TPTP Problem File: SCT170^3.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SCT170^3 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 204, 1000 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_1000_thf_l204 [Bla11]
% Status : Theorem
% Rating : 0.70 v8.2.0, 0.85 v8.1.0, 0.82 v7.5.0, 1.00 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.71 v6.0.0, 0.86 v5.5.0, 0.83 v5.4.0, 1.00 v5.3.0
% Syntax : Number of formulae : 1619 ( 208 unt; 413 typ; 0 def)
% Number of atoms : 4068 ( 830 equ; 38 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 11911 ( 449 ~; 60 |; 168 &;9526 @)
% ( 224 <=>;1484 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 33 ( 32 usr)
% Number of type conns : 5025 (5025 >; 0 *; 0 +; 0 <<)
% Number of symbols : 386 ( 381 usr; 20 con; 0-4 aty)
% Number of variables : 3847 ( 178 ^;3475 !; 194 ?;3847 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 19:41:50
%------------------------------------------------------------------------------
%----Should-be-implicit typings (32)
thf(ty_ty_tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
arrow_1389031998le_alt: $tType ).
thf(ty_ty_tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
arrow_1196572341e_indi: $tType ).
thf(ty_ty_tc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
list_A869418500_alt_o: $tType ).
thf(ty_ty_tc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oind,type,
list_A115096904_alt_o: $tType ).
thf(ty_ty_tc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyecc,type,
list_P811970973_alt_o: $tType ).
thf(ty_ty_tc__List__Olist_I_Eo_J,type,
list_o: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_J,type,
list_A1402527603le_alt: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_J,type,
list_A1206016470e_indi: $tType ).
thf(ty_ty_tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____piyec,type,
list_l1230899348le_alt: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Nat__Onat_J,type,
list_nat: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
list_P1402680776le_alt: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
list_P1338624854le_alt: $tType ).
thf(ty_ty_tc__Nat__Onat,type,
nat: $tType ).
thf(ty_ty_tc__prod_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
produc1182572821_alt_o: $tType ).
thf(ty_ty_tc__prod_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_062,type,
produc346017511_alt_o: $tType ).
thf(ty_ty_tc__prod_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__O,type,
produc563823143_alt_o: $tType ).
thf(ty_ty_tc__prod_I_Eo_M_Eo_J,type,
product_prod_o_o: $tType ).
thf(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_Mtc__Arrow__,type,
produc1572197287le_alt: $tType ).
thf(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_Mtc__Arrow_,type,
produc1723200057e_indi: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mirabelle____,type,
produc91324199_alt_o: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle____piyecc,type,
produc584853983_alt_o: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle,type,
produc324312073_alt_o: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_I_Eo_J_Mtc__List__Olist_I_Eo_J_J,type,
produc1191881495list_o: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
produc2069254453le_alt: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccggrh___001,type,
produc628564903e_indi: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
produc1458164519le_alt: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Nat__Onat_J_Mtc__List__Olist_Itc__Nat__Onat,type,
produc78950733st_nat: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____pi,type,
produc651043879le_alt: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__,type,
produc1474806439le_alt: $tType ).
thf(ty_ty_tc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J,type,
product_prod_nat_nat: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_Mt,type,
produc307320605le_alt: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____pi,type,
produc2139050425le_alt: $tType ).
%----Explicit typings (381)
thf(sy_c_All1,type,
all1: ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_All2,type,
all2: ( produc2069254453le_alt > $o ) > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_OIIA,type,
arrow_1955289568le_IIA: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_OLin,type,
arrow_1982173296le_Lin: ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_OProf,type,
arrow_1647925946e_Prof: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_Oabove,type,
arrow_556571452_above: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_Obelow,type,
arrow_1865170000_below: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_Odictator,type,
arrow_968343245ctator: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_Omkbot,type,
arrow_1821416136_mkbot: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_Omktop,type,
arrow_1970123222_mktop: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(sy_c_Arrow__Order__Mirabelle__piyeccggrh_Ounanimity,type,
arrow_1282657667nimity: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Ex1,type,
ex1: ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Ex2,type,
ex2: ( produc2069254453le_alt > $o ) > $o ).
thf(sy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_000t,type,
in_rel802931714le_alt: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(sy_c_FunDef_Oin__rel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piye,type,
in_rel1395039894le_alt: ( produc2069254453le_alt > $o ) > list_A1402527603le_alt > list_A1402527603le_alt > $o ).
thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O,type,
pi_Arr1865419731lt_o_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O_002,type,
pi_Arr620498146le_alt: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O_003,type,
pi_Arr470535441e_indi: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O_004,type,
pi_Arr1985384878_o_nat: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O_005,type,
pi_Arr634123665le_alt: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M,type,
pi_Arr1196397536_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_006,type,
pi_Arr1709554855lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_007,type,
pi_Arr1963576758le_alt: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_008,type,
pi_Arr272777533e_indi: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_009,type,
pi_Arr1012822146_o_nat: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_010,type,
pi_Arr507332541le_alt: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr,type,
pi_Pro386796690lt_o_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr_011,type,
pi_Pro198875553le_alt: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o ) > ( ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr_012,type,
pi_Pro2039443474e_indi: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr_013,type,
pi_Pro1597367533_o_nat: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > nat > $o ) > ( ( produc1572197287le_alt > $o ) > nat ) > $o ).
thf(sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr_014,type,
pi_Pro216985362le_alt: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o ) > ( ( produc1572197287le_alt > $o ) > produc2069254453le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000_Eo_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyecc,type,
pi_o_A1994447367_alt_o: ( $o > $o ) > ( $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_Eo_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
pi_o_A1479825007_alt_o: ( $o > $o ) > ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( $o > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_Eo_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____pi,type,
pi_o_P1417870404_alt_o: ( $o > $o ) > ( $o > ( produc1572197287le_alt > $o ) > $o ) > ( $o > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg,type,
pi_o_P728361163le_alt: ( $o > $o ) > ( $o > produc1572197287le_alt > $o ) > ( $o > produc1572197287le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_000_062_,type,
pi_Arr1191743126_alt_o: ( arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_000_062__015,type,
pi_Arr1349212320_alt_o: ( arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_000_062__016,type,
pi_Arr1480001013_alt_o: ( arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > ( produc1572197287le_alt > $o ) > $o ) > ( arrow_1389031998le_alt > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_000tc__p,type,
pi_Arr564047834le_alt: ( arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > produc1572197287le_alt > $o ) > ( arrow_1389031998le_alt > produc1572197287le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000_062,type,
pi_Arr583278353_alt_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000_062_017,type,
pi_Arr456308197_alt_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000_062_018,type,
pi_Arr1309696186_alt_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000tc__,type,
pi_Arr1762714837le_alt: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Nat__Onat_000_062_I_062_Itc__Arrow____Order____Mirabelle,type,
pi_nat1912012898_alt_o: ( nat > $o ) > ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Nat__Onat_000_062_Itc__Arrow____Order____Mirabelle____pi,type,
pi_nat1869411796_alt_o: ( nat > $o ) > ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( nat > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Nat__Onat_000_062_Itc__prod_Itc__Arrow____Order____Mirab,type,
pi_nat2104527145_alt_o: ( nat > $o ) > ( nat > ( produc1572197287le_alt > $o ) > $o ) > ( nat > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__prod_Itc__Arrow____Order____Mirabelle__,type,
pi_nat1240400806le_alt: ( nat > $o ) > ( nat > produc1572197287le_alt > $o ) > ( nat > produc1572197287le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oal,type,
pi_Pro418549519_alt_o: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oal_019,type,
pi_Pro39698462le_alt: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > arrow_1389031998le_alt > $o ) > ( produc1572197287le_alt > arrow_1389031998le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oal_020,type,
pi_Pro1246947541e_indi: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > arrow_1196572341e_indi > $o ) > ( produc1572197287le_alt > arrow_1196572341e_indi ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oal_021,type,
pi_Pro403816170lt_nat: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > nat > $o ) > ( produc1572197287le_alt > nat ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oal_022,type,
pi_Pro1816316757le_alt: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > produc2069254453le_alt > $o ) > ( produc1572197287le_alt > produc2069254453le_alt ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__,type,
pi_Pro1325670033_alt_o: ( produc2069254453le_alt > $o ) > ( produc2069254453le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___023,type,
pi_Pro1888753253_alt_o: ( produc2069254453le_alt > $o ) > ( produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___024,type,
pi_Pro986808634_alt_o: ( produc2069254453le_alt > $o ) > ( produc2069254453le_alt > ( produc1572197287le_alt > $o ) > $o ) > ( produc2069254453le_alt > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___025,type,
pi_Pro726541397le_alt: ( produc2069254453le_alt > $o ) > ( produc2069254453le_alt > produc1572197287le_alt > $o ) > ( produc2069254453le_alt > produc1572197287le_alt ) > $o ).
thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
minus_minus_nat: nat > nat > nat ).
thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
one_one_nat: nat ).
thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
plus_plus_nat: nat > nat > nat ).
thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
zero_zero_nat: nat ).
thf(sy_c_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Arrow____Order____Mirabell,type,
equal_1919384209le_alt: list_A1402527603le_alt > list_A1402527603le_alt > $o ).
thf(sy_c_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccg,type,
if_Pro1021494213le_alt: $o > produc2069254453le_alt > produc2069254453le_alt > produc2069254453le_alt ).
thf(sy_c_List_Oappend_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
append1134377438_alt_o: list_A869418500_alt_o > list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_Oappend_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_,type,
append592815960_alt_o: list_A115096904_alt_o > list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_Oappend_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg,type,
append1477507245_alt_o: list_P811970973_alt_o > list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_Oappend_000_Eo,type,
append_o: list_o > list_o > list_o ).
thf(sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
append1092755459le_alt: list_A1402527603le_alt > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
append478904880e_indi: list_A1206016470e_indi > list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_Oappend_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccg,type,
append453290350le_alt: list_l1230899348le_alt > list_l1230899348le_alt > list_l1230899348le_alt ).
thf(sy_c_List_Oappend_000tc__Nat__Onat,type,
append_nat: list_nat > list_nat > list_nat ).
thf(sy_c_List_Oappend_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa,type,
append1300326178le_alt: list_P1402680776le_alt > list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_Oappend_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
append1130570800le_alt: list_P1338624854le_alt > list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Obutlast_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh_,type,
butlas1946565607_alt_o: list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_Obutlast_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
butlas1110035599_alt_o: list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_Obutlast_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccg,type,
butlas1233216100_alt_o: list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_Obutlast_000_Eo,type,
butlast_o: list_o > list_o ).
thf(sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
butlas1188620858le_alt: list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
butlas1321092537e_indi: list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_Obutlast_000tc__Nat__Onat,type,
butlast_nat: list_nat > list_nat ).
thf(sy_c_List_Obutlast_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__O,type,
butlas732535467le_alt: list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_Obutlast_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle,type,
butlas1171206713le_alt: list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Odistinct_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
distin568845696_alt_o: list_A869418500_alt_o > $o ).
thf(sy_c_List_Odistinct_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oind,type,
distin19168822_alt_o: list_A115096904_alt_o > $o ).
