prod__conv,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc25129173e_tv_o @ F3 @ ( produc2058540732lle_tv @ A @ B ) )
= ( F3 @ A @ B ) ) ).
% case_prod_conv
thf(fact_149_case__prod__conv,axiom,
! [F3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm,A: paraco1604210848lle_fm,B: list_char > paraco1605129243lle_tv] :
( ( produc811245928lle_fm @ F3 @ ( produc1943344577lle_tv @ A @ B ) )
= ( F3 @ A @ B ) ) ).
% case_prod_conv
thf(fact_150_case__prod__conv,axiom,
! [F3: produc1647334210lle_tv > produc1647334210lle_tv > $o,A: produc1647334210lle_tv,B: produc1647334210lle_tv] :
( ( produc648306805e_tv_o @ F3 @ ( produc1537086518lle_tv @ A @ B ) )
= ( F3 @ A @ B ) ) ).
% case_prod_conv
thf(fact_151_case__prod__conv,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( produc427355858lle_fm @ F3 @ ( produc1710735575lle_fm @ A @ B ) )
= ( F3 @ A @ B ) ) ).
% case_prod_conv
thf(fact_152_case__prod__conv,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( produc1221696404e_fm_o @ F3 @ ( produc1710735575lle_fm @ A @ B ) )
= ( F3 @ A @ B ) ) ).
% case_prod_conv
thf(fact_153_case__prod__conv,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc1882560353lle_tv @ F3 @ ( produc2058540732lle_tv @ A @ B ) )
= ( F3 @ A @ B ) ) ).
% case_prod_conv
thf(fact_154_case__prod__curry,axiom,
! [F3: produc1647334210lle_tv > $o] :
( ( produc852673135e_tv_o @ ( produc621423502e_tv_o @ F3 ) )
= F3 ) ).
% case_prod_curry
thf(fact_155_case__prod__curry,axiom,
! [F3: produc1647334210lle_tv > produc1647334210lle_tv > $o] :
( ( produc25129173e_tv_o @ ( produc2005494902e_tv_o @ F3 ) )
= F3 ) ).
% case_prod_curry
thf(fact_156_case__prod__curry,axiom,
! [F3: produc1443694919lle_tv > produc696645085lle_fm] :
( ( produc811245928lle_fm @ ( produc635060359lle_fm @ F3 ) )
= F3 ) ).
% case_prod_curry
thf(fact_157_case__prod__curry,axiom,
! [F3: produc484385668lle_tv > $o] :
( ( produc648306805e_tv_o @ ( produc1113543188e_tv_o @ F3 ) )
= F3 ) ).
% case_prod_curry
thf(fact_158_case__prod__curry,axiom,
! [F3: produc696645085lle_fm > produc696645085lle_fm] :
( ( produc427355858lle_fm @ ( produc251170289lle_fm @ F3 ) )
= F3 ) ).
% case_prod_curry
thf(fact_159_case__prod__curry,axiom,
! [F3: produc696645085lle_fm > $o] :
( ( produc1221696404e_fm_o @ ( produc275353523e_fm_o @ F3 ) )
= F3 ) ).
% case_prod_curry
thf(fact_160_case__prod__curry,axiom,
! [F3: produc1647334210lle_tv > paraco1605129243lle_tv] :
( ( produc1882560353lle_tv @ ( produc724036226lle_tv @ F3 ) )
= F3 ) ).
% case_prod_curry
thf(fact_161_curry__case__prod,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > $o] :
( ( produc621423502e_tv_o @ ( produc852673135e_tv_o @ F3 ) )
= F3 ) ).
% curry_case_prod
thf(fact_162_curry__case__prod,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o] :
( ( produc2005494902e_tv_o @ ( produc25129173e_tv_o @ F3 ) )
= F3 ) ).
% curry_case_prod
thf(fact_163_curry__case__prod,axiom,
! [F3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm] :
( ( produc635060359lle_fm @ ( produc811245928lle_fm @ F3 ) )
= F3 ) ).
% curry_case_prod
thf(fact_164_curry__case__prod,axiom,
! [F3: produc1647334210lle_tv > produc1647334210lle_tv > $o] :
( ( produc1113543188e_tv_o @ ( produc648306805e_tv_o @ F3 ) )
= F3 ) ).
% curry_case_prod
thf(fact_165_curry__case__prod,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm] :
( ( produc251170289lle_fm @ ( produc427355858lle_fm @ F3 ) )
= F3 ) ).
% curry_case_prod
thf(fact_166_curry__case__prod,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o] :
( ( produc275353523e_fm_o @ ( produc1221696404e_fm_o @ F3 ) )
= F3 ) ).
% curry_case_prod
thf(fact_167_curry__case__prod,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( produc724036226lle_tv @ ( produc1882560353lle_tv @ F3 ) )
= F3 ) ).
% curry_case_prod
thf(fact_168_case__swap,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,P2: produc696645085lle_fm] :
( ( produc1244905514e_tv_o
@ ^ [Y5: paraco1604210848lle_fm,X5: list_char > paraco1605129243lle_tv] : ( F3 @ X5 @ Y5 )
@ ( produc1000205111lle_fm @ P2 ) )
= ( produc1221696404e_fm_o @ F3 @ P2 ) ) ).
% case_swap
thf(fact_169_case__swap,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,P2: produc1647334210lle_tv] :
( ( produc25129173e_tv_o
@ ^ [Y5: paraco1605129243lle_tv,X5: paraco1605129243lle_tv] : ( F3 @ X5 @ Y5 )
@ ( produc211755292lle_tv @ P2 ) )
= ( produc25129173e_tv_o @ F3 @ P2 ) ) ).
% case_swap
thf(fact_170_case__swap,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,P2: produc696645085lle_fm] :
( ( produc811245928lle_fm
@ ^ [Y5: paraco1604210848lle_fm,X5: list_char > paraco1605129243lle_tv] : ( F3 @ X5 @ Y5 )
@ ( produc1000205111lle_fm @ P2 ) )
= ( produc427355858lle_fm @ F3 @ P2 ) ) ).
% case_swap
thf(fact_171_case__swap,axiom,
! [F3: produc1647334210lle_tv > produc1647334210lle_tv > $o,P2: produc484385668lle_tv] :
( ( produc648306805e_tv_o
@ ^ [Y5: produc1647334210lle_tv,X5: produc1647334210lle_tv] : ( F3 @ X5 @ Y5 )
@ ( produc1733045910lle_tv @ P2 ) )
= ( produc648306805e_tv_o @ F3 @ P2 ) ) ).
% case_swap
thf(fact_172_case__swap,axiom,
! [F3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm,P2: produc1443694919lle_tv] :
( ( produc427355858lle_fm
@ ^ [Y5: list_char > paraco1605129243lle_tv,X5: paraco1604210848lle_fm] : ( F3 @ X5 @ Y5 )
@ ( produc1232814113lle_tv @ P2 ) )
= ( produc811245928lle_fm @ F3 @ P2 ) ) ).
% case_swap
thf(fact_173_case__swap,axiom,
! [F3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o,P2: produc1443694919lle_tv] :
( ( produc1221696404e_fm_o
@ ^ [Y5: list_char > paraco1605129243lle_tv,X5: paraco1604210848lle_fm] : ( F3 @ X5 @ Y5 )
@ ( produc1232814113lle_tv @ P2 ) )
= ( produc1244905514e_tv_o @ F3 @ P2 ) ) ).
% case_swap
thf(fact_174_case__swap,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,P2: produc1647334210lle_tv] :
( ( produc1882560353lle_tv
@ ^ [Y5: paraco1605129243lle_tv,X5: paraco1605129243lle_tv] : ( F3 @ X5 @ Y5 )
@ ( produc211755292lle_tv @ P2 ) )
= ( produc1882560353lle_tv @ F3 @ P2 ) ) ).
% case_swap
thf(fact_175_cond__case__prod__eta,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,G: produc1647334210lle_tv > produc1647334210lle_tv > $o] :
( ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( F3 @ X @ Y4 )
= ( G @ ( produc2058540732lle_tv @ X @ Y4 ) ) )
=> ( ( produc25129173e_tv_o @ F3 )
= G ) ) ).
% cond_case_prod_eta
thf(fact_176_cond__case__prod__eta,axiom,
! [F3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm,G: produc1443694919lle_tv > produc696645085lle_fm] :
( ! [X: paraco1604210848lle_fm,Y4: list_char > paraco1605129243lle_tv] :
( ( F3 @ X @ Y4 )
= ( G @ ( produc1943344577lle_tv @ X @ Y4 ) ) )
=> ( ( produc811245928lle_fm @ F3 )
= G ) ) ).
% cond_case_prod_eta
thf(fact_177_cond__case__prod__eta,axiom,
! [F3: produc1647334210lle_tv > produc1647334210lle_tv > $o,G: produc484385668lle_tv > $o] :
( ! [X: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
( ( F3 @ X @ Y4 )
= ( G @ ( produc1537086518lle_tv @ X @ Y4 ) ) )
=> ( ( produc648306805e_tv_o @ F3 )
= G ) ) ).