thf(sy_c_List_Odistinct_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyecc,type,
distin299901067_alt_o: list_P811970973_alt_o > $o ).
thf(sy_c_List_Odistinct_000_Eo,type,
distinct_o: list_o > $o ).
thf(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
distin1149997281le_alt: list_A1402527603le_alt > $o ).
thf(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
distin1683769554e_indi: list_A1206016470e_indi > $o ).
thf(sy_c_List_Odistinct_000tc__Nat__Onat,type,
distinct_nat: list_nat > $o ).
thf(sy_c_List_Odistinct_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
distin1847856580le_alt: list_P1402680776le_alt > $o ).
thf(sy_c_List_Odistinct_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
distin1268295634le_alt: list_P1338624854le_alt > $o ).
thf(sy_c_List_OdropWhile_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggr,type,
dropWh1391670354_alt_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_OdropWhile_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oin,type,
dropWh370535908_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_OdropWhile_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyec,type,
dropWh1914665273_alt_o: ( ( produc1572197287le_alt > $o ) > $o ) > list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_OdropWhile_000_Eo,type,
dropWhile_o: ( $o > $o ) > list_o > list_o ).
thf(sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
dropWh82971279le_alt: ( arrow_1389031998le_alt > $o ) > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
dropWh927087268e_indi: ( arrow_1196572341e_indi > $o ) > list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_OdropWhile_000tc__Nat__Onat,type,
dropWhile_nat: ( nat > $o ) > list_nat > list_nat ).
thf(sy_c_List_OdropWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_,type,
dropWh751361942le_alt: ( produc1572197287le_alt > $o ) > list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_OdropWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
dropWh1319308964le_alt: ( produc2069254453le_alt > $o ) > list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Odrop_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oi,type,
drop_A2135190771_alt_o: nat > list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_Odrop_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_,type,
drop_A1073592963_alt_o: nat > list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_Odrop_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
drop_P1484576344_alt_o: nat > list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_Odrop_000_Eo,type,
drop_o: nat > list_o > list_o ).
thf(sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
drop_A112899118le_alt: nat > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
drop_A1363343557e_indi: nat > list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_Odrop_000tc__Nat__Onat,type,
drop_nat: nat > list_nat > list_nat ).
thf(sy_c_List_Odrop_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
drop_P1004899767le_alt: nat > list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_Odrop_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
drop_P2145219397le_alt: nat > list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Ohd_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oind,type,
hd_Arr447217824_alt_o: list_A869418500_alt_o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_c_List_Ohd_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_06,type,
hd_Arr871484182_alt_o: list_A115096904_alt_o > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(sy_c_List_Ohd_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
hd_Pro1487076715_alt_o: list_P811970973_alt_o > produc1572197287le_alt > $o ).
thf(sy_c_List_Ohd_000_Eo,type,
hd_o: list_o > $o ).
thf(sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
hd_Arr731872705le_alt: list_A1402527603le_alt > arrow_1389031998le_alt ).
thf(sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
hd_Arr790860786e_indi: list_A1206016470e_indi > arrow_1196572341e_indi ).
thf(sy_c_List_Ohd_000tc__Nat__Onat,type,
hd_nat: list_nat > nat ).
thf(sy_c_List_Ohd_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_M,type,
hd_Pro368662756le_alt: list_P1402680776le_alt > produc1572197287le_alt ).
thf(sy_c_List_Ohd_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____p,type,
hd_Pro1563575026le_alt: list_P1338624854le_alt > produc2069254453le_alt ).
thf(sy_c_List_Oinsert_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
insert889535645_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_Oinsert_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_,type,
insert425285465_alt_o: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_Oinsert_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg,type,
insert1316276270_alt_o: ( produc1572197287le_alt > $o ) > list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_Oinsert_000_Eo,type,
insert_o: $o > list_o > list_o ).
thf(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
insert886756100le_alt: arrow_1389031998le_alt > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
insert1241550703e_indi: arrow_1196572341e_indi > list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_Oinsert_000tc__Nat__Onat,type,
insert_nat: nat > list_nat > list_nat ).
thf(sy_c_List_Oinsert_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa,type,
insert1248101473le_alt: produc1572197287le_alt > list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_Oinsert_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
insert2040953583le_alt: produc2069254453le_alt > list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Olast_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oi,type,
last_A2082186202_alt_o: list_A869418500_alt_o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_c_List_Olast_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_,type,
last_A1346422876_alt_o: list_A115096904_alt_o > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(sy_c_List_Olast_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
last_P1550587825_alt_o: list_P811970973_alt_o > produc1572197287le_alt > $o ).
thf(sy_c_List_Olast_000_Eo,type,
last_o: list_o > $o ).
thf(sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
last_A2130988295le_alt: list_A1402527603le_alt > arrow_1389031998le_alt ).
thf(sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
last_A70817324e_indi: list_A1206016470e_indi > arrow_1196572341e_indi ).
thf(sy_c_List_Olast_000tc__Nat__Onat,type,
last_nat: list_nat > nat ).
thf(sy_c_List_Olast_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
last_P1727445790le_alt: list_P1402680776le_alt > produc1572197287le_alt ).
thf(sy_c_List_Olast_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
last_P438492716le_alt: list_P1338624854le_alt > produc2069254453le_alt ).
thf(sy_c_List_Olex_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
lex_Ar181706578le_alt: ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o ).
thf(sy_c_List_Olex_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
lex_li2097910111le_alt: ( produc2069254453le_alt > $o ) > produc1458164519le_alt > $o ).
thf(sy_c_List_Olexn_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
lexn_A1084034446le_alt: ( produc1572197287le_alt > $o ) > nat > produc2069254453le_alt > $o ).
thf(sy_c_List_Olexord_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
lexord1912481926_alt_o: ( produc1182572821_alt_o > $o ) > produc91324199_alt_o > $o ).
thf(sy_c_List_Olexord_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_,type,
lexord1942121136_alt_o: ( produc346017511_alt_o > $o ) > produc584853983_alt_o > $o ).
thf(sy_c_List_Olexord_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg,type,
lexord1707544581_alt_o: ( produc563823143_alt_o > $o ) > produc324312073_alt_o > $o ).
thf(sy_c_List_Olexord_000_Eo,type,
lexord_o: ( product_prod_o_o > $o ) > produc1191881495list_o > $o ).
thf(sy_c_List_Olexord_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
lexord1871768411le_alt: ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o ).
thf(sy_c_List_Olexord_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
lexord1428655320e_indi: ( produc1723200057e_indi > $o ) > produc628564903e_indi > $o ).
thf(sy_c_List_Olexord_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccg,type,
lexord1904689174le_alt: ( produc2069254453le_alt > $o ) > produc1458164519le_alt > $o ).
thf(sy_c_List_Olexord_000tc__Nat__Onat,type,
lexord_nat: ( product_prod_nat_nat > $o ) > produc78950733st_nat > $o ).
thf(sy_c_List_Olexord_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa,type,
lexord572715466le_alt: ( produc307320605le_alt > $o ) > produc651043879le_alt > $o ).
thf(sy_c_List_Olexord_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
lexord1680143064le_alt: ( produc2139050425le_alt > $o ) > produc1474806439le_alt > $o ).
thf(sy_c_List_Olist_OCons_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccgg,type,
cons_A1087586947_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_Olist_OCons_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oi,type,
cons_A160405747_alt_o: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_Olist_OCons_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piye,type,
cons_P2104327368_alt_o: ( produc1572197287le_alt > $o ) > list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_Olist_OCons_000_Eo,type,
cons_o: $o > list_o > list_o ).
thf(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
cons_A1142416030le_alt: arrow_1389031998le_alt > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
cons_A430007893e_indi: arrow_1196572341e_indi > list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_Olist_OCons_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piy,type,
cons_l2069870355le_alt: list_A1402527603le_alt > list_l1230899348le_alt > list_l1230899348le_alt ).
thf(sy_c_List_Olist_OCons_000tc__Nat__Onat,type,
cons_nat: nat > list_nat > list_nat ).
thf(sy_c_List_Olist_OCons_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
cons_P1984625479le_alt: produc1572197287le_alt > list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_Olist_OCons_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe,type,
cons_P607717589le_alt: produc2069254453le_alt > list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Olist_ONil_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggr,type,
nil_Ar1062052403_alt_o: list_A869418500_alt_o ).
thf(sy_c_List_Olist_ONil_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oin,type,
nil_Ar26350915_alt_o: list_A115096904_alt_o ).
thf(sy_c_List_Olist_ONil_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyec,type,
nil_Pr893112600_alt_o: list_P811970973_alt_o ).
thf(sy_c_List_Olist_ONil_000_Eo,type,
nil_o: list_o ).
thf(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
nil_Ar52383470le_alt: list_A1402527603le_alt ).
thf(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
nil_Ar147131909e_indi: list_A1206016470e_indi ).
thf(sy_c_List_Olist_ONil_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piye,type,
nil_li1194575555le_alt: list_l1230899348le_alt ).
thf(sy_c_List_Olist_ONil_000tc__Nat__Onat,type,
nil_nat: list_nat ).
thf(sy_c_List_Olist_ONil_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_,type,
nil_Pr932422391le_alt: list_P1402680776le_alt ).
thf(sy_c_List_Olist_ONil_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
nil_Pr1072539781le_alt: list_P1338624854le_alt ).
thf(sy_c_List_Olist_Olist__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
list_c1300280951le_alt: list_A1402527603le_alt > ( arrow_1389031998le_alt > list_A1402527603le_alt > list_A1402527603le_alt ) > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Olist__update_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
list_u976150870le_alt: list_A1402527603le_alt > nat > arrow_1389031998le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Olistrel1_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
listre830192455le_alt: ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o ).
thf(sy_c_List_Olistrel1_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyec,type,
listre2055328042le_alt: ( produc2069254453le_alt > $o ) > produc1458164519le_alt > $o ).
thf(sy_c_List_Olistrel_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
listre686844950le_alt: ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o ).
thf(sy_c_List_Olistrel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyecc,type,
listre2057938843le_alt: ( produc2069254453le_alt > $o ) > produc1458164519le_alt > $o ).
thf(sy_c_List_Olistrelp_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
listre2126835016le_alt: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > list_A1402527603le_alt > list_A1402527603le_alt > $o ).
thf(sy_c_List_Olistrelp_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyec,type,
listre103969769le_alt: ( list_A1402527603le_alt > list_A1402527603le_alt > $o ) > list_l1230899348le_alt > list_l1230899348le_alt > $o ).
thf(sy_c_List_Omaps_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_000tc__Ar,type,
maps_A2106577089le_alt: ( arrow_1389031998le_alt > list_A1402527603le_alt ) > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
null_A287154422le_alt: list_A1402527603le_alt > $o ).
thf(sy_c_List_Opartition_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
partit253767143le_alt: ( arrow_1389031998le_alt > $o ) > list_A1402527603le_alt > produc2069254453le_alt ).