% cond_case_prod_eta
thf(fact_178_cond__case__prod__eta,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,G: produc696645085lle_fm > produc696645085lle_fm] :
( ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( F3 @ X @ Y4 )
= ( G @ ( produc1710735575lle_fm @ X @ Y4 ) ) )
=> ( ( produc427355858lle_fm @ F3 )
= G ) ) ).
% cond_case_prod_eta
thf(fact_179_cond__case__prod__eta,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,G: produc696645085lle_fm > $o] :
( ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( F3 @ X @ Y4 )
= ( G @ ( produc1710735575lle_fm @ X @ Y4 ) ) )
=> ( ( produc1221696404e_fm_o @ F3 )
= G ) ) ).
% cond_case_prod_eta
thf(fact_180_cond__case__prod__eta,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,G: produc1647334210lle_tv > paraco1605129243lle_tv] :
( ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( F3 @ X @ Y4 )
= ( G @ ( produc2058540732lle_tv @ X @ Y4 ) ) )
=> ( ( produc1882560353lle_tv @ F3 )
= G ) ) ).
% cond_case_prod_eta
thf(fact_181_case__prod__eta,axiom,
! [F3: produc1647334210lle_tv > produc1647334210lle_tv > $o] :
( ( produc25129173e_tv_o
@ ^ [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] : ( F3 @ ( produc2058540732lle_tv @ X5 @ Y5 ) ) )
= F3 ) ).
% case_prod_eta
thf(fact_182_case__prod__eta,axiom,
! [F3: produc1443694919lle_tv > produc696645085lle_fm] :
( ( produc811245928lle_fm
@ ^ [X5: paraco1604210848lle_fm,Y5: list_char > paraco1605129243lle_tv] : ( F3 @ ( produc1943344577lle_tv @ X5 @ Y5 ) ) )
= F3 ) ).
% case_prod_eta
thf(fact_183_case__prod__eta,axiom,
! [F3: produc484385668lle_tv > $o] :
( ( produc648306805e_tv_o
@ ^ [X5: produc1647334210lle_tv,Y5: produc1647334210lle_tv] : ( F3 @ ( produc1537086518lle_tv @ X5 @ Y5 ) ) )
= F3 ) ).
% case_prod_eta
thf(fact_184_case__prod__eta,axiom,
! [F3: produc696645085lle_fm > produc696645085lle_fm] :
( ( produc427355858lle_fm
@ ^ [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] : ( F3 @ ( produc1710735575lle_fm @ X5 @ Y5 ) ) )
= F3 ) ).
% case_prod_eta
thf(fact_185_case__prod__eta,axiom,
! [F3: produc696645085lle_fm > $o] :
( ( produc1221696404e_fm_o
@ ^ [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] : ( F3 @ ( produc1710735575lle_fm @ X5 @ Y5 ) ) )
= F3 ) ).
% case_prod_eta
thf(fact_186_case__prod__eta,axiom,
! [F3: produc1647334210lle_tv > paraco1605129243lle_tv] :
( ( produc1882560353lle_tv
@ ^ [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] : ( F3 @ ( produc2058540732lle_tv @ X5 @ Y5 ) ) )
= F3 ) ).
% case_prod_eta
thf(fact_187_case__prodE2,axiom,
! [Q3: ( produc1647334210lle_tv > $o ) > $o,P3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,Z: produc1647334210lle_tv] :
( ( Q3 @ ( produc25129173e_tv_o @ P3 @ Z ) )
=> ~ ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( Z
= ( produc2058540732lle_tv @ X @ Y4 ) )
=> ~ ( Q3 @ ( P3 @ X @ Y4 ) ) ) ) ).
% case_prodE2
thf(fact_188_case__prodE2,axiom,
! [Q3: produc696645085lle_fm > $o,P3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm,Z: produc1443694919lle_tv] :
( ( Q3 @ ( produc811245928lle_fm @ P3 @ Z ) )
=> ~ ! [X: paraco1604210848lle_fm,Y4: list_char > paraco1605129243lle_tv] :
( ( Z
= ( produc1943344577lle_tv @ X @ Y4 ) )
=> ~ ( Q3 @ ( P3 @ X @ Y4 ) ) ) ) ).
% case_prodE2
thf(fact_189_case__prodE2,axiom,
! [Q3: $o > $o,P3: produc1647334210lle_tv > produc1647334210lle_tv > $o,Z: produc484385668lle_tv] :
( ( Q3 @ ( produc648306805e_tv_o @ P3 @ Z ) )
=> ~ ! [X: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
( ( Z
= ( produc1537086518lle_tv @ X @ Y4 ) )
=> ~ ( Q3 @ ( P3 @ X @ Y4 ) ) ) ) ).
% case_prodE2
thf(fact_190_case__prodE2,axiom,
! [Q3: produc696645085lle_fm > $o,P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,Z: produc696645085lle_fm] :
( ( Q3 @ ( produc427355858lle_fm @ P3 @ Z ) )
=> ~ ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( Z
= ( produc1710735575lle_fm @ X @ Y4 ) )
=> ~ ( Q3 @ ( P3 @ X @ Y4 ) ) ) ) ).
% case_prodE2
thf(fact_191_case__prodE2,axiom,
! [Q3: $o > $o,P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,Z: produc696645085lle_fm] :
( ( Q3 @ ( produc1221696404e_fm_o @ P3 @ Z ) )
=> ~ ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( Z
= ( produc1710735575lle_fm @ X @ Y4 ) )
=> ~ ( Q3 @ ( P3 @ X @ Y4 ) ) ) ) ).
% case_prodE2
thf(fact_192_case__prodE2,axiom,
! [Q3: paraco1605129243lle_tv > $o,P3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,Z: produc1647334210lle_tv] :
( ( Q3 @ ( produc1882560353lle_tv @ P3 @ Z ) )
=> ~ ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( Z
= ( produc2058540732lle_tv @ X @ Y4 ) )
=> ~ ( Q3 @ ( P3 @ X @ Y4 ) ) ) ) ).
% case_prodE2
thf(fact_193_curry__def,axiom,
( produc621423502e_tv_o
= ( ^ [C3: produc1647334210lle_tv > $o,X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] : ( C3 @ ( produc2058540732lle_tv @ X5 @ Y5 ) ) ) ) ).
% curry_def
thf(fact_194_curry__def,axiom,
( produc275353523e_fm_o
= ( ^ [C3: produc696645085lle_fm > $o,X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] : ( C3 @ ( produc1710735575lle_fm @ X5 @ Y5 ) ) ) ) ).
% curry_def
thf(fact_195_curry__def,axiom,
( produc724036226lle_tv
= ( ^ [C3: produc1647334210lle_tv > paraco1605129243lle_tv,X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] : ( C3 @ ( produc2058540732lle_tv @ X5 @ Y5 ) ) ) ) ).
% curry_def
thf(fact_196_curry__K,axiom,
! [C2: $o] :
( ( produc621423502e_tv_o
@ ^ [X5: produc1647334210lle_tv] : C2 )
= ( ^ [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] : C2 ) ) ).
% curry_K
thf(fact_197_curry__K,axiom,
! [C2: $o] :
( ( produc275353523e_fm_o
@ ^ [X5: produc696645085lle_fm] : C2 )
= ( ^ [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] : C2 ) ) ).
% curry_K
thf(fact_198_curry__K,axiom,
! [C2: paraco1605129243lle_tv] :
( ( produc724036226lle_tv
@ ^ [X5: produc1647334210lle_tv] : C2 )
= ( ^ [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] : C2 ) ) ).
% curry_K
thf(fact_199_prod_Ocase__distrib,axiom,
! [H: paraco1605129243lle_tv > produc1647334210lle_tv > $o,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,Prod: produc1647334210lle_tv] :
( ( H @ ( produc1882560353lle_tv @ F3 @ Prod ) )
= ( produc25129173e_tv_o
@ ^ [X13: paraco1605129243lle_tv,X23: paraco1605129243lle_tv] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_200_prod_Ocase__distrib,axiom,
! [H: ( produc1647334210lle_tv > $o ) > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,Prod: produc1647334210lle_tv] :
( ( H @ ( produc25129173e_tv_o @ F3 @ Prod ) )
= ( produc1882560353lle_tv
@ ^ [X13: paraco1605129243lle_tv,X23: paraco1605129243lle_tv] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_201_prod_Ocase__distrib,axiom,
! [H: ( produc1647334210lle_tv > $o ) > produc1647334210lle_tv > $o,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,Prod: produc1647334210lle_tv] :
( ( H @ ( produc25129173e_tv_o @ F3 @ Prod ) )
= ( produc25129173e_tv_o
@ ^ [X13: paraco1605129243lle_tv,X23: paraco1605129243lle_tv] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_202_prod_Ocase__distrib,axiom,
! [H: produc696645085lle_fm > produc696645085lle_fm,F3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm,Prod: produc1443694919lle_tv] :
( ( H @ ( produc811245928lle_fm @ F3 @ Prod ) )
= ( produc811245928lle_fm
@ ^ [X13: paraco1604210848lle_fm,X23: list_char > paraco1605129243lle_tv] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_203_prod_Ocase__distrib,axiom,
! [H: $o > $o,F3: produc1647334210lle_tv > produc1647334210lle_tv > $o,Prod: produc484385668lle_tv] :
( ( H @ ( produc648306805e_tv_o @ F3 @ Prod ) )
= ( produc648306805e_tv_o
@ ^ [X13: produc1647334210lle_tv,X23: produc1647334210lle_tv] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_204_prod_Ocase__distrib,axiom,
! [H: produc696645085lle_fm > produc696645085lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,Prod: produc696645085lle_fm] :
( ( H @ ( produc427355858lle_fm @ F3 @ Prod ) )
= ( produc427355858lle_fm
@ ^ [X13: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_205_prod_Ocase__distrib,axiom,
! [H: produc696645085lle_fm > $o,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,Prod: produc696645085lle_fm] :
( ( H @ ( produc427355858lle_fm @ F3 @ Prod ) )
= ( produc1221696404e_fm_o
@ ^ [X13: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_206_prod_Ocase__distrib,axiom,
! [H: $o > produc696645085lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,Prod: produc696645085lle_fm] :
( ( H @ ( produc1221696404e_fm_o @ F3 @ Prod ) )
= ( produc427355858lle_fm
@ ^ [X13: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_207_prod_Ocase__distrib,axiom,
! [H: $o > $o,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,Prod: produc696645085lle_fm] :
( ( H @ ( produc1221696404e_fm_o @ F3 @ Prod ) )
= ( produc1221696404e_fm_o
@ ^ [X13: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_208_prod_Ocase__distrib,axiom,
! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,Prod: produc1647334210lle_tv] :
( ( H @ ( produc1882560353lle_tv @ F3 @ Prod ) )
= ( produc1882560353lle_tv
@ ^ [X13: paraco1605129243lle_tv,X23: paraco1605129243lle_tv] : ( H @ ( F3 @ X13 @ X23 ) )
@ Prod ) ) ).
% prod.case_distrib
thf(fact_209_internal__case__prod__def,axiom,
produc2050176383e_tv_o = produc25129173e_tv_o ).
% internal_case_prod_def
thf(fact_210_internal__case__prod__def,axiom,
produc527953982lle_fm = produc811245928lle_fm ).
% internal_case_prod_def
thf(fact_211_internal__case__prod__def,axiom,
produc323213387e_tv_o = produc648306805e_tv_o ).
% internal_case_prod_def
thf(fact_212_internal__case__prod__def,axiom,
produc144063912lle_fm = produc427355858lle_fm ).
% internal_case_prod_def
thf(fact_213_internal__case__prod__def,axiom,
produc1504058474e_fm_o = produc1221696404e_fm_o ).
% internal_case_prod_def
thf(fact_214_internal__case__prod__def,axiom,
produc192124683lle_tv = produc1882560353lle_tv ).
% internal_case_prod_def
thf(fact_215_tv_Ocase__distrib,axiom,
! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F1: $o > paraco1605129243lle_tv,F2: nat > paraco1605129243lle_tv,Tv: paraco1605129243lle_tv] :
( ( H @ ( paraco2051596139lle_tv @ F1 @ F2 @ Tv ) )
= ( paraco2051596139lle_tv
@ ^ [X5: $o] : ( H @ ( F1 @ X5 ) )
@ ^ [X5: nat] : ( H @ ( F2 @ X5 ) )
@ Tv ) ) ).
% tv.case_distrib
thf(fact_216_old_Oprod_Ocase,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,X1: paraco1605129243lle_tv,X2: paraco1605129243lle_tv] :
( ( produc25129173e_tv_o @ F3 @ ( produc2058540732lle_tv @ X1 @ X2 ) )
= ( F3 @ X1 @ X2 ) ) ).
% old.prod.case
thf(fact_217_old_Oprod_Ocase,axiom,
! [F3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm,X1: paraco1604210848lle_fm,X2: list_char > paraco1605129243lle_tv] :
( ( produc811245928lle_fm @ F3 @ ( produc1943344577lle_tv @ X1 @ X2 ) )
= ( F3 @ X1 @ X2 ) ) ).
% old.prod.case
thf(fact_218_old_Oprod_Ocase,axiom,
! [F3: produc1647334210lle_tv > produc1647334210lle_tv > $o,X1: produc1647334210lle_tv,X2: produc1647334210lle_tv] :
( ( produc648306805e_tv_o @ F3 @ ( produc1537086518lle_tv @ X1 @ X2 ) )
= ( F3 @ X1 @ X2 ) ) ).
% old.prod.case
thf(fact_219_old_Oprod_Ocase,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
( ( produc427355858lle_fm @ F3 @ ( produc1710735575lle_fm @ X1 @ X2 ) )
= ( F3 @ X1 @ X2 ) ) ).
% old.prod.case
thf(fact_220_old_Oprod_Ocase,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
( ( produc1221696404e_fm_o @ F3 @ ( produc1710735575lle_fm @ X1 @ X2 ) )
= ( F3 @ X1 @ X2 ) ) ).
% old.prod.case
thf(fact_221_old_Oprod_Ocase,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,X1: paraco1605129243lle_tv,X2: paraco1605129243lle_tv] :
( ( produc1882560353lle_tv @ F3 @ ( produc2058540732lle_tv @ X1 @ X2 ) )
= ( F3 @ X1 @ X2 ) ) ).
% old.prod.case
thf(fact_222_curryE,axiom,
! [F3: produc1443694919lle_tv > $o,A: paraco1604210848lle_fm,B: list_char > paraco1605129243lle_tv] :
( ( produc298562633e_tv_o @ F3 @ A @ B )
=> ( F3 @ ( produc1943344577lle_tv @ A @ B ) ) ) ).
% curryE
thf(fact_223_curryE,axiom,
! [F3: produc484385668lle_tv > $o,A: produc1647334210lle_tv,B: produc1647334210lle_tv] :
( ( produc1113543188e_tv_o @ F3 @ A @ B )
=> ( F3 @ ( produc1537086518lle_tv @ A @ B ) ) ) ).
% curryE
thf(fact_224_curryE,axiom,
! [F3: produc450659916lle_fm > $o,A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( produc1339594628e_fm_o @ F3 @ A @ B )
=> ( F3 @ ( produc1126104134lle_fm @ A @ B ) ) ) ).
% curryE
thf(fact_225_curryE,axiom,
! [F3: produc1250255278lle_fm > $o,A: produc696645085lle_fm,B: produc696645085lle_fm] :
( ( produc408556266e_fm_o @ F3 @ A @ B )
=> ( F3 @ ( produc407632608lle_fm @ A @ B ) ) ) ).
% curryE
thf(fact_226_curryE,axiom,
! [F3: produc1852595672lle_tv > $o,A: list_char > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv] :
( ( produc1667860344e_tv_o @ F3 @ A @ B )
=> ( F3 @ ( produc1297923922lle_tv @ A @ B ) ) ) ).
% curryE
thf(fact_227_curryE,axiom,
! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( produc275353523e_fm_o @ F3 @ A @ B )
=> ( F3 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% curryE
thf(fact_228_curryE,axiom,
! [F3: produc1647334210lle_tv > $o,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc621423502e_tv_o @ F3 @ A @ B )
=> ( F3 @ ( produc2058540732lle_tv @ A @ B ) ) ) ).
% curryE
thf(fact_229_curryD,axiom,
! [F3: produc1443694919lle_tv > $o,A: paraco1604210848lle_fm,B: list_char > paraco1605129243lle_tv] :
( ( produc298562633e_tv_o @ F3 @ A @ B )
=> ( F3 @ ( produc1943344577lle_tv @ A @ B ) ) ) ).
% curryD
thf(fact_230_curryD,axiom,
! [F3: produc484385668lle_tv > $o,A: produc1647334210lle_tv,B: produc1647334210lle_tv] :
( ( produc1113543188e_tv_o @ F3 @ A @ B )
=> ( F3 @ ( produc1537086518lle_tv @ A @ B ) ) ) ).
% curryD
thf(fact_231_curryD,axiom,
! [F3: produc450659916lle_fm > $o,A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( produc1339594628e_fm_o @ F3 @ A @ B )
=> ( F3 @ ( produc1126104134lle_fm @ A @ B ) ) ) ).
% curryD
thf(fact_232_curryD,axiom,
! [F3: produc1250255278lle_fm > $o,A: produc696645085lle_fm,B: produc696645085lle_fm] :
( ( produc408556266e_fm_o @ F3 @ A @ B )
=> ( F3 @ ( produc407632608lle_fm @ A @ B ) ) ) ).
% curryD
thf(fact_233_curryD,axiom,
! [F3: produc1852595672lle_tv > $o,A: list_char > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv] :
( ( produc1667860344e_tv_o @ F3 @ A @ B )
=> ( F3 @ ( produc1297923922lle_tv @ A @ B ) ) ) ).
% curryD
thf(fact_234_curryD,axiom,
! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( produc275353523e_fm_o @ F3 @ A @ B )
=> ( F3 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% curryD
thf(fact_235_curryD,axiom,
! [F3: produc1647334210lle_tv > $o,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc621423502e_tv_o @ F3 @ A @ B )
=> ( F3 @ ( produc2058540732lle_tv @ A @ B ) ) ) ).