thf(sy_c_List_Oreplicate_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
replic277728168le_alt: nat > arrow_1389031998le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Orev_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oin,type,
rev_Ar813866963_alt_o: list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_Orev_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_0,type,
rev_Ar710647715_alt_o: list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_Orev_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_,type,
rev_Pr1871457144_alt_o: list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_Orev_000_Eo,type,
rev_o: list_o > list_o ).
thf(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
rev_Ar2020079950le_alt: list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
rev_Ar268893093e_indi: list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_Orev_000tc__Nat__Onat,type,
rev_nat: list_nat > list_nat ).
thf(sy_c_List_Orev_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_,type,
rev_Pr1287360663le_alt: list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_Orev_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
rev_Pr178923045le_alt: list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Orotate1_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
rotate1249022267le_alt: list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Oset_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oin,type,
set_Ar17109714_alt_o: list_A869418500_alt_o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_List_Oset_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_0,type,
set_Ar868233060_alt_o: list_A115096904_alt_o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_List_Oset_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_,type,
set_Pr1457060537_alt_o: list_P811970973_alt_o > ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_List_Oset_000_Eo,type,
set_o: list_o > $o > $o ).
thf(sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
set_Ar1491127311le_alt: list_A1402527603le_alt > arrow_1389031998le_alt > $o ).
thf(sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
set_Ar545511716e_indi: list_A1206016470e_indi > arrow_1196572341e_indi > $o ).
thf(sy_c_List_Oset_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
set_li919271010le_alt: list_l1230899348le_alt > list_A1402527603le_alt > $o ).
thf(sy_c_List_Oset_000tc__Nat__Onat,type,
set_nat: list_nat > nat > $o ).
thf(sy_c_List_Oset_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_,type,
set_Pr1596096022le_alt: list_P1402680776le_alt > produc1572197287le_alt > $o ).
thf(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
set_Pr1119022372le_alt: list_P1338624854le_alt > produc2069254453le_alt > $o ).
thf(sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
splice287087809le_alt: list_A1402527603le_alt > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_OtakeWhile_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggr,type,
takeWh1686115066_alt_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_OtakeWhile_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oin,type,
takeWh2122498364_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_OtakeWhile_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyec,type,
takeWh432906385_alt_o: ( ( produc1572197287le_alt > $o ) > $o ) > list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_OtakeWhile_000_Eo,type,
takeWhile_o: ( $o > $o ) > list_o > list_o ).
thf(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
takeWh462480871le_alt: ( arrow_1389031998le_alt > $o ) > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
takeWh598881612e_indi: ( arrow_1196572341e_indi > $o ) > list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_OtakeWhile_000tc__Nat__Onat,type,
takeWhile_nat: ( nat > $o ) > list_nat > list_nat ).
thf(sy_c_List_OtakeWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_,type,
takeWh373185086le_alt: ( produc1572197287le_alt > $o ) > list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_OtakeWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
takeWh131124556le_alt: ( produc2069254453le_alt > $o ) > list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Otake_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oi,type,
take_A1941683275_alt_o: nat > list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_Otake_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_,type,
take_A1888368939_alt_o: nat > list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_Otake_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
take_P1700987136_alt_o: nat > list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_Otake_000_Eo,type,
take_o: nat > list_o > list_o ).
thf(sy_c_List_Otake_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
take_A1527720662le_alt: nat > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Otake_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
take_A146025501e_indi: nat > list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_Otake_000tc__Nat__Onat,type,
take_nat: nat > list_nat > list_nat ).
thf(sy_c_List_Otake_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
take_P124862735le_alt: nat > list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_Otake_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
take_P295428765le_alt: nat > list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_List_Otl_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oind,type,
tl_Arr678695324_alt_o: list_A869418500_alt_o > list_A869418500_alt_o ).
thf(sy_c_List_Otl_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_06,type,
tl_Arr2000946458_alt_o: list_A115096904_alt_o > list_A115096904_alt_o ).
thf(sy_c_List_Otl_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
tl_Pro452506991_alt_o: list_P811970973_alt_o > list_P811970973_alt_o ).
thf(sy_c_List_Otl_000_Eo,type,
tl_o: list_o > list_o ).
thf(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
tl_Arr1379124165le_alt: list_A1402527603le_alt > list_A1402527603le_alt ).
thf(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
tl_Arr1940180718e_indi: list_A1206016470e_indi > list_A1206016470e_indi ).
thf(sy_c_List_Otl_000tc__Nat__Onat,type,
tl_nat: list_nat > list_nat ).
thf(sy_c_List_Otl_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_M,type,
tl_Pro1003672544le_alt: list_P1402680776le_alt > list_P1402680776le_alt ).
thf(sy_c_List_Otl_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____p,type,
tl_Pro7578606le_alt: list_P1338624854le_alt > list_P1338624854le_alt ).
thf(sy_c_Nat_OSuc,type,
suc: nat > nat ).
thf(sy_c_Nat_Onat_Onat__case_000_Eo,type,
nat_case_o: $o > ( nat > $o ) > nat > $o ).
thf(sy_c_Nat_Onat_Onat__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
nat_ca1434653759le_alt: list_A1402527603le_alt > ( nat > list_A1402527603le_alt ) > nat > list_A1402527603le_alt ).
thf(sy_c_Nat_Onat_Onat__case_000tc__Nat__Onat,type,
nat_case_nat: nat > ( nat > nat ) > nat > nat ).
thf(sy_c_Nat_Onat_Onat__size,type,
nat_size: nat > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
size_s1146069981le_alt: list_A1402527603le_alt > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Or,type,
size_s1667586986le_alt: list_l1230899348le_alt > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__Nat__Onat,type,
size_size_nat: nat > nat ).
thf(sy_c_Order__Relation_Ostrict__linear__order__on_000tc__Arrow____Order____Mirabel,type,
order_762106470le_alt: ( arrow_1389031998le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
ord_less_nat: nat > nat > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Arrow____Order____,type,
ord_le1805007862lt_o_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Arrow____Order____Mirabe,type,
ord_le602483040lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__prod_Itc__Arrow____Order,type,
ord_le1027220427lt_o_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_Eo_M_Eo_J,type,
ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle___,type,
ord_le1423491573_alt_o: ( arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle____026,type,
ord_le865407012indi_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__Arrow____Order____Mi,type,
ord_le962286258_alt_o: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Arr,type,
ord_le2064394532_alt_o: ( produc2069254453le_alt > $o ) > ( produc2069254453le_alt > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
ord_less_eq_o: $o > $o > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(sy_c_Orderings_Oord__class_Omin_000tc__Nat__Onat,type,
ord_min_nat: nat > nat > nat ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_I_062_Itc__Arrow____Order____Mirab,type,
top_to1492351398lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__Arrow____Order____Mirabelle__,type,
top_to732317616lt_o_o: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__prod_Itc__Arrow____Order____M,type,
top_to1806834203lt_o_o: ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_I_Eo_M_Eo_J,type,
top_top_o_o: $o > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____piye,type,
top_to1031852101_alt_o: arrow_1389031998le_alt > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____piye_027,type,
top_to54564308indi_o: arrow_1196572341e_indi > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Nat__Onat_M_Eo_J,type,
top_top_nat_o: nat > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__Arrow____Order____Mirabel,type,
top_to558618722_alt_o: produc1572197287le_alt > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow___,type,
top_to1489741524_alt_o: produc2069254453le_alt > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_Eo,type,
top_top_o: $o ).
thf(sy_c_Product__Type_OPair_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyec,type,
produc1729571083_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc1182572821_alt_o ).
thf(sy_c_Product__Type_OPair_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh_,type,
produc843458519_alt_o: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc346017511_alt_o ).
thf(sy_c_Product__Type_OPair_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____p,type,
produc1739106583_alt_o: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > produc563823143_alt_o ).
thf(sy_c_Product__Type_OPair_000_Eo_000_Eo,type,
product_Pair_o_o: $o > $o > product_prod_o_o ).
thf(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_,type,
produc897867031le_alt: arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt ).
thf(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
produc381140399e_indi: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1723200057e_indi ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_I_062_I_062_Itc__Arrow____Order____M,type,
produc1459025175_alt_o: list_A869418500_alt_o > list_A869418500_alt_o > produc91324199_alt_o ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_I_062_Itc__Arrow____Order____Mirabel,type,
produc1670706773_alt_o: list_A115096904_alt_o > list_A115096904_alt_o > produc584853983_alt_o ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order_,type,
produc1859089279_alt_o: list_P811970973_alt_o > list_P811970973_alt_o > produc324312073_alt_o ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_I_Eo_J_000tc__List__Olist_I_Eo_J,type,
produc1835210381list_o: list_o > list_o > produc1191881495list_o ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
produc1014865963le_alt: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_____028,type,
produc1625955351e_indi: list_A1206016470e_indi > list_A1206016470e_indi > produc628564903e_indi ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order,type,
produc110512663le_alt: list_l1230899348le_alt > list_l1230899348le_alt > produc1458164519le_alt ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Nat__Onat_J_000tc__List__Olist_,type,
produc1869962435st_nat: list_nat > list_nat > produc78950733st_nat ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mir,type,
produc2092721559le_alt: list_P1402680776le_alt > list_P1402680776le_alt > produc651043879le_alt ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arro,type,
produc535661975le_alt: list_P1338624854le_alt > list_P1338624854le_alt > produc1474806439le_alt ).
thf(sy_c_Product__Type_OPair_000tc__Nat__Onat_000tc__Nat__Onat,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccg,type,
produc2131135379le_alt: produc1572197287le_alt > produc1572197287le_alt > produc307320605le_alt ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mir,type,
produc310818479le_alt: produc2069254453le_alt > produc2069254453le_alt > produc2139050425le_alt ).
thf(sy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
produc1084757966_alt_o: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
produc28228666_alt_o: ( produc2069254453le_alt > $o ) > list_A1402527603le_alt > list_A1402527603le_alt > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____029,type,
produc1300022634le_alt: ( produc2069254453le_alt > produc2069254453le_alt ) > list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt ).
thf(sy_c_Product__Type_Ointernal__split_000tc__Arrow____Order____Mirabelle____piyecc,type,
produc403413048_alt_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__Arrow____Order____Mi,type,
produc1014699392le_alt: ( list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt ) > produc2069254453le_alt > produc2069254453le_alt ).