% curryD
thf(fact_236_split__cong,axiom,
! [Q: produc1647334210lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,G: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,P2: produc1647334210lle_tv] :
( ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( ( produc2058540732lle_tv @ X @ Y4 )
= Q )
=> ( ( F3 @ X @ Y4 )
= ( G @ X @ Y4 ) ) )
=> ( ( P2 = Q )
=> ( ( produc25129173e_tv_o @ F3 @ P2 )
= ( produc25129173e_tv_o @ G @ Q ) ) ) ) ).
% split_cong
thf(fact_237_split__cong,axiom,
! [Q: produc1443694919lle_tv,F3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm,G: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm,P2: produc1443694919lle_tv] :
( ! [X: paraco1604210848lle_fm,Y4: list_char > paraco1605129243lle_tv] :
( ( ( produc1943344577lle_tv @ X @ Y4 )
= Q )
=> ( ( F3 @ X @ Y4 )
= ( G @ X @ Y4 ) ) )
=> ( ( P2 = Q )
=> ( ( produc811245928lle_fm @ F3 @ P2 )
= ( produc811245928lle_fm @ G @ Q ) ) ) ) ).
% split_cong
thf(fact_238_split__cong,axiom,
! [Q: produc484385668lle_tv,F3: produc1647334210lle_tv > produc1647334210lle_tv > $o,G: produc1647334210lle_tv > produc1647334210lle_tv > $o,P2: produc484385668lle_tv] :
( ! [X: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
( ( ( produc1537086518lle_tv @ X @ Y4 )
= Q )
=> ( ( F3 @ X @ Y4 )
= ( G @ X @ Y4 ) ) )
=> ( ( P2 = Q )
=> ( ( produc648306805e_tv_o @ F3 @ P2 )
= ( produc648306805e_tv_o @ G @ Q ) ) ) ) ).
% split_cong
thf(fact_239_split__cong,axiom,
! [Q: produc696645085lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,G: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm,P2: produc696645085lle_fm] :
( ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ X @ Y4 )
= Q )
=> ( ( F3 @ X @ Y4 )
= ( G @ X @ Y4 ) ) )
=> ( ( P2 = Q )
=> ( ( produc427355858lle_fm @ F3 @ P2 )
= ( produc427355858lle_fm @ G @ Q ) ) ) ) ).
% split_cong
thf(fact_240_split__cong,axiom,
! [Q: produc696645085lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,G: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,P2: produc696645085lle_fm] :
( ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( ( produc1710735575lle_fm @ X @ Y4 )
= Q )
=> ( ( F3 @ X @ Y4 )
= ( G @ X @ Y4 ) ) )
=> ( ( P2 = Q )
=> ( ( produc1221696404e_fm_o @ F3 @ P2 )
= ( produc1221696404e_fm_o @ G @ Q ) ) ) ) ).
% split_cong
thf(fact_241_split__cong,axiom,
! [Q: produc1647334210lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,P2: produc1647334210lle_tv] :
( ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( ( produc2058540732lle_tv @ X @ Y4 )
= Q )
=> ( ( F3 @ X @ Y4 )
= ( G @ X @ Y4 ) ) )
=> ( ( P2 = Q )
=> ( ( produc1882560353lle_tv @ F3 @ P2 )
= ( produc1882560353lle_tv @ G @ Q ) ) ) ) ).
% split_cong
thf(fact_242_case__bool__if,axiom,
( produc234482697lle_tv
= ( ^ [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv,P5: $o] : ( if_Par1134130401lle_tv @ P5 @ X5 @ Y5 ) ) ) ).
% case_bool_if
thf(fact_243_case__prod__app,axiom,
( produc25129173e_tv_o
= ( ^ [F: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o,X5: produc1647334210lle_tv,Y5: produc1647334210lle_tv] :
( produc852673135e_tv_o
@ ^ [L: paraco1605129243lle_tv,R3: paraco1605129243lle_tv] : ( F @ L @ R3 @ Y5 )
@ X5 ) ) ) ).
% case_prod_app
thf(fact_244_pred__equals__eq2,axiom,
! [R2: set_Pr1723822845lle_tv,S4: set_Pr1723822845lle_tv] :
( ( ( ^ [X5: paraco1604210848lle_fm,Y5: list_char > paraco1605129243lle_tv] : ( member74361182lle_tv @ ( produc1943344577lle_tv @ X5 @ Y5 ) @ R2 ) )
= ( ^ [X5: paraco1604210848lle_fm,Y5: list_char > paraco1605129243lle_tv] : ( member74361182lle_tv @ ( produc1943344577lle_tv @ X5 @ Y5 ) @ S4 ) ) )
= ( R2 = S4 ) ) ).
% pred_equals_eq2
thf(fact_245_pred__equals__eq2,axiom,
! [R2: set_Pr2012908090lle_tv,S4: set_Pr2012908090lle_tv] :
( ( ( ^ [X5: produc1647334210lle_tv,Y5: produc1647334210lle_tv] : ( member1074212123lle_tv @ ( produc1537086518lle_tv @ X5 @ Y5 ) @ R2 ) )
= ( ^ [X5: produc1647334210lle_tv,Y5: produc1647334210lle_tv] : ( member1074212123lle_tv @ ( produc1537086518lle_tv @ X5 @ Y5 ) @ S4 ) ) )
= ( R2 = S4 ) ) ).
% pred_equals_eq2
thf(fact_246_pred__equals__eq2,axiom,
! [R2: set_Pr1019238018lle_fm,S4: set_Pr1019238018lle_fm] :
( ( ( ^ [X5: paraco1604210848lle_fm,Y5: paraco1604210848lle_fm] : ( member334644067lle_fm @ ( produc1126104134lle_fm @ X5 @ Y5 ) @ R2 ) )
= ( ^ [X5: paraco1604210848lle_fm,Y5: paraco1604210848lle_fm] : ( member334644067lle_fm @ ( produc1126104134lle_fm @ X5 @ Y5 ) @ S4 ) ) )
= ( R2 = S4 ) ) ).
% pred_equals_eq2
thf(fact_247_pred__equals__eq2,axiom,
! [R2: set_Pr1475944804lle_fm,S4: set_Pr1475944804lle_fm] :
( ( ( ^ [X5: produc696645085lle_fm,Y5: produc696645085lle_fm] : ( member1592865093lle_fm @ ( produc407632608lle_fm @ X5 @ Y5 ) @ R2 ) )
= ( ^ [X5: produc696645085lle_fm,Y5: produc696645085lle_fm] : ( member1592865093lle_fm @ ( produc407632608lle_fm @ X5 @ Y5 ) @ S4 ) ) )
= ( R2 = S4 ) ) ).
% pred_equals_eq2
thf(fact_248_pred__equals__eq2,axiom,
! [R2: set_Pr2061825550lle_tv,S4: set_Pr2061825550lle_tv] :
( ( ( ^ [X5: list_char > paraco1605129243lle_tv,Y5: list_char > paraco1605129243lle_tv] : ( member146333935lle_tv @ ( produc1297923922lle_tv @ X5 @ Y5 ) @ R2 ) )
= ( ^ [X5: list_char > paraco1605129243lle_tv,Y5: list_char > paraco1605129243lle_tv] : ( member146333935lle_tv @ ( produc1297923922lle_tv @ X5 @ Y5 ) @ S4 ) ) )
= ( R2 = S4 ) ) ).
% pred_equals_eq2
thf(fact_249_pred__equals__eq2,axiom,
! [R2: set_Pr2120184979lle_fm,S4: set_Pr2120184979lle_fm] :
( ( ( ^ [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] : ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ R2 ) )
= ( ^ [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] : ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ S4 ) ) )
= ( R2 = S4 ) ) ).
% pred_equals_eq2
thf(fact_250_pred__equals__eq2,axiom,
! [R2: set_Pr2014382200lle_tv,S4: set_Pr2014382200lle_tv] :
( ( ( ^ [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] : ( member1531318361lle_tv @ ( produc2058540732lle_tv @ X5 @ Y5 ) @ R2 ) )
= ( ^ [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] : ( member1531318361lle_tv @ ( produc2058540732lle_tv @ X5 @ Y5 ) @ S4 ) ) )
= ( R2 = S4 ) ) ).