thf(sy_c_Product__Type_Omap__pair_000tc__List__Olist_Itc__Arrow____Order____Mirabell,type,
produc1315215393le_alt: ( list_A1402527603le_alt > list_A1402527603le_alt ) > ( list_A1402527603le_alt > list_A1402527603le_alt ) > produc2069254453le_alt > produc2069254453le_alt ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____piyec,type,
produc443852560lt_o_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o > $o ) > produc1572197287le_alt > $o > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____piyec_030,type,
produc1662252097_alt_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > produc1572197287le_alt > arrow_1389031998le_alt > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____piyec_031,type,
produc1718776024indi_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1196572341e_indi > $o ) > produc1572197287le_alt > arrow_1196572341e_indi > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____piyec_032,type,
produc147560437_nat_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > nat > $o ) > produc1572197287le_alt > nat > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____piyec_033,type,
produc1563188184_alt_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > produc2069254453le_alt > $o ) > produc1572197287le_alt > produc2069254453le_alt > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____piyec_034,type,
produc536934701_alt_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M,type,
produc1628065942lt_o_o: ( list_A1402527603le_alt > list_A1402527603le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > produc2069254453le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_035,type,
produc1882479808lt_o_o: ( list_A1402527603le_alt > list_A1402527603le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_036,type,
produc123184939lt_o_o: ( list_A1402527603le_alt > list_A1402527603le_alt > ( produc1572197287le_alt > $o ) > $o ) > produc2069254453le_alt > ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_037,type,
produc2042681170_alt_o: ( list_A1402527603le_alt > list_A1402527603le_alt > produc1572197287le_alt > $o ) > produc2069254453le_alt > produc1572197287le_alt > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_038,type,
produc236889881_alt_o: ( list_A1402527603le_alt > list_A1402527603le_alt > $o ) > produc2069254453le_alt > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_039,type,
produc1712983243le_alt: ( list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt ) > produc2069254453le_alt > produc2069254453le_alt ).
thf(sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
collec670126350_alt_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_,type,
collec979749928_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Set_OCollect_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg,type,
collec958969213_alt_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
collec1655747795le_alt: ( arrow_1389031998le_alt > $o ) > arrow_1389031998le_alt > $o ).
thf(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
collec1936859488e_indi: ( arrow_1196572341e_indi > $o ) > arrow_1196572341e_indi > $o ).
thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa,type,
collec940901970le_alt: ( produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__Arrow____Order____Mirabelle____piyeccgg,type,
transi1182735211le_alt: ( produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__List__Olist_Itc__Arrow____Order____Mira,type,
transi264395782le_alt: ( produc2069254453le_alt > $o ) > produc2069254453le_alt > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__List__Olist_Itc__List__Olist_Itc__Arrow,type,
transi452343361le_alt: ( produc1458164519le_alt > $o ) > produc1458164519le_alt > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Arrow____Order____Mirabelle__,type,
transi1571931578le_alt: ( produc307320605le_alt > $o ) > produc307320605le_alt > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Arrow____Ord,type,
transi1916231368le_alt: ( produc2139050425le_alt > $o ) > produc2139050425le_alt > $o ).
thf(sy_c_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccggrh__O,type,
fequal68576820le_alt: list_A1402527603le_alt > list_A1402527603le_alt > $o ).
thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
member1346253567lt_o_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh___040,type,
member610734222le_alt: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh___041,type,
member1539010427e_indi: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh___042,type,
member901499098_o_nat: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh___043,type,
member886874491le_alt: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_,type,
member1425217232_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi__044,type,
member1696373143lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi__045,type,
member449992486le_alt: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi__046,type,
member1186582243e_indi: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi__047,type,
member1278554994_o_nat: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi__048,type,
member1883481315le_alt: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg,type,
member1925470338lt_o_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( ( produc1572197287le_alt > $o ) > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg_049,type,
member376345105le_alt: ( ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > ( ( ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg_050,type,
member1830244024e_indi: ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > ( ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg_051,type,
member2133235421_o_nat: ( ( produc1572197287le_alt > $o ) > nat ) > ( ( ( produc1572197287le_alt > $o ) > nat ) > $o ) > $o ).
thf(sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg_052,type,
member1122245944le_alt: ( ( produc1572197287le_alt > $o ) > produc2069254453le_alt ) > ( ( ( produc1572197287le_alt > $o ) > produc2069254453le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_I_Eo_M_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccg,type,
member161783341_alt_o: ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_Eo_M_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O,type,
member984757343_alt_o: ( $o > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( $o > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_Eo_M_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piy,type,
member1495989556_alt_o: ( $o > produc1572197287le_alt > $o ) > ( ( $o > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_I_Eo_Mtc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr,type,
member1158049649le_alt: ( $o > produc1572197287le_alt ) > ( ( $o > produc1572197287le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_M_062_I,type,
member308341436_alt_o: ( arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_M_062_I_053,type,
member1941085840_alt_o: ( arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_M_062_I_054,type,
member636776165_alt_o: ( arrow_1389031998le_alt > produc1572197287le_alt > $o ) > ( ( arrow_1389031998le_alt > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_Mtc__pr,type,
member85184128le_alt: ( arrow_1389031998le_alt > produc1572197287le_alt ) > ( ( arrow_1389031998le_alt > produc1572197287le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_062_,type,
member1521294075_alt_o: ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_062__055,type,
member2071265553_alt_o: ( arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_062__056,type,
member822980838_alt_o: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_Mtc__p,type,
member232085823le_alt: ( arrow_1196572341e_indi > produc1572197287le_alt ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Nat__Onat_M_062_I_062_Itc__Arrow____Order____Mirabelle_,type,
member1908242824_alt_o: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Nat__Onat_M_062_Itc__Arrow____Order____Mirabelle____piy,type,
member1899388612_alt_o: ( nat > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( nat > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Nat__Onat_M_062_Itc__prod_Itc__Arrow____Order____Mirabe,type,
member1425970457_alt_o: ( nat > produc1572197287le_alt > $o ) > ( ( nat > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Nat__Onat_Mtc__prod_Itc__Arrow____Order____Mirabelle___,type,
member57786188le_alt: ( nat > produc1572197287le_alt ) > ( ( nat > produc1572197287le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa,type,
member1241905979_alt_o: ( produc1572197287le_alt > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa_057,type,
member1662126282le_alt: ( produc1572197287le_alt > arrow_1389031998le_alt ) > ( ( produc1572197287le_alt > arrow_1389031998le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa_058,type,
member1074431551e_indi: ( produc1572197287le_alt > arrow_1196572341e_indi ) > ( ( produc1572197287le_alt > arrow_1196572341e_indi ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa_059,type,
member1516223254lt_nat: ( produc1572197287le_alt > nat ) > ( ( produc1572197287le_alt > nat ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa_060,type,
member707457599le_alt: ( produc1572197287le_alt > produc2069254453le_alt ) > ( ( produc1572197287le_alt > produc2069254453le_alt ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
member1082283899_alt_o: ( produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__061,type,
member1452893329_alt_o: ( produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__062,type,
member1248875622_alt_o: ( produc2069254453le_alt > produc1572197287le_alt > $o ) > ( ( produc2069254453le_alt > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__063,type,
member41375167le_alt: ( produc2069254453le_alt > produc1572197287le_alt ) > ( ( produc2069254453le_alt > produc1572197287le_alt ) > $o ) > $o ).
thf(sy_c_member_000_Eo,type,
member_o: $o > ( $o > $o ) > $o ).
thf(sy_c_member_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt,type,
member998036369le_alt: arrow_1389031998le_alt > ( arrow_1389031998le_alt > $o ) > $o ).
thf(sy_c_member_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
member1818997282e_indi: arrow_1196572341e_indi > ( arrow_1196572341e_indi > $o ) > $o ).
thf(sy_c_member_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____piyeccggrh__O,type,
member285423712le_alt: list_A1402527603le_alt > ( list_A1402527603le_alt > $o ) > $o ).
thf(sy_c_member_000tc__Nat__Onat,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(sy_c_member_000tc__prod_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccgg,type,
member599543554_alt_o: produc1182572821_alt_o > ( produc1182572821_alt_o > $o ) > $o ).
thf(sy_c_member_000tc__prod_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oi,type,
member135324756_alt_o: produc346017511_alt_o > ( produc346017511_alt_o > $o ) > $o ).
thf(sy_c_member_000tc__prod_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piye,type,
member1958570644_alt_o: produc563823143_alt_o > ( produc563823143_alt_o > $o ) > $o ).
thf(sy_c_member_000tc__prod_I_Eo_M_Eo_J,type,
member1392690260od_o_o: product_prod_o_o > ( product_prod_o_o > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_Mtc,type,
member285112084le_alt: produc1572197287le_alt > ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_Mt,type,
member1871294246e_indi: produc1723200057e_indi > ( produc1723200057e_indi > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mira,type,
member995889556_alt_o: produc91324199_alt_o > ( produc91324199_alt_o > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle_,type,
member405332940_alt_o: produc584853983_alt_o > ( produc584853983_alt_o > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____,type,
member1189996790_alt_o: produc324312073_alt_o > ( produc324312073_alt_o > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_I_Eo_J_Mtc__List__Olist_I_Eo_J_J,type,
member806300420list_o: produc1191881495list_o > ( produc1191881495list_o > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____piy,type,
member735418658le_alt: produc2069254453le_alt > ( produc2069254453le_alt > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____piy_064,type,
member1903641876e_indi: produc628564903e_indi > ( produc628564903e_indi > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order___,type,
member104660884le_alt: produc1458164519le_alt > ( produc1458164519le_alt > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Nat__Onat_J_Mtc__List__Olist_Itc__,type,
member910422074st_nat: produc78950733st_nat > ( produc78950733st_nat > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabe,type,
member778872212le_alt: produc651043879le_alt > ( produc651043879le_alt > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow__,type,
member198626580le_alt: produc1474806439le_alt > ( produc1474806439le_alt > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J,type,
member232255508at_nat: product_prod_nat_nat > ( product_prod_nat_nat > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh,type,
member894661642le_alt: produc307320605le_alt > ( produc307320605le_alt > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe,type,
member1253537702le_alt: produc2139050425le_alt > ( produc2139050425le_alt > $o ) > $o ).
thf(sy_v_F,type,
f: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_v_P_H____,type,
p_1: arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(sy_v_P____,type,
p: arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(sy_v_a____,type,
a: arrow_1389031998le_alt ).
thf(sy_v_b____,type,
b: arrow_1389031998le_alt ).
thf(sy_v_c____,type,
c: arrow_1389031998le_alt ).
%----Relevant facts (1200)
thf(fact_0__096P_A_058_AProf_096,axiom,
member822980838_alt_o @ p @ arrow_1647925946e_Prof ).
thf(fact_1_assms_I3_J,axiom,
arrow_1955289568le_IIA @ f ).
thf(fact_2_u,axiom,
arrow_1282657667nimity @ f ).
thf(fact_3__096a_A_126_061_Ab_096,axiom,
a != b ).
thf(fact_4_dist,axiom,
distin1149997281le_alt @ ( cons_A1142416030le_alt @ a @ ( cons_A1142416030le_alt @ b @ ( cons_A1142416030le_alt @ c @ nil_Ar52383470le_alt ) ) ) ).
thf(fact_5_iff,axiom,
! [I: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ ( p @ I ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ b @ a ) @ ( p_1 @ I ) ) ) ).
thf(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_,axiom,
~ ! [C_6: arrow_1389031998le_alt] :
~ ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ a @ ( cons_A1142416030le_alt @ b @ ( cons_A1142416030le_alt @ C_6 @ nil_Ar52383470le_alt ) ) ) ) ).
thf(fact_7__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096,axiom,
( member822980838_alt_o
@ ^ [P_50: arrow_1196572341e_indi] : ( arrow_1865170000_below @ ( arrow_1865170000_below @ ( p @ P_50 ) @ c @ b ) @ b @ a )
@ arrow_1647925946e_Prof ) ).
thf(fact_8__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_,axiom,
( member822980838_alt_o
@ ^ [P_50: arrow_1196572341e_indi] : ( arrow_1865170000_below @ ( arrow_1865170000_below @ ( arrow_1865170000_below @ ( p @ P_50 ) @ c @ b ) @ b @ a ) @ a @ c )
@ arrow_1647925946e_Prof ) ).
thf(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
( member822980838_alt_o
@ ^ [P_50: arrow_1196572341e_indi] : ( arrow_1865170000_below @ ( p @ P_50 ) @ c @ b )
@ arrow_1647925946e_Prof ) ).
thf(fact_10_in__mkbot,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o,Z: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_1821416136_mkbot @ L_4 @ Z ) )
<=> ( ( Y != Z )
& ( ( X = Z )
=> ( X != Y ) )
& ( ( X != Z )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_4 ) ) ) ) ).
thf(fact_11_in__mktop,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o,Z: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_1970123222_mktop @ L_4 @ Z ) )
<=> ( ( X != Z )
& ( ( Y = Z )
=> ( X != Y ) )
& ( ( Y != Z )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_4 ) ) ) ) ).
thf(fact_12_in__below,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o,A: arrow_1389031998le_alt,B: arrow_1389031998le_alt] :
( ( A != B )
=> ( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_1865170000_below @ L_4 @ A @ B ) )
<=> ( ( X != Y )
& ( ( Y = A )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ B ) @ L_4 ) )
& ( ( Y != A )
=> ( ( ( X = A )
=> ( ( Y = B )
| ( member285112084le_alt @ ( produc897867031le_alt @ B @ Y ) @ L_4 ) ) )
& ( ( X != A )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_4 ) ) ) ) ) ) ) ) ).
thf(fact_13_split__paired__All,axiom,
! [P_53: produc2069254453le_alt > $o] :
( ( all2 @ P_53 )
<=> ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] : ( P_53 @ ( produc1014865963le_alt @ A_14 @ B_10 ) ) ) ).
thf(fact_14_split__paired__All,axiom,
! [P_53: produc1572197287le_alt > $o] :
( ( all1 @ P_53 )
<=> ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] : ( P_53 @ ( produc897867031le_alt @ A_14 @ B_10 ) ) ) ).
thf(fact_15_Pair__eq,axiom,
! [A_54: list_A1402527603le_alt,B_41: list_A1402527603le_alt,A_53: list_A1402527603le_alt,B_40: list_A1402527603le_alt] :
( ( ( produc1014865963le_alt @ A_54 @ B_41 )
= ( produc1014865963le_alt @ A_53 @ B_40 ) )
<=> ( ( A_54 = A_53 )
& ( B_41 = B_40 ) ) ) ).
thf(fact_16_Pair__eq,axiom,
! [A_54: arrow_1389031998le_alt,B_41: arrow_1389031998le_alt,A_53: arrow_1389031998le_alt,B_40: arrow_1389031998le_alt] :
( ( ( produc897867031le_alt @ A_54 @ B_41 )
= ( produc897867031le_alt @ A_53 @ B_40 ) )
<=> ( ( A_54 = A_53 )
& ( B_41 = B_40 ) ) ) ).
thf(fact_17_Pair__inject,axiom,
! [A_52: list_A1402527603le_alt,B_39: list_A1402527603le_alt,A_51: list_A1402527603le_alt,B_38: list_A1402527603le_alt] :
( ( ( produc1014865963le_alt @ A_52 @ B_39 )
= ( produc1014865963le_alt @ A_51 @ B_38 ) )
=> ~ ( ( A_52 = A_51 )
=> ( B_39 != B_38 ) ) ) ).
thf(fact_18_Pair__inject,axiom,
! [A_52: arrow_1389031998le_alt,B_39: arrow_1389031998le_alt,A_51: arrow_1389031998le_alt,B_38: arrow_1389031998le_alt] :
( ( ( produc897867031le_alt @ A_52 @ B_39 )
= ( produc897867031le_alt @ A_51 @ B_38 ) )
=> ~ ( ( A_52 = A_51 )
=> ( B_39 != B_38 ) ) ) ).
thf(fact_19_in__rel__def,axiom,
! [R_65: produc2069254453le_alt > $o,X_110: list_A1402527603le_alt,Y_41: list_A1402527603le_alt] :
( ( in_rel1395039894le_alt @ R_65 @ X_110 @ Y_41 )
<=> ( member735418658le_alt @ ( produc1014865963le_alt @ X_110 @ Y_41 ) @ R_65 ) ) ).
thf(fact_20_in__rel__def,axiom,
! [R_65: produc1572197287le_alt > $o,X_110: arrow_1389031998le_alt,Y_41: arrow_1389031998le_alt] :
( ( in_rel802931714le_alt @ R_65 @ X_110 @ Y_41 )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ X_110 @ Y_41 ) @ R_65 ) ) ).
thf(fact_21_below__Lin,axiom,
! [L_4: produc1572197287le_alt > $o,X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt] :
( ( X != Y )
=> ( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( member1241905979_alt_o @ ( arrow_1865170000_below @ L_4 @ X @ Y ) @ arrow_1982173296le_Lin ) ) ) ).
thf(fact_22__096P_H_A_058_AProf_096,axiom,
member822980838_alt_o @ p_1 @ arrow_1647925946e_Prof ).
thf(fact_23__C1_C,axiom,
! [P_52: arrow_1196572341e_indi > produc1572197287le_alt > $o,P_51: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_50: arrow_1389031998le_alt,B_37: arrow_1389031998le_alt,A_49: arrow_1389031998le_alt,B_36: arrow_1389031998le_alt] :
( ( A_49 != B_36 )
=> ( ( A_50 != B_37 )
=> ( ( A_49 != B_37 )
=> ( ( B_36 != A_50 )
=> ( ( member822980838_alt_o @ P_51 @ arrow_1647925946e_Prof )
=> ( ( member822980838_alt_o @ P_52 @ arrow_1647925946e_Prof )
=> ( ! [I: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_49 @ B_36 ) @ ( P_51 @ I ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_50 @ B_37 ) @ ( P_52 @ I ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_49 @ B_36 ) @ ( f @ P_51 ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_50 @ B_37 ) @ ( f @ P_52 ) ) ) ) ) ) ) ) ) ) ).
thf(fact_24__C2_C,axiom,
! [P_52: arrow_1196572341e_indi > produc1572197287le_alt > $o,P_51: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_50: arrow_1389031998le_alt,B_37: arrow_1389031998le_alt,A_49: arrow_1389031998le_alt,B_36: arrow_1389031998le_alt] :
( ( A_49 != B_36 )
=> ( ( A_50 != B_37 )
=> ( ( A_49 != B_37 )
=> ( ( B_36 != A_50 )
=> ( ( member822980838_alt_o @ P_51 @ arrow_1647925946e_Prof )
=> ( ( member822980838_alt_o @ P_52 @ arrow_1647925946e_Prof )
=> ( ! [I: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_49 @ B_36 ) @ ( P_51 @ I ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_50 @ B_37 ) @ ( P_52 @ I ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_49 @ B_36 ) @ ( f @ P_51 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_50 @ B_37 ) @ ( f @ P_52 ) ) ) ) ) ) ) ) ) ) ).
thf(fact_25_assms_I1_J,axiom,
( member1425217232_alt_o @ f
@ ( pi_Arr1196397536_alt_o @ arrow_1647925946e_Prof
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : arrow_1982173296le_Lin ) ) ).
thf(fact_26_const__Lin__Prof,axiom,
! [L_4: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( member822980838_alt_o
@ ^ [P_50: arrow_1196572341e_indi] : L_4
@ arrow_1647925946e_Prof ) ) ).
thf(fact_27_mkbot__Lin,axiom,
! [X: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( member1241905979_alt_o @ ( arrow_1821416136_mkbot @ L_4 @ X ) @ arrow_1982173296le_Lin ) ) ).
thf(fact_28_mktop__Lin,axiom,
! [X: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( member1241905979_alt_o @ ( arrow_1970123222_mktop @ L_4 @ X ) @ arrow_1982173296le_Lin ) ) ).
thf(fact_29_Lin__irrefl,axiom,
! [A: arrow_1389031998le_alt,B: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A @ B ) @ L_4 )
=> ~ ( member285112084le_alt @ ( produc897867031le_alt @ B @ A ) @ L_4 ) ) ) ).
thf(fact_30_notin__Lin__iff,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( ( X != Y )
=> ( ~ ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_4 )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ Y @ X ) @ L_4 ) ) ) ) ).
thf(fact_31_third__alt,axiom,
! [A: arrow_1389031998le_alt,B: arrow_1389031998le_alt] :
( ( A != B )
=> ? [C_6: arrow_1389031998le_alt] : ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ A @ ( cons_A1142416030le_alt @ B @ ( cons_A1142416030le_alt @ C_6 @ nil_Ar52383470le_alt ) ) ) ) ) ).
thf(fact_32_IIA__def,axiom,
! [F_22: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( arrow_1955289568le_IIA @ F_22 )
<=> ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ arrow_1647925946e_Prof )
=> ! [Xa: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ Xa @ arrow_1647925946e_Prof )
=> ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ! [I: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( X_1 @ I ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( Xa @ I ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( F_22 @ X_1 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( F_22 @ Xa ) ) ) ) ) ) ) ).
thf(fact_33_unanimity__def,axiom,
! [F_22: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( arrow_1282657667nimity @ F_22 )
<=> ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ arrow_1647925946e_Prof )
=> ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ! [I: arrow_1196572341e_indi] : ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( X_1 @ I ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( F_22 @ X_1 ) ) ) ) ) ).
thf(fact_34_complete__Lin,axiom,
! [A: arrow_1389031998le_alt,B: arrow_1389031998le_alt] :
( ( A != B )
=> ? [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ arrow_1982173296le_Lin )
& ( member285112084le_alt @ ( produc897867031le_alt @ A @ B ) @ X_1 ) ) ) ).
thf(fact_35_in__above,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o,A: arrow_1389031998le_alt,B: arrow_1389031998le_alt] :
( ( A != B )
=> ( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_556571452_above @ L_4 @ A @ B ) )
<=> ( ( X != Y )
& ( ( X = B )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A @ Y ) @ L_4 ) )
& ( ( X != B )
=> ( ( ( Y = B )
=> ( ( X = A )
| ( member285112084le_alt @ ( produc897867031le_alt @ X @ A ) @ L_4 ) ) )
& ( ( Y != B )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_4 ) ) ) ) ) ) ) ) ).
thf(fact_36_distinct_Osimps_I1_J,axiom,
distin1149997281le_alt @ nil_Ar52383470le_alt ).
thf(fact_37_list_Osimps_I2_J,axiom,
! [A_48: arrow_1389031998le_alt,List_5: list_A1402527603le_alt] :
( nil_Ar52383470le_alt
!= ( cons_A1142416030le_alt @ A_48 @ List_5 ) ) ).