% pred_equals_eq2
thf(fact_251_pair__imageI,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A2: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ A2 )
=> ( member266900804lle_tv @ ( F3 @ A @ B ) @ ( image_1263514817lle_tv @ ( produc1882560353lle_tv @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_252_pair__imageI,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A2: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > list_char > paraco1605129243lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ A2 )
=> ( member894927066lle_tv @ ( F3 @ A @ B ) @ ( image_1070648001lle_tv @ ( produc1370344801lle_tv @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_253_pair__imageI,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,A2: set_Pr1019238018lle_fm,F3: paraco1604210848lle_fm > paraco1604210848lle_fm > list_char > paraco1605129243lle_tv] :
( ( member334644067lle_fm @ ( produc1126104134lle_fm @ A @ B ) @ A2 )
=> ( member894927066lle_tv @ ( F3 @ A @ B ) @ ( image_496052427lle_tv @ ( produc1629543915lle_tv @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_254_pair__imageI,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ A2 )
=> ( member_o @ ( F3 @ A @ B ) @ ( image_1402739636e_fm_o @ ( produc1221696404e_fm_o @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_255_pair__imageI,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A2: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv > $o] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ A2 )
=> ( member1832524214e_tv_o @ ( F3 @ A @ B ) @ ( image_1015627317e_tv_o @ ( produc25129173e_tv_o @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_256_pair__imageI,axiom,
! [A: produc1647334210lle_tv,B: produc1647334210lle_tv,A2: set_Pr2012908090lle_tv,F3: produc1647334210lle_tv > produc1647334210lle_tv > $o] :
( ( member1074212123lle_tv @ ( produc1537086518lle_tv @ A @ B ) @ A2 )
=> ( member_o @ ( F3 @ A @ B ) @ ( image_1610089293e_tv_o @ ( produc648306805e_tv_o @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_257_pair__imageI,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc1647334210lle_tv] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ A2 )
=> ( member1531318361lle_tv @ ( F3 @ A @ B ) @ ( image_1110913773lle_tv @ ( produc401650381lle_tv @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_258_pair__imageI,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A2: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > produc696645085lle_fm] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ A2 )
=> ( member1474794996lle_fm @ ( F3 @ A @ B ) @ ( image_937396045lle_fm @ ( produc377990317lle_fm @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_259_pair__imageI,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,A2: set_Pr1019238018lle_fm,F3: paraco1604210848lle_fm > paraco1604210848lle_fm > produc696645085lle_fm] :
( ( member334644067lle_fm @ ( produc1126104134lle_fm @ A @ B ) @ A2 )
=> ( member1474794996lle_fm @ ( F3 @ A @ B ) @ ( image_1662022595lle_fm @ ( produc182748835lle_fm @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_260_pair__imageI,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > list_char > paraco1605129243lle_tv] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ A2 )
=> ( member894927066lle_tv @ ( F3 @ A @ B ) @ ( image_305309148lle_tv @ ( produc1949847036lle_tv @ F3 ) @ A2 ) ) ) ).
% pair_imageI
thf(fact_261_case__prodI,axiom,
! [F3: produc696645085lle_fm > produc696645085lle_fm > $o,A: produc696645085lle_fm,B: produc696645085lle_fm] :
( ( F3 @ A @ B )
=> ( produc1234307915e_fm_o @ F3 @ ( produc407632608lle_fm @ A @ B ) ) ) ).
% case_prodI
thf(fact_262_case__prodI,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > $o,A: list_char > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv] :
( ( F3 @ A @ B )
=> ( produc101320793e_tv_o @ F3 @ ( produc1297923922lle_tv @ A @ B ) ) ) ).
% case_prodI
thf(fact_263_case__prodI,axiom,
! [F3: produc1647334210lle_tv > produc1647334210lle_tv > $o,A: produc1647334210lle_tv,B: produc1647334210lle_tv] :
( ( F3 @ A @ B )
=> ( produc648306805e_tv_o @ F3 @ ( produc1537086518lle_tv @ A @ B ) ) ) ).
% case_prodI
thf(fact_264_case__prodI,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( F3 @ A @ B )
=> ( produc1221696404e_fm_o @ F3 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% case_prodI
thf(fact_265_case__prodI,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > $o,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( F3 @ A @ B )
=> ( produc852673135e_tv_o @ F3 @ ( produc2058540732lle_tv @ A @ B ) ) ) ).
% case_prodI
thf(fact_266_case__prodI2,axiom,
! [P2: produc696645085lle_fm,C2: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o] :
( ! [A4: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
( ( P2
= ( produc1710735575lle_fm @ A4 @ B3 ) )
=> ( C2 @ A4 @ B3 ) )
=> ( produc1221696404e_fm_o @ C2 @ P2 ) ) ).
% case_prodI2
thf(fact_267_case__prodI2,axiom,
! [P2: produc1647334210lle_tv,C2: paraco1605129243lle_tv > paraco1605129243lle_tv > $o] :
( ! [A4: paraco1605129243lle_tv,B3: paraco1605129243lle_tv] :
( ( P2
= ( produc2058540732lle_tv @ A4 @ B3 ) )
=> ( C2 @ A4 @ B3 ) )
=> ( produc852673135e_tv_o @ C2 @ P2 ) ) ).
% case_prodI2
thf(fact_268_pair__in__swap__image,axiom,
! [Y: paraco1604210848lle_fm,X4: list_char > paraco1605129243lle_tv,A2: set_Pr2120184979lle_fm] :
( ( member74361182lle_tv @ ( produc1943344577lle_tv @ Y @ X4 ) @ ( image_924970994lle_tv @ produc1000205111lle_fm @ A2 ) )
= ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y ) @ A2 ) ) ).
% pair_in_swap_image
thf(fact_269_pair__in__swap__image,axiom,
! [Y: list_char > paraco1605129243lle_tv,X4: paraco1604210848lle_fm,A2: set_Pr1723822845lle_tv] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ Y @ X4 ) @ ( image_326034184lle_fm @ produc1232814113lle_tv @ A2 ) )
= ( member74361182lle_tv @ ( produc1943344577lle_tv @ X4 @ Y ) @ A2 ) ) ).
% pair_in_swap_image
thf(fact_270_pair__in__swap__image,axiom,
! [Y: paraco1605129243lle_tv,X4: paraco1605129243lle_tv,A2: set_Pr2014382200lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ Y @ X4 ) @ ( image_1221801032lle_tv @ produc211755292lle_tv @ A2 ) )
= ( member1531318361lle_tv @ ( produc2058540732lle_tv @ X4 @ Y ) @ A2 ) ) ).
% pair_in_swap_image
thf(fact_271_case__prod__Pair__iden,axiom,
! [P2: produc696645085lle_fm] :
( ( produc427355858lle_fm @ produc1710735575lle_fm @ P2 )
= P2 ) ).
% case_prod_Pair_iden
thf(fact_272_case__prod__Pair__iden,axiom,
! [P2: produc1647334210lle_tv] :
( ( produc942307752lle_tv @ produc2058540732lle_tv @ P2 )
= P2 ) ).
% case_prod_Pair_iden
thf(fact_273_case__prodD,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( produc1221696404e_fm_o @ F3 @ ( produc1710735575lle_fm @ A @ B ) )
=> ( F3 @ A @ B ) ) ).
% case_prodD
thf(fact_274_case__prodD,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv > $o,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc852673135e_tv_o @ F3 @ ( produc2058540732lle_tv @ A @ B ) )
=> ( F3 @ A @ B ) ) ).
% case_prodD
thf(fact_275_case__prodE,axiom,
! [C2: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,P2: produc696645085lle_fm] :
( ( produc1221696404e_fm_o @ C2 @ P2 )
=> ~ ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( P2
= ( produc1710735575lle_fm @ X @ Y4 ) )
=> ~ ( C2 @ X @ Y4 ) ) ) ).
% case_prodE
thf(fact_276_case__prodE,axiom,
! [C2: paraco1605129243lle_tv > paraco1605129243lle_tv > $o,P2: produc1647334210lle_tv] :
( ( produc852673135e_tv_o @ C2 @ P2 )
=> ~ ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( P2
= ( produc2058540732lle_tv @ X @ Y4 ) )
=> ~ ( C2 @ X @ Y4 ) ) ) ).
% case_prodE
thf(fact_277_swap__product,axiom,
! [A2: set_Pa1499417344lle_fm,B5: set_li72793489lle_tv] :
( ( image_326034184lle_fm
@ ( produc811245928lle_fm
@ ^ [I: paraco1604210848lle_fm,J: list_char > paraco1605129243lle_tv] : ( produc1710735575lle_fm @ J @ I ) )
@ ( produc559987792lle_tv @ A2
@ ^ [Uu: paraco1604210848lle_fm] : B5 ) )
= ( produc327378790lle_fm @ B5
@ ^ [Uu: list_char > paraco1605129243lle_tv] : A2 ) ) ).
% swap_product
thf(fact_278_swap__product,axiom,
! [A2: set_Pa1764573435lle_tv,B5: set_Pa1764573435lle_tv] :
( ( image_1221801032lle_tv
@ ( produc942307752lle_tv
@ ^ [I: paraco1605129243lle_tv,J: paraco1605129243lle_tv] : ( produc2058540732lle_tv @ J @ I ) )
@ ( produc479904331lle_tv @ A2
@ ^ [Uu: paraco1605129243lle_tv] : B5 ) )
= ( produc479904331lle_tv @ B5
@ ^ [Uu: paraco1605129243lle_tv] : A2 ) ) ).
% swap_product
thf(fact_279_SigmaI,axiom,
! [A: list_char > paraco1605129243lle_tv,A2: set_li72793489lle_tv,B: paraco1604210848lle_fm,B5: ( list_char > paraco1605129243lle_tv ) > set_Pa1499417344lle_fm] :
( ( member894927066lle_tv @ A @ A2 )
=> ( ( member265982409lle_fm @ B @ ( B5 @ A ) )
=> ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc327378790lle_fm @ A2 @ B5 ) ) ) ) ).