thf(fact_38_list_Osimps_I3_J,axiom,
! [A_47: arrow_1389031998le_alt,List_4: list_A1402527603le_alt] :
( ( cons_A1142416030le_alt @ A_47 @ List_4 )
!= nil_Ar52383470le_alt ) ).
thf(fact_39_alt3,axiom,
? [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt,C_6: arrow_1389031998le_alt] : ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ A_14 @ ( cons_A1142416030le_alt @ B_10 @ ( cons_A1142416030le_alt @ C_6 @ nil_Ar52383470le_alt ) ) ) ) ).
thf(fact_40_linear__alt,axiom,
? [L_5: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ L_5 @ arrow_1982173296le_Lin ) ).
thf(fact_41_dictator__def,axiom,
! [F_22: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,I_1: arrow_1196572341e_indi] :
( ( arrow_968343245ctator @ F_22 @ I_1 )
<=> ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ arrow_1647925946e_Prof )
=> ( ( F_22 @ X_1 )
= ( X_1 @ I_1 ) ) ) ) ).
thf(fact_42_list_Oinject,axiom,
! [A_46: arrow_1389031998le_alt,List_3: list_A1402527603le_alt,A_45: arrow_1389031998le_alt,List_2: list_A1402527603le_alt] :
( ( ( cons_A1142416030le_alt @ A_46 @ List_3 )
= ( cons_A1142416030le_alt @ A_45 @ List_2 ) )
<=> ( ( A_46 = A_45 )
& ( List_3 = List_2 ) ) ) ).
thf(fact_43_not__Cons__self2,axiom,
! [X_109: arrow_1389031998le_alt,Xs_165: list_A1402527603le_alt] :
( ( cons_A1142416030le_alt @ X_109 @ Xs_165 )
!= Xs_165 ) ).
thf(fact_44_not__Cons__self,axiom,
! [Xs_164: list_A1402527603le_alt,X_108: arrow_1389031998le_alt] :
( Xs_164
!= ( cons_A1142416030le_alt @ X_108 @ Xs_164 ) ) ).
thf(fact_45_above__Lin,axiom,
! [L_4: produc1572197287le_alt > $o,X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt] :
( ( X != Y )
=> ( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( member1241905979_alt_o @ ( arrow_556571452_above @ L_4 @ X @ Y ) @ arrow_1982173296le_Lin ) ) ) ).
thf(fact_46_dictatorI,axiom,
! [I_1: arrow_1196572341e_indi,F_22: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ F_22
@ ( pi_Arr1196397536_alt_o @ arrow_1647925946e_Prof
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : arrow_1982173296le_Lin ) )
=> ( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ arrow_1647925946e_Prof )
=> ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( A_14 != B_10 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( X_1 @ I_1 ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( F_22 @ X_1 ) ) ) ) )
=> ( arrow_968343245ctator @ F_22 @ I_1 ) ) ) ).
thf(fact_47_PiE,axiom,
! [X_107: produc1572197287le_alt,F_21: produc1572197287le_alt > $o,A_44: produc1572197287le_alt > $o,B_35: produc1572197287le_alt > $o > $o] :
( ( member1241905979_alt_o @ F_21 @ ( pi_Pro418549519_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member285112084le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_48_PiE,axiom,
! [X_107: nat,F_21: nat > produc1572197287le_alt,A_44: nat > $o,B_35: nat > produc1572197287le_alt > $o] :
( ( member57786188le_alt @ F_21 @ ( pi_nat1240400806le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member285112084le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member_nat @ X_107 @ A_44 ) ) ) ).
thf(fact_49_PiE,axiom,
! [X_107: produc2069254453le_alt,F_21: produc2069254453le_alt > produc1572197287le_alt,A_44: produc2069254453le_alt > $o,B_35: produc2069254453le_alt > produc1572197287le_alt > $o] :
( ( member41375167le_alt @ F_21 @ ( pi_Pro726541397le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member285112084le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member735418658le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_50_PiE,axiom,
! [X_107: arrow_1389031998le_alt,F_21: arrow_1389031998le_alt > produc1572197287le_alt,A_44: arrow_1389031998le_alt > $o,B_35: arrow_1389031998le_alt > produc1572197287le_alt > $o] :
( ( member85184128le_alt @ F_21 @ ( pi_Arr564047834le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member285112084le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member998036369le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_51_PiE,axiom,
! [X_107: arrow_1196572341e_indi,F_21: arrow_1196572341e_indi > produc1572197287le_alt,A_44: arrow_1196572341e_indi > $o,B_35: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member232085823le_alt @ F_21 @ ( pi_Arr1762714837le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member285112084le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1818997282e_indi @ X_107 @ A_44 ) ) ) ).
thf(fact_52_PiE,axiom,
! [X_107: $o,F_21: $o > produc1572197287le_alt,A_44: $o > $o,B_35: $o > produc1572197287le_alt > $o] :
( ( member1158049649le_alt @ F_21 @ ( pi_o_P728361163le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member285112084le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member_o @ X_107 @ A_44 ) ) ) ).
thf(fact_53_PiE,axiom,
! [X_107: nat,F_21: nat > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_44: nat > $o,B_35: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1899388612_alt_o @ F_21 @ ( pi_nat1869411796_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member822980838_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member_nat @ X_107 @ A_44 ) ) ) ).
thf(fact_54_PiE,axiom,
! [X_107: produc2069254453le_alt,F_21: produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_44: produc2069254453le_alt > $o,B_35: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1452893329_alt_o @ F_21 @ ( pi_Pro1888753253_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member822980838_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member735418658le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_55_PiE,axiom,
! [X_107: arrow_1389031998le_alt,F_21: arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_44: arrow_1389031998le_alt > $o,B_35: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1941085840_alt_o @ F_21 @ ( pi_Arr1349212320_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member822980838_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member998036369le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_56_PiE,axiom,
! [X_107: arrow_1196572341e_indi,F_21: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_44: arrow_1196572341e_indi > $o,B_35: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2071265553_alt_o @ F_21 @ ( pi_Arr456308197_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member822980838_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1818997282e_indi @ X_107 @ A_44 ) ) ) ).
thf(fact_57_PiE,axiom,
! [X_107: $o,F_21: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_44: $o > $o,B_35: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member984757343_alt_o @ F_21 @ ( pi_o_A1479825007_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member822980838_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member_o @ X_107 @ A_44 ) ) ) ).
thf(fact_58_PiE,axiom,
! [X_107: nat,F_21: nat > produc1572197287le_alt > $o,A_44: nat > $o,B_35: nat > ( produc1572197287le_alt > $o ) > $o] :
( ( member1425970457_alt_o @ F_21 @ ( pi_nat2104527145_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member_nat @ X_107 @ A_44 ) ) ) ).
thf(fact_59_PiE,axiom,
! [X_107: produc2069254453le_alt,F_21: produc2069254453le_alt > produc1572197287le_alt > $o,A_44: produc2069254453le_alt > $o,B_35: produc2069254453le_alt > ( produc1572197287le_alt > $o ) > $o] :
( ( member1248875622_alt_o @ F_21 @ ( pi_Pro986808634_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member735418658le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_60_PiE,axiom,
! [X_107: arrow_1389031998le_alt,F_21: arrow_1389031998le_alt > produc1572197287le_alt > $o,A_44: arrow_1389031998le_alt > $o,B_35: arrow_1389031998le_alt > ( produc1572197287le_alt > $o ) > $o] :
( ( member636776165_alt_o @ F_21 @ ( pi_Arr1480001013_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member998036369le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_61_PiE,axiom,
! [X_107: $o,F_21: $o > produc1572197287le_alt > $o,A_44: $o > $o,B_35: $o > ( produc1572197287le_alt > $o ) > $o] :
( ( member1495989556_alt_o @ F_21 @ ( pi_o_P1417870404_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member_o @ X_107 @ A_44 ) ) ) ).
thf(fact_62_PiE,axiom,
! [X_107: nat,F_21: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_44: nat > $o,B_35: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1908242824_alt_o @ F_21 @ ( pi_nat1912012898_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1425217232_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member_nat @ X_107 @ A_44 ) ) ) ).
thf(fact_63_PiE,axiom,
! [X_107: produc2069254453le_alt,F_21: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_44: produc2069254453le_alt > $o,B_35: produc2069254453le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1082283899_alt_o @ F_21 @ ( pi_Pro1325670033_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1425217232_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member735418658le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_64_PiE,axiom,
! [X_107: arrow_1389031998le_alt,F_21: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_44: arrow_1389031998le_alt > $o,B_35: arrow_1389031998le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member308341436_alt_o @ F_21 @ ( pi_Arr1191743126_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1425217232_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member998036369le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_65_PiE,axiom,
! [X_107: arrow_1196572341e_indi,F_21: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_44: arrow_1196572341e_indi > $o,B_35: arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1521294075_alt_o @ F_21 @ ( pi_Arr583278353_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1425217232_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1818997282e_indi @ X_107 @ A_44 ) ) ) ).
thf(fact_66_PiE,axiom,
! [X_107: $o,F_21: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_44: $o > $o,B_35: $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member161783341_alt_o @ F_21 @ ( pi_o_A1994447367_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1425217232_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member_o @ X_107 @ A_44 ) ) ) ).
thf(fact_67_PiE,axiom,
! [X_107: produc1572197287le_alt,F_21: produc1572197287le_alt > nat,A_44: produc1572197287le_alt > $o,B_35: produc1572197287le_alt > nat > $o] :
( ( member1516223254lt_nat @ F_21 @ ( pi_Pro403816170lt_nat @ A_44 @ B_35 ) )
=> ( ~ ( member_nat @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member285112084le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_68_PiE,axiom,
! [X_107: produc1572197287le_alt,F_21: produc1572197287le_alt > produc2069254453le_alt,A_44: produc1572197287le_alt > $o,B_35: produc1572197287le_alt > produc2069254453le_alt > $o] :
( ( member707457599le_alt @ F_21 @ ( pi_Pro1816316757le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member735418658le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member285112084le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_69_PiE,axiom,
! [X_107: produc1572197287le_alt,F_21: produc1572197287le_alt > arrow_1389031998le_alt,A_44: produc1572197287le_alt > $o,B_35: produc1572197287le_alt > arrow_1389031998le_alt > $o] :
( ( member1662126282le_alt @ F_21 @ ( pi_Pro39698462le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member998036369le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member285112084le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_70_PiE,axiom,
! [X_107: produc1572197287le_alt,F_21: produc1572197287le_alt > arrow_1196572341e_indi,A_44: produc1572197287le_alt > $o,B_35: produc1572197287le_alt > arrow_1196572341e_indi > $o] :
( ( member1074431551e_indi @ F_21 @ ( pi_Pro1246947541e_indi @ A_44 @ B_35 ) )
=> ( ~ ( member1818997282e_indi @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member285112084le_alt @ X_107 @ A_44 ) ) ) ).