% SigmaI
thf(fact_280_SigmaI,axiom,
! [A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv,B5: paraco1605129243lle_tv > set_Pa1764573435lle_tv] :
( ( member266900804lle_tv @ A @ A2 )
=> ( ( member266900804lle_tv @ B @ ( B5 @ A ) )
=> ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ ( produc479904331lle_tv @ A2 @ B5 ) ) ) ) ).
% SigmaI
thf(fact_281_mem__Sigma__iff,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A2: set_li72793489lle_tv,B5: ( list_char > paraco1605129243lle_tv ) > set_Pa1499417344lle_fm] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc327378790lle_fm @ A2 @ B5 ) )
= ( ( member894927066lle_tv @ A @ A2 )
& ( member265982409lle_fm @ B @ ( B5 @ A ) ) ) ) ).
% mem_Sigma_iff
thf(fact_282_mem__Sigma__iff,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B5: paraco1605129243lle_tv > set_Pa1764573435lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ ( produc479904331lle_tv @ A2 @ B5 ) )
= ( ( member266900804lle_tv @ A @ A2 )
& ( member266900804lle_tv @ B @ ( B5 @ A ) ) ) ) ).
% mem_Sigma_iff
thf(fact_283_in__inv__image,axiom,
! [X4: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,R: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ X4 @ Y ) @ ( inv_im719552961lle_tv @ R @ F3 ) )
= ( member1531318361lle_tv @ ( produc2058540732lle_tv @ ( F3 @ X4 ) @ ( F3 @ Y ) ) @ R ) ) ).
% in_inv_image
thf(fact_284_same__fstI,axiom,
! [P3: ( list_char > paraco1605129243lle_tv ) > $o,X4: list_char > paraco1605129243lle_tv,Y6: paraco1604210848lle_fm,Y: paraco1604210848lle_fm,R2: ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm] :
( ( P3 @ X4 )
=> ( ( member334644067lle_fm @ ( produc1126104134lle_fm @ Y6 @ Y ) @ ( R2 @ X4 ) )
=> ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ X4 @ Y6 ) @ ( produc1710735575lle_fm @ X4 @ Y ) ) @ ( same_f1581085506lle_fm @ P3 @ R2 ) ) ) ) ).
% same_fstI
thf(fact_285_same__fstI,axiom,
! [P3: paraco1605129243lle_tv > $o,X4: paraco1605129243lle_tv,Y6: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,R2: paraco1605129243lle_tv > set_Pr2014382200lle_tv] :
( ( P3 @ X4 )
=> ( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ Y6 @ Y ) @ ( R2 @ X4 ) )
=> ( member1074212123lle_tv @ ( produc1537086518lle_tv @ ( produc2058540732lle_tv @ X4 @ Y6 ) @ ( produc2058540732lle_tv @ X4 @ Y ) ) @ ( same_f1119076903lle_tv @ P3 @ R2 ) ) ) ) ).
% same_fstI
thf(fact_286_SigmaE,axiom,
! [C2: produc696645085lle_fm,A2: set_li72793489lle_tv,B5: ( list_char > paraco1605129243lle_tv ) > set_Pa1499417344lle_fm] :
( ( member1474794996lle_fm @ C2 @ ( produc327378790lle_fm @ A2 @ B5 ) )
=> ~ ! [X: list_char > paraco1605129243lle_tv] :
( ( member894927066lle_tv @ X @ A2 )
=> ! [Y4: paraco1604210848lle_fm] :
( ( member265982409lle_fm @ Y4 @ ( B5 @ X ) )
=> ( C2
!= ( produc1710735575lle_fm @ X @ Y4 ) ) ) ) ) ).
% SigmaE
thf(fact_287_SigmaE,axiom,
! [C2: produc1647334210lle_tv,A2: set_Pa1764573435lle_tv,B5: paraco1605129243lle_tv > set_Pa1764573435lle_tv] :
( ( member1531318361lle_tv @ C2 @ ( produc479904331lle_tv @ A2 @ B5 ) )
=> ~ ! [X: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ X @ A2 )
=> ! [Y4: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ Y4 @ ( B5 @ X ) )
=> ( C2
!= ( produc2058540732lle_tv @ X @ Y4 ) ) ) ) ) ).
% SigmaE
thf(fact_288_SigmaD1,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A2: set_li72793489lle_tv,B5: ( list_char > paraco1605129243lle_tv ) > set_Pa1499417344lle_fm] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc327378790lle_fm @ A2 @ B5 ) )
=> ( member894927066lle_tv @ A @ A2 ) ) ).
% SigmaD1
thf(fact_289_SigmaD1,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B5: paraco1605129243lle_tv > set_Pa1764573435lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ ( produc479904331lle_tv @ A2 @ B5 ) )
=> ( member266900804lle_tv @ A @ A2 ) ) ).
% SigmaD1
thf(fact_290_SigmaD2,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A2: set_li72793489lle_tv,B5: ( list_char > paraco1605129243lle_tv ) > set_Pa1499417344lle_fm] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc327378790lle_fm @ A2 @ B5 ) )
=> ( member265982409lle_fm @ B @ ( B5 @ A ) ) ) ).
% SigmaD2
thf(fact_291_SigmaD2,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B5: paraco1605129243lle_tv > set_Pa1764573435lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ ( produc479904331lle_tv @ A2 @ B5 ) )
=> ( member266900804lle_tv @ B @ ( B5 @ A ) ) ) ).
% SigmaD2
thf(fact_292_SigmaE2,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A2: set_li72793489lle_tv,B5: ( list_char > paraco1605129243lle_tv ) > set_Pa1499417344lle_fm] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc327378790lle_fm @ A2 @ B5 ) )
=> ~ ( ( member894927066lle_tv @ A @ A2 )
=> ~ ( member265982409lle_fm @ B @ ( B5 @ A ) ) ) ) ).
% SigmaE2
thf(fact_293_SigmaE2,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B5: paraco1605129243lle_tv > set_Pa1764573435lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ ( produc479904331lle_tv @ A2 @ B5 ) )
=> ~ ( ( member266900804lle_tv @ A @ A2 )
=> ~ ( member266900804lle_tv @ B @ ( B5 @ A ) ) ) ) ).
% SigmaE2
thf(fact_294_lex__prod__def,axiom,
( lex_pr567812260lle_tv
= ( ^ [Ra: set_Pr2014382200lle_tv,Rb: set_Pr2014382200lle_tv] :
( collec1900284505lle_tv
@ ( produc648306805e_tv_o
@ ( produc25129173e_tv_o
@ ^ [A5: paraco1605129243lle_tv,B4: paraco1605129243lle_tv] :
( produc852673135e_tv_o
@ ^ [A6: paraco1605129243lle_tv,B6: paraco1605129243lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A5 @ A6 ) @ Ra )
| ( ( A5 = A6 )
& ( member1531318361lle_tv @ ( produc2058540732lle_tv @ B4 @ B6 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% lex_prod_def
thf(fact_295_in__lex__prod,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm,R: set_Pr2061825550lle_tv,S: set_Pr1019238018lle_fm] :
( ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc1710735575lle_fm @ A3 @ B2 ) ) @ ( lex_pr2001015487lle_fm @ R @ S ) )
= ( ( member146333935lle_tv @ ( produc1297923922lle_tv @ A @ A3 ) @ R )
| ( ( A = A3 )
& ( member334644067lle_fm @ ( produc1126104134lle_fm @ B @ B2 ) @ S ) ) ) ) ).
% in_lex_prod
thf(fact_296_in__lex__prod,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,A3: paraco1605129243lle_tv,B2: paraco1605129243lle_tv,R: set_Pr2014382200lle_tv,S: set_Pr2014382200lle_tv] :
( ( member1074212123lle_tv @ ( produc1537086518lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ ( produc2058540732lle_tv @ A3 @ B2 ) ) @ ( lex_pr567812260lle_tv @ R @ S ) )
= ( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ A3 ) @ R )
| ( ( A = A3 )
& ( member1531318361lle_tv @ ( produc2058540732lle_tv @ B @ B2 ) @ S ) ) ) ) ).
% in_lex_prod
thf(fact_297_relation__of__def,axiom,
( order_1215526505lle_tv
= ( ^ [P5: paraco1605129243lle_tv > paraco1605129243lle_tv > $o,A7: set_Pa1764573435lle_tv] :
( collec15260823lle_tv
@ ( produc852673135e_tv_o
@ ^ [A5: paraco1605129243lle_tv,B4: paraco1605129243lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A5 @ B4 )
@ ( produc479904331lle_tv @ A7
@ ^ [Uu: paraco1605129243lle_tv] : A7 ) )
& ( P5 @ A5 @ B4 ) ) ) ) ) ) ).
% relation_of_def
thf(fact_298_map__prod__simp,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( produc1900967599lle_fm @ F3 @ G @ ( produc1710735575lle_fm @ A @ B ) )
= ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% map_prod_simp
thf(fact_299_map__prod__simp,axiom,
! [F3: ( list_char > paraco1605129243lle_tv ) > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1605129243lle_tv,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( produc918997546lle_tv @ F3 @ G @ ( produc1710735575lle_fm @ A @ B ) )
= ( produc2058540732lle_tv @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% map_prod_simp
thf(fact_300_map__prod__simp,axiom,
! [F3: paraco1605129243lle_tv > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc2008706836lle_fm @ F3 @ G @ ( produc2058540732lle_tv @ A @ B ) )
= ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% map_prod_simp
thf(fact_301_map__prod__simp,axiom,
! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( produc1345917071lle_tv @ F3 @ G @ ( produc2058540732lle_tv @ A @ B ) )
= ( produc2058540732lle_tv @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% map_prod_simp
thf(fact_302_map__prod__imageI,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
=> ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F3 @ G ) @ R2 ) ) ) ).
% map_prod_imageI
thf(fact_303_map__prod__imageI,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1605129243lle_tv] :
( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
=> ( member1531318361lle_tv @ ( produc2058540732lle_tv @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_1110913773lle_tv @ ( produc918997546lle_tv @ F3 @ G ) @ R2 ) ) ) ).
% map_prod_imageI
thf(fact_304_map__prod__imageI,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,R2: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ R2 )
=> ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_937396045lle_fm @ ( produc2008706836lle_fm @ F3 @ G ) @ R2 ) ) ) ).
% map_prod_imageI
thf(fact_305_map__prod__imageI,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv,R2: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A @ B ) @ R2 )
=> ( member1531318361lle_tv @ ( produc2058540732lle_tv @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ F3 @ G ) @ R2 ) ) ) ).
% map_prod_imageI
thf(fact_306_case__prod__map__prod,axiom,
! [H: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,X4: produc1647334210lle_tv] :
( ( produc1882560353lle_tv @ H @ ( produc1345917071lle_tv @ F3 @ G @ X4 ) )
= ( produc1882560353lle_tv
@ ^ [L: paraco1605129243lle_tv,R3: paraco1605129243lle_tv] : ( H @ ( F3 @ L ) @ ( G @ R3 ) )
@ X4 ) ) ).
% case_prod_map_prod
thf(fact_307_prod__fun__imageE,axiom,
! [C2: produc696645085lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm] :
( ( member1474794996lle_fm @ C2 @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F3 @ G ) @ R2 ) )
=> ~ ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( C2
= ( produc1710735575lle_fm @ ( F3 @ X ) @ ( G @ Y4 ) ) )
=> ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X @ Y4 ) @ R2 ) ) ) ).
% prod_fun_imageE
thf(fact_308_prod__fun__imageE,axiom,
! [C2: produc696645085lle_fm,F3: paraco1605129243lle_tv > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,R2: set_Pr2014382200lle_tv] :
( ( member1474794996lle_fm @ C2 @ ( image_937396045lle_fm @ ( produc2008706836lle_fm @ F3 @ G ) @ R2 ) )
=> ~ ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( C2
= ( produc1710735575lle_fm @ ( F3 @ X ) @ ( G @ Y4 ) ) )
=> ~ ( member1531318361lle_tv @ ( produc2058540732lle_tv @ X @ Y4 ) @ R2 ) ) ) ).
% prod_fun_imageE
thf(fact_309_prod__fun__imageE,axiom,
! [C2: produc1647334210lle_tv,F3: ( list_char > paraco1605129243lle_tv ) > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1605129243lle_tv,R2: set_Pr2120184979lle_fm] :
( ( member1531318361lle_tv @ C2 @ ( image_1110913773lle_tv @ ( produc918997546lle_tv @ F3 @ G ) @ R2 ) )
=> ~ ! [X: list_char > paraco1605129243lle_tv,Y4: paraco1604210848lle_fm] :
( ( C2
= ( produc2058540732lle_tv @ ( F3 @ X ) @ ( G @ Y4 ) ) )
=> ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X @ Y4 ) @ R2 ) ) ) ).
% prod_fun_imageE
thf(fact_310_prod__fun__imageE,axiom,
! [C2: produc1647334210lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,R2: set_Pr2014382200lle_tv] :
( ( member1531318361lle_tv @ C2 @ ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ F3 @ G ) @ R2 ) )
=> ~ ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( C2
= ( produc2058540732lle_tv @ ( F3 @ X ) @ ( G @ Y4 ) ) )
=> ~ ( member1531318361lle_tv @ ( produc2058540732lle_tv @ X @ Y4 ) @ R2 ) ) ) ).
% prod_fun_imageE
thf(fact_311_aboveS__def,axiom,
( order_1376767238lle_tv
= ( ^ [R3: set_Pr2014382200lle_tv,A5: paraco1605129243lle_tv] :
( collec1111687558lle_tv
@ ^ [B4: paraco1605129243lle_tv] :
( ( B4 != A5 )
& ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A5 @ B4 ) @ R3 ) ) ) ) ) ).
% aboveS_def
thf(fact_312_above__def,axiom,
( order_1434492699lle_tv
= ( ^ [R3: set_Pr2014382200lle_tv,A5: paraco1605129243lle_tv] :
( collec1111687558lle_tv
@ ^ [B4: paraco1605129243lle_tv] : ( member1531318361lle_tv @ ( produc2058540732lle_tv @ A5 @ B4 ) @ R3 ) ) ) ) ).
% above_def
thf(fact_313_The__split__eq,axiom,
! [X4: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
( ( the_Pr1724341910lle_fm
@ ( produc1221696404e_fm_o
@ ^ [X6: list_char > paraco1605129243lle_tv,Y7: paraco1604210848lle_fm] :
( ( X4 = X6 )
& ( Y = Y7 ) ) ) )
= ( produc1710735575lle_fm @ X4 @ Y ) ) ).
% The_split_eq
thf(fact_314_The__split__eq,axiom,
! [X4: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
( ( the_Pr304385787lle_tv
@ ( produc852673135e_tv_o
@ ^ [X6: paraco1605129243lle_tv,Y7: paraco1605129243lle_tv] :
( ( X4 = X6 )
& ( Y = Y7 ) ) ) )
= ( produc2058540732lle_tv @ X4 @ Y ) ) ).
% The_split_eq
thf(fact_315_fst__eqD,axiom,
! [X4: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv] :
( ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X4 @ Y ) )
= A )
=> ( X4 = A ) ) ).
% fst_eqD
thf(fact_316_fst__eqD,axiom,
! [X4: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,A: paraco1605129243lle_tv] :
( ( ( produc488585168lle_tv @ ( produc2058540732lle_tv @ X4 @ Y ) )
= A )
=> ( X4 = A ) ) ).
% fst_eqD
thf(fact_317_fst__conv,axiom,
! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X1 @ X2 ) )
= X1 ) ).
% fst_conv
thf(fact_318_fst__conv,axiom,
! [X1: paraco1605129243lle_tv,X2: paraco1605129243lle_tv] :
( ( produc488585168lle_tv @ ( produc2058540732lle_tv @ X1 @ X2 ) )
= X1 ) ).
% fst_conv
thf(fact_319_fst__def,axiom,
( produc488585168lle_tv
= ( produc1882560353lle_tv
@ ^ [X13: paraco1605129243lle_tv,X23: paraco1605129243lle_tv] : X13 ) ) ).
% fst_def
thf(fact_320_eq__fst__iff,axiom,
! [A: list_char > paraco1605129243lle_tv,P2: produc696645085lle_fm] :
( ( A
= ( produc29804011lle_fm @ P2 ) )
= ( ? [B4: paraco1604210848lle_fm] :
( P2
= ( produc1710735575lle_fm @ A @ B4 ) ) ) ) ).
% eq_fst_iff
thf(fact_321_eq__fst__iff,axiom,
! [A: paraco1605129243lle_tv,P2: produc1647334210lle_tv] :
( ( A
= ( produc488585168lle_tv @ P2 ) )
= ( ? [B4: paraco1605129243lle_tv] :
( P2
= ( produc2058540732lle_tv @ A @ B4 ) ) ) ) ).
% eq_fst_iff
thf(fact_322_fstI,axiom,
! [X4: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
( ( X4
= ( produc1710735575lle_fm @ Y @ Z ) )
=> ( ( produc29804011lle_fm @ X4 )
= Y ) ) ).
% fstI
thf(fact_323_fstI,axiom,
! [X4: produc1647334210lle_tv,Y: paraco1605129243lle_tv,Z: paraco1605129243lle_tv] :
( ( X4
= ( produc2058540732lle_tv @ Y @ Z ) )
=> ( ( produc488585168lle_tv @ X4 )
= Y ) ) ).
% fstI
thf(fact_324_prod_Ocollapse,axiom,
! [Prod: produc696645085lle_fm] :
( ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_325_prod_Ocollapse,axiom,
! [Prod: produc1647334210lle_tv] :
( ( produc2058540732lle_tv @ ( produc488585168lle_tv @ Prod ) @ ( produc1837067022lle_tv @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_326_sndI,axiom,
! [X4: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
( ( X4
= ( produc1710735575lle_fm @ Y @ Z ) )
=> ( ( produc148705065lle_fm @ X4 )
= Z ) ) ).
% sndI
thf(fact_327_sndI,axiom,
! [X4: produc1647334210lle_tv,Y: paraco1605129243lle_tv,Z: paraco1605129243lle_tv] :
( ( X4
= ( produc2058540732lle_tv @ Y @ Z ) )
=> ( ( produc1837067022lle_tv @ X4 )
= Z ) ) ).