thf(fact_71_PiE,axiom,
! [X_107: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat,A_44: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat > $o] :
( ( member1278554994_o_nat @ F_21 @ ( pi_Arr1012822146_o_nat @ A_44 @ B_35 ) )
=> ( ~ ( member_nat @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member822980838_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_72_PiE,axiom,
! [X_107: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt,A_44: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o] :
( ( member1883481315le_alt @ F_21 @ ( pi_Arr507332541le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member735418658le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member822980838_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_73_PiE,axiom,
! [X_107: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_44: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o] :
( ( member449992486le_alt @ F_21 @ ( pi_Arr1963576758le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member998036369le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member822980838_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_74_PiE,axiom,
! [X_107: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_44: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1186582243e_indi @ F_21 @ ( pi_Arr272777533e_indi @ A_44 @ B_35 ) )
=> ( ~ ( member1818997282e_indi @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member822980838_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_75_PiE,axiom,
! [X_107: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_44: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o] :
( ( member1696373143lt_o_o @ F_21 @ ( pi_Arr1709554855lt_o_o @ A_44 @ B_35 ) )
=> ( ~ ( member_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member822980838_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_76_PiE,axiom,
! [X_107: produc1572197287le_alt > $o,F_21: ( produc1572197287le_alt > $o ) > nat,A_44: ( produc1572197287le_alt > $o ) > $o,B_35: ( produc1572197287le_alt > $o ) > nat > $o] :
( ( member2133235421_o_nat @ F_21 @ ( pi_Pro1597367533_o_nat @ A_44 @ B_35 ) )
=> ( ~ ( member_nat @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1241905979_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_77_PiE,axiom,
! [X_107: produc1572197287le_alt > $o,F_21: ( produc1572197287le_alt > $o ) > produc2069254453le_alt,A_44: ( produc1572197287le_alt > $o ) > $o,B_35: ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o] :
( ( member1122245944le_alt @ F_21 @ ( pi_Pro216985362le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member735418658le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1241905979_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_78_PiE,axiom,
! [X_107: produc1572197287le_alt > $o,F_21: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_44: ( produc1572197287le_alt > $o ) > $o,B_35: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o] :
( ( member376345105le_alt @ F_21 @ ( pi_Pro198875553le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member998036369le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1241905979_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_79_PiE,axiom,
! [X_107: produc1572197287le_alt > $o,F_21: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_44: ( produc1572197287le_alt > $o ) > $o,B_35: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1830244024e_indi @ F_21 @ ( pi_Pro2039443474e_indi @ A_44 @ B_35 ) )
=> ( ~ ( member1818997282e_indi @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1241905979_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_80_PiE,axiom,
! [X_107: produc1572197287le_alt > $o,F_21: ( produc1572197287le_alt > $o ) > $o,A_44: ( produc1572197287le_alt > $o ) > $o,B_35: ( produc1572197287le_alt > $o ) > $o > $o] :
( ( member1925470338lt_o_o @ F_21 @ ( pi_Pro386796690lt_o_o @ A_44 @ B_35 ) )
=> ( ~ ( member_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1241905979_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_81_PiE,axiom,
! [X_107: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat,A_44: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_35: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat > $o] :
( ( member901499098_o_nat @ F_21 @ ( pi_Arr1985384878_o_nat @ A_44 @ B_35 ) )
=> ( ~ ( member_nat @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1425217232_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_82_PiE,axiom,
! [X_107: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt,A_44: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_35: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o] :
( ( member886874491le_alt @ F_21 @ ( pi_Arr634123665le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member735418658le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1425217232_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_83_PiE,axiom,
! [X_107: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_44: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_35: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o] :
( ( member610734222le_alt @ F_21 @ ( pi_Arr620498146le_alt @ A_44 @ B_35 ) )
=> ( ~ ( member998036369le_alt @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1425217232_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_84_PiE,axiom,
! [X_107: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_44: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_35: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1539010427e_indi @ F_21 @ ( pi_Arr470535441e_indi @ A_44 @ B_35 ) )
=> ( ~ ( member1818997282e_indi @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1425217232_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_85_PiE,axiom,
! [X_107: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_44: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_35: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o] :
( ( member1346253567lt_o_o @ F_21 @ ( pi_Arr1865419731lt_o_o @ A_44 @ B_35 ) )
=> ( ~ ( member_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1425217232_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_86_PiE,axiom,
! [X_107: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_44: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ F_21 @ ( pi_Arr1196397536_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member822980838_alt_o @ X_107 @ A_44 ) ) ) ).
thf(fact_87_PiE,axiom,
! [X_107: arrow_1196572341e_indi,F_21: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_44: arrow_1196572341e_indi > $o,B_35: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ F_21 @ ( pi_Arr1309696186_alt_o @ A_44 @ B_35 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_21 @ X_107 ) @ ( B_35 @ X_107 ) )
=> ~ ( member1818997282e_indi @ X_107 @ A_44 ) ) ) ).
thf(fact_88_list_Oexhaust,axiom,
! [Y_40: list_A1402527603le_alt] :
( ( Y_40 != nil_Ar52383470le_alt )
=> ~ ! [A_14: arrow_1389031998le_alt,List_1: list_A1402527603le_alt] :
( Y_40
!= ( cons_A1142416030le_alt @ A_14 @ List_1 ) ) ) ).
thf(fact_89_neq__Nil__conv,axiom,
! [Xs_163: list_A1402527603le_alt] :
( ( Xs_163 != nil_Ar52383470le_alt )
<=> ? [Y_10: arrow_1389031998le_alt,Ys: list_A1402527603le_alt] :
( Xs_163
= ( cons_A1142416030le_alt @ Y_10 @ Ys ) ) ) ).
thf(fact_90_funcset__mem,axiom,
! [X_106: produc1572197287le_alt,F_20: produc1572197287le_alt > $o,A_43: produc1572197287le_alt > $o,B_34: $o > $o] :
( ( member1241905979_alt_o @ F_20
@ ( pi_Pro418549519_alt_o @ A_43
@ ^ [Uu: produc1572197287le_alt] : B_34 ) )
=> ( ( member285112084le_alt @ X_106 @ A_43 )
=> ( member_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_91_funcset__mem,axiom,
! [X_106: produc1572197287le_alt,F_20: produc1572197287le_alt > nat,A_43: produc1572197287le_alt > $o,B_34: nat > $o] :
( ( member1516223254lt_nat @ F_20
@ ( pi_Pro403816170lt_nat @ A_43
@ ^ [Uu: produc1572197287le_alt] : B_34 ) )
=> ( ( member285112084le_alt @ X_106 @ A_43 )
=> ( member_nat @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_92_funcset__mem,axiom,
! [X_106: produc1572197287le_alt,F_20: produc1572197287le_alt > produc2069254453le_alt,A_43: produc1572197287le_alt > $o,B_34: produc2069254453le_alt > $o] :
( ( member707457599le_alt @ F_20
@ ( pi_Pro1816316757le_alt @ A_43
@ ^ [Uu: produc1572197287le_alt] : B_34 ) )
=> ( ( member285112084le_alt @ X_106 @ A_43 )
=> ( member735418658le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_93_funcset__mem,axiom,
! [X_106: produc1572197287le_alt,F_20: produc1572197287le_alt > arrow_1389031998le_alt,A_43: produc1572197287le_alt > $o,B_34: arrow_1389031998le_alt > $o] :
( ( member1662126282le_alt @ F_20
@ ( pi_Pro39698462le_alt @ A_43
@ ^ [Uu: produc1572197287le_alt] : B_34 ) )
=> ( ( member285112084le_alt @ X_106 @ A_43 )
=> ( member998036369le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_94_funcset__mem,axiom,
! [X_106: produc1572197287le_alt,F_20: produc1572197287le_alt > arrow_1196572341e_indi,A_43: produc1572197287le_alt > $o,B_34: arrow_1196572341e_indi > $o] :
( ( member1074431551e_indi @ F_20
@ ( pi_Pro1246947541e_indi @ A_43
@ ^ [Uu: produc1572197287le_alt] : B_34 ) )
=> ( ( member285112084le_alt @ X_106 @ A_43 )
=> ( member1818997282e_indi @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_95_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat,A_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_34: nat > $o] :
( ( member1278554994_o_nat @ F_20
@ ( pi_Arr1012822146_o_nat @ A_43
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member822980838_alt_o @ X_106 @ A_43 )
=> ( member_nat @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_96_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt,A_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_34: produc2069254453le_alt > $o] :
( ( member1883481315le_alt @ F_20
@ ( pi_Arr507332541le_alt @ A_43
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member822980838_alt_o @ X_106 @ A_43 )
=> ( member735418658le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_97_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_34: arrow_1389031998le_alt > $o] :
( ( member449992486le_alt @ F_20
@ ( pi_Arr1963576758le_alt @ A_43
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member822980838_alt_o @ X_106 @ A_43 )
=> ( member998036369le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_98_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_34: arrow_1196572341e_indi > $o] :
( ( member1186582243e_indi @ F_20
@ ( pi_Arr272777533e_indi @ A_43
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member822980838_alt_o @ X_106 @ A_43 )
=> ( member1818997282e_indi @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_99_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_34: $o > $o] :
( ( member1696373143lt_o_o @ F_20
@ ( pi_Arr1709554855lt_o_o @ A_43
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member822980838_alt_o @ X_106 @ A_43 )
=> ( member_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_100_funcset__mem,axiom,
! [X_106: produc1572197287le_alt > $o,F_20: ( produc1572197287le_alt > $o ) > nat,A_43: ( produc1572197287le_alt > $o ) > $o,B_34: nat > $o] :
( ( member2133235421_o_nat @ F_20
@ ( pi_Pro1597367533_o_nat @ A_43
@ ^ [Uu: produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1241905979_alt_o @ X_106 @ A_43 )
=> ( member_nat @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_101_funcset__mem,axiom,
! [X_106: produc1572197287le_alt > $o,F_20: ( produc1572197287le_alt > $o ) > produc2069254453le_alt,A_43: ( produc1572197287le_alt > $o ) > $o,B_34: produc2069254453le_alt > $o] :
( ( member1122245944le_alt @ F_20
@ ( pi_Pro216985362le_alt @ A_43
@ ^ [Uu: produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1241905979_alt_o @ X_106 @ A_43 )
=> ( member735418658le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_102_funcset__mem,axiom,