% sndI
thf(fact_328_eq__snd__iff,axiom,
! [B: paraco1604210848lle_fm,P2: produc696645085lle_fm] :
( ( B
= ( produc148705065lle_fm @ P2 ) )
= ( ? [A5: list_char > paraco1605129243lle_tv] :
( P2
= ( produc1710735575lle_fm @ A5 @ B ) ) ) ) ).
% eq_snd_iff
thf(fact_329_eq__snd__iff,axiom,
! [B: paraco1605129243lle_tv,P2: produc1647334210lle_tv] :
( ( B
= ( produc1837067022lle_tv @ P2 ) )
= ( ? [A5: paraco1605129243lle_tv] :
( P2
= ( produc2058540732lle_tv @ A5 @ B ) ) ) ) ).
% eq_snd_iff
thf(fact_330_snd__eqD,axiom,
! [X4: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: paraco1604210848lle_fm] :
( ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X4 @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_331_snd__eqD,axiom,
! [X4: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,A: paraco1605129243lle_tv] :
( ( ( produc1837067022lle_tv @ ( produc2058540732lle_tv @ X4 @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_332_snd__conv,axiom,
! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_333_snd__conv,axiom,
! [X1: paraco1605129243lle_tv,X2: paraco1605129243lle_tv] :
( ( produc1837067022lle_tv @ ( produc2058540732lle_tv @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_334_snd__def,axiom,
( produc1837067022lle_tv
= ( produc1882560353lle_tv
@ ^ [X13: paraco1605129243lle_tv,X23: paraco1605129243lle_tv] : X23 ) ) ).
% snd_def
thf(fact_335_case__prod__beta,axiom,
( produc1882560353lle_tv
= ( ^ [F: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,P: produc1647334210lle_tv] : ( F @ ( produc488585168lle_tv @ P ) @ ( produc1837067022lle_tv @ P ) ) ) ) ).
% case_prod_beta
thf(fact_336_case__prod__beta_H,axiom,
( produc1882560353lle_tv
= ( ^ [F: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,X5: produc1647334210lle_tv] : ( F @ ( produc488585168lle_tv @ X5 ) @ ( produc1837067022lle_tv @ X5 ) ) ) ) ).
% case_prod_beta'
thf(fact_337_prod_Ocase__eq__if,axiom,
( produc1882560353lle_tv
= ( ^ [F: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,Prod2: produc1647334210lle_tv] : ( F @ ( produc488585168lle_tv @ Prod2 ) @ ( produc1837067022lle_tv @ Prod2 ) ) ) ) ).
% prod.case_eq_if
thf(fact_338_case__prod__unfold,axiom,
( produc1882560353lle_tv
= ( ^ [C3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,P: produc1647334210lle_tv] : ( C3 @ ( produc488585168lle_tv @ P ) @ ( produc1837067022lle_tv @ P ) ) ) ) ).
% case_prod_unfold
thf(fact_339_prod_Oexhaust__sel,axiom,
! [Prod: produc696645085lle_fm] :
( Prod
= ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_340_prod_Oexhaust__sel,axiom,
! [Prod: produc1647334210lle_tv] :
( Prod
= ( produc2058540732lle_tv @ ( produc488585168lle_tv @ Prod ) @ ( produc1837067022lle_tv @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_341_surjective__pairing,axiom,
! [T: produc696645085lle_fm] :
( T
= ( produc1710735575lle_fm @ ( produc29804011lle_fm @ T ) @ ( produc148705065lle_fm @ T ) ) ) ).
% surjective_pairing
thf(fact_342_surjective__pairing,axiom,
! [T: produc1647334210lle_tv] :
( T
= ( produc2058540732lle_tv @ ( produc488585168lle_tv @ T ) @ ( produc1837067022lle_tv @ T ) ) ) ).
% surjective_pairing
thf(fact_343_prod_Osplit__sel,axiom,
! [P3: paraco1605129243lle_tv > $o,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,Prod: produc1647334210lle_tv] :
( ( P3 @ ( produc1882560353lle_tv @ F3 @ Prod ) )
= ( ( Prod
= ( produc2058540732lle_tv @ ( produc488585168lle_tv @ Prod ) @ ( produc1837067022lle_tv @ Prod ) ) )
=> ( P3 @ ( F3 @ ( produc488585168lle_tv @ Prod ) @ ( produc1837067022lle_tv @ Prod ) ) ) ) ) ).
% prod.split_sel
thf(fact_344_prod_Osplit__sel__asm,axiom,
! [P3: paraco1605129243lle_tv > $o,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv,Prod: produc1647334210lle_tv] :
( ( P3 @ ( produc1882560353lle_tv @ F3 @ Prod ) )
= ( ~ ( ( Prod
= ( produc2058540732lle_tv @ ( produc488585168lle_tv @ Prod ) @ ( produc1837067022lle_tv @ Prod ) ) )
& ~ ( P3 @ ( F3 @ ( produc488585168lle_tv @ Prod ) @ ( produc1837067022lle_tv @ Prod ) ) ) ) ) ) ).
% prod.split_sel_asm
thf(fact_345_prod_Oswap__def,axiom,
( produc1232814113lle_tv
= ( ^ [P: produc1443694919lle_tv] : ( produc1710735575lle_fm @ ( produc381314067lle_tv @ P ) @ ( produc262413013lle_tv @ P ) ) ) ) ).
% prod.swap_def
thf(fact_346_prod_Oswap__def,axiom,
( produc211755292lle_tv
= ( ^ [P: produc1647334210lle_tv] : ( produc2058540732lle_tv @ ( produc1837067022lle_tv @ P ) @ ( produc488585168lle_tv @ P ) ) ) ) ).
% prod.swap_def
thf(fact_347_exE__realizer,axiom,
! [P3: paraco1605129243lle_tv > paraco1605129243lle_tv > $o,P2: produc1647334210lle_tv,Q3: paraco1605129243lle_tv > $o,F3: paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( P3 @ ( produc1837067022lle_tv @ P2 ) @ ( produc488585168lle_tv @ P2 ) )
=> ( ! [X: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
( ( P3 @ Y4 @ X )
=> ( Q3 @ ( F3 @ X @ Y4 ) ) )
=> ( Q3 @ ( produc1882560353lle_tv @ F3 @ P2 ) ) ) ) ).
% exE_realizer
thf(fact_348_exI__realizer,axiom,
! [P3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o,Y: paraco1604210848lle_fm,X4: list_char > paraco1605129243lle_tv] :
( ( P3 @ Y @ X4 )
=> ( P3 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X4 @ Y ) ) @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X4 @ Y ) ) ) ) ).
% exI_realizer
thf(fact_349_exI__realizer,axiom,
! [P3: paraco1605129243lle_tv > paraco1605129243lle_tv > $o,Y: paraco1605129243lle_tv,X4: paraco1605129243lle_tv] :
( ( P3 @ Y @ X4 )
=> ( P3 @ ( produc1837067022lle_tv @ ( produc2058540732lle_tv @ X4 @ Y ) ) @ ( produc488585168lle_tv @ ( produc2058540732lle_tv @ X4 @ Y ) ) ) ) ).
% exI_realizer
thf(fact_350_conjI__realizer,axiom,
! [P3: ( list_char > paraco1605129243lle_tv ) > $o,P2: list_char > paraco1605129243lle_tv,Q3: paraco1604210848lle_fm > $o,Q: paraco1604210848lle_fm] :
( ( P3 @ P2 )
=> ( ( Q3 @ Q )
=> ( ( P3 @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) )
& ( Q3 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_351_conjI__realizer,axiom,
! [P3: paraco1605129243lle_tv > $o,P2: paraco1605129243lle_tv,Q3: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv] :
( ( P3 @ P2 )
=> ( ( Q3 @ Q )
=> ( ( P3 @ ( produc488585168lle_tv @ ( produc2058540732lle_tv @ P2 @ Q ) ) )
& ( Q3 @ ( produc1837067022lle_tv @ ( produc2058540732lle_tv @ P2 @ Q ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_352_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,X4: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: produc696645085lle_fm] :
( ( P3 @ X4 @ Y )
=> ( ( A
= ( produc1710735575lle_fm @ X4 @ Y ) )
=> ( P3 @ ( produc29804011lle_fm @ A ) @ ( produc148705065lle_fm @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_353_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P3: paraco1605129243lle_tv > paraco1605129243lle_tv > $o,X4: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,A: produc1647334210lle_tv] :
( ( P3 @ X4 @ Y )
=> ( ( A
= ( produc2058540732lle_tv @ X4 @ Y ) )
=> ( P3 @ ( produc488585168lle_tv @ A ) @ ( produc1837067022lle_tv @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
% Helper facts (3)
thf(help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
! [P3: $o] :
( ( P3 = $true )
| ( P3 = $false ) ) ).
thf(help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
! [X4: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
( ( if_Par1134130401lle_tv @ $false @ X4 @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
! [X4: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
( ( if_Par1134130401lle_tv @ $true @ X4 @ Y )
= X4 ) ).
% Conjectures (1)
thf(conj_0,conjecture,
? [I4: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ I4 @ p )
!= ( paraco1344940915le_Det @ $true ) ) ).
%------------------------------------------------------------------------------