! [X_106: produc1572197287le_alt > $o,F_20: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_43: ( produc1572197287le_alt > $o ) > $o,B_34: arrow_1389031998le_alt > $o] :
( ( member376345105le_alt @ F_20
@ ( pi_Pro198875553le_alt @ A_43
@ ^ [Uu: produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1241905979_alt_o @ X_106 @ A_43 )
=> ( member998036369le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_103_funcset__mem,axiom,
! [X_106: produc1572197287le_alt > $o,F_20: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_43: ( produc1572197287le_alt > $o ) > $o,B_34: arrow_1196572341e_indi > $o] :
( ( member1830244024e_indi @ F_20
@ ( pi_Pro2039443474e_indi @ A_43
@ ^ [Uu: produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1241905979_alt_o @ X_106 @ A_43 )
=> ( member1818997282e_indi @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_104_funcset__mem,axiom,
! [X_106: produc1572197287le_alt > $o,F_20: ( produc1572197287le_alt > $o ) > $o,A_43: ( produc1572197287le_alt > $o ) > $o,B_34: $o > $o] :
( ( member1925470338lt_o_o @ F_20
@ ( pi_Pro386796690lt_o_o @ A_43
@ ^ [Uu: produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1241905979_alt_o @ X_106 @ A_43 )
=> ( member_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_105_funcset__mem,axiom,
! [X_106: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat,A_43: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_34: nat > $o] :
( ( member901499098_o_nat @ F_20
@ ( pi_Arr1985384878_o_nat @ A_43
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1425217232_alt_o @ X_106 @ A_43 )
=> ( member_nat @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_106_funcset__mem,axiom,
! [X_106: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt,A_43: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_34: produc2069254453le_alt > $o] :
( ( member886874491le_alt @ F_20
@ ( pi_Arr634123665le_alt @ A_43
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1425217232_alt_o @ X_106 @ A_43 )
=> ( member735418658le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_107_funcset__mem,axiom,
! [X_106: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_43: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_34: arrow_1389031998le_alt > $o] :
( ( member610734222le_alt @ F_20
@ ( pi_Arr620498146le_alt @ A_43
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1425217232_alt_o @ X_106 @ A_43 )
=> ( member998036369le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_108_funcset__mem,axiom,
! [X_106: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_43: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_34: arrow_1196572341e_indi > $o] :
( ( member1539010427e_indi @ F_20
@ ( pi_Arr470535441e_indi @ A_43
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1425217232_alt_o @ X_106 @ A_43 )
=> ( member1818997282e_indi @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_109_funcset__mem,axiom,
! [X_106: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_43: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_34: $o > $o] :
( ( member1346253567lt_o_o @ F_20
@ ( pi_Arr1865419731lt_o_o @ A_43
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member1425217232_alt_o @ X_106 @ A_43 )
=> ( member_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_110_funcset__mem,axiom,
! [X_106: nat,F_20: nat > produc1572197287le_alt,A_43: nat > $o,B_34: produc1572197287le_alt > $o] :
( ( member57786188le_alt @ F_20
@ ( pi_nat1240400806le_alt @ A_43
@ ^ [Uu: nat] : B_34 ) )
=> ( ( member_nat @ X_106 @ A_43 )
=> ( member285112084le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_111_funcset__mem,axiom,
! [X_106: produc2069254453le_alt,F_20: produc2069254453le_alt > produc1572197287le_alt,A_43: produc2069254453le_alt > $o,B_34: produc1572197287le_alt > $o] :
( ( member41375167le_alt @ F_20
@ ( pi_Pro726541397le_alt @ A_43
@ ^ [Uu: produc2069254453le_alt] : B_34 ) )
=> ( ( member735418658le_alt @ X_106 @ A_43 )
=> ( member285112084le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_112_funcset__mem,axiom,
! [X_106: arrow_1389031998le_alt,F_20: arrow_1389031998le_alt > produc1572197287le_alt,A_43: arrow_1389031998le_alt > $o,B_34: produc1572197287le_alt > $o] :
( ( member85184128le_alt @ F_20
@ ( pi_Arr564047834le_alt @ A_43
@ ^ [Uu: arrow_1389031998le_alt] : B_34 ) )
=> ( ( member998036369le_alt @ X_106 @ A_43 )
=> ( member285112084le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_113_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > produc1572197287le_alt,A_43: arrow_1196572341e_indi > $o,B_34: produc1572197287le_alt > $o] :
( ( member232085823le_alt @ F_20
@ ( pi_Arr1762714837le_alt @ A_43
@ ^ [Uu: arrow_1196572341e_indi] : B_34 ) )
=> ( ( member1818997282e_indi @ X_106 @ A_43 )
=> ( member285112084le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_114_funcset__mem,axiom,
! [X_106: $o,F_20: $o > produc1572197287le_alt,A_43: $o > $o,B_34: produc1572197287le_alt > $o] :
( ( member1158049649le_alt @ F_20
@ ( pi_o_P728361163le_alt @ A_43
@ ^ [Uu: $o] : B_34 ) )
=> ( ( member_o @ X_106 @ A_43 )
=> ( member285112084le_alt @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_115_funcset__mem,axiom,
! [X_106: nat,F_20: nat > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_43: nat > $o,B_34: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1899388612_alt_o @ F_20
@ ( pi_nat1869411796_alt_o @ A_43
@ ^ [Uu: nat] : B_34 ) )
=> ( ( member_nat @ X_106 @ A_43 )
=> ( member822980838_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_116_funcset__mem,axiom,
! [X_106: produc2069254453le_alt,F_20: produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_43: produc2069254453le_alt > $o,B_34: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1452893329_alt_o @ F_20
@ ( pi_Pro1888753253_alt_o @ A_43
@ ^ [Uu: produc2069254453le_alt] : B_34 ) )
=> ( ( member735418658le_alt @ X_106 @ A_43 )
=> ( member822980838_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_117_funcset__mem,axiom,
! [X_106: arrow_1389031998le_alt,F_20: arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_43: arrow_1389031998le_alt > $o,B_34: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1941085840_alt_o @ F_20
@ ( pi_Arr1349212320_alt_o @ A_43
@ ^ [Uu: arrow_1389031998le_alt] : B_34 ) )
=> ( ( member998036369le_alt @ X_106 @ A_43 )
=> ( member822980838_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_118_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_43: arrow_1196572341e_indi > $o,B_34: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2071265553_alt_o @ F_20
@ ( pi_Arr456308197_alt_o @ A_43
@ ^ [Uu: arrow_1196572341e_indi] : B_34 ) )
=> ( ( member1818997282e_indi @ X_106 @ A_43 )
=> ( member822980838_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_119_funcset__mem,axiom,
! [X_106: $o,F_20: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_43: $o > $o,B_34: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member984757343_alt_o @ F_20
@ ( pi_o_A1479825007_alt_o @ A_43
@ ^ [Uu: $o] : B_34 ) )
=> ( ( member_o @ X_106 @ A_43 )
=> ( member822980838_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_120_funcset__mem,axiom,
! [X_106: nat,F_20: nat > produc1572197287le_alt > $o,A_43: nat > $o,B_34: ( produc1572197287le_alt > $o ) > $o] :
( ( member1425970457_alt_o @ F_20
@ ( pi_nat2104527145_alt_o @ A_43
@ ^ [Uu: nat] : B_34 ) )
=> ( ( member_nat @ X_106 @ A_43 )
=> ( member1241905979_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_121_funcset__mem,axiom,
! [X_106: produc2069254453le_alt,F_20: produc2069254453le_alt > produc1572197287le_alt > $o,A_43: produc2069254453le_alt > $o,B_34: ( produc1572197287le_alt > $o ) > $o] :
( ( member1248875622_alt_o @ F_20
@ ( pi_Pro986808634_alt_o @ A_43
@ ^ [Uu: produc2069254453le_alt] : B_34 ) )
=> ( ( member735418658le_alt @ X_106 @ A_43 )
=> ( member1241905979_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_122_funcset__mem,axiom,
! [X_106: arrow_1389031998le_alt,F_20: arrow_1389031998le_alt > produc1572197287le_alt > $o,A_43: arrow_1389031998le_alt > $o,B_34: ( produc1572197287le_alt > $o ) > $o] :
( ( member636776165_alt_o @ F_20
@ ( pi_Arr1480001013_alt_o @ A_43
@ ^ [Uu: arrow_1389031998le_alt] : B_34 ) )
=> ( ( member998036369le_alt @ X_106 @ A_43 )
=> ( member1241905979_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_123_funcset__mem,axiom,
! [X_106: $o,F_20: $o > produc1572197287le_alt > $o,A_43: $o > $o,B_34: ( produc1572197287le_alt > $o ) > $o] :
( ( member1495989556_alt_o @ F_20
@ ( pi_o_P1417870404_alt_o @ A_43
@ ^ [Uu: $o] : B_34 ) )
=> ( ( member_o @ X_106 @ A_43 )
=> ( member1241905979_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_124_funcset__mem,axiom,
! [X_106: nat,F_20: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_43: nat > $o,B_34: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1908242824_alt_o @ F_20
@ ( pi_nat1912012898_alt_o @ A_43
@ ^ [Uu: nat] : B_34 ) )
=> ( ( member_nat @ X_106 @ A_43 )
=> ( member1425217232_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_125_funcset__mem,axiom,
! [X_106: produc2069254453le_alt,F_20: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_43: produc2069254453le_alt > $o,B_34: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1082283899_alt_o @ F_20
@ ( pi_Pro1325670033_alt_o @ A_43
@ ^ [Uu: produc2069254453le_alt] : B_34 ) )
=> ( ( member735418658le_alt @ X_106 @ A_43 )
=> ( member1425217232_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_126_funcset__mem,axiom,
! [X_106: arrow_1389031998le_alt,F_20: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_43: arrow_1389031998le_alt > $o,B_34: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member308341436_alt_o @ F_20
@ ( pi_Arr1191743126_alt_o @ A_43
@ ^ [Uu: arrow_1389031998le_alt] : B_34 ) )
=> ( ( member998036369le_alt @ X_106 @ A_43 )
=> ( member1425217232_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_127_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_43: arrow_1196572341e_indi > $o,B_34: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1521294075_alt_o @ F_20
@ ( pi_Arr583278353_alt_o @ A_43
@ ^ [Uu: arrow_1196572341e_indi] : B_34 ) )
=> ( ( member1818997282e_indi @ X_106 @ A_43 )
=> ( member1425217232_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_128_funcset__mem,axiom,
! [X_106: $o,F_20: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_43: $o > $o,B_34: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member161783341_alt_o @ F_20
@ ( pi_o_A1994447367_alt_o @ A_43
@ ^ [Uu: $o] : B_34 ) )
=> ( ( member_o @ X_106 @ A_43 )
=> ( member1425217232_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_129_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_34: ( produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ F_20
@ ( pi_Arr1196397536_alt_o @ A_43
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_34 ) )
=> ( ( member822980838_alt_o @ X_106 @ A_43 )
=> ( member1241905979_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_130_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_43: arrow_1196572341e_indi > $o,B_34: ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ F_20
@ ( pi_Arr1309696186_alt_o @ A_43
@ ^ [Uu: arrow_1196572341e_indi] : B_34 ) )
=> ( ( member1818997282e_indi @ X_106 @ A_43 )
=> ( member1241905979_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(fact_131_splice_Osimps_I2_J,axiom,
! [V_4: arrow_1389031998le_alt,Va: list_A1402527603le_alt] :
( ( splice287087809le_alt @ ( cons_A1142416030le_alt @ V_4 @ Va ) @ nil_Ar52383470le_alt )
= ( cons_A1142416030le_alt @ V_4 @ Va ) ) ).
thf(fact_132_list_Osimps_I4_J,axiom,
! [F1_3: list_A1402527603le_alt,F2_1: arrow_1389031998le_alt > list_A1402527603le_alt > list_A1402527603le_alt] :
( ( list_c1300280951le_alt @ F1_3 @ F2_1 @ nil_Ar52383470le_alt )
= F1_3 ) ).
thf(fact_133_list_Osimps_I5_J,axiom,
! [F1_2: list_A1402527603le_alt,F2: arrow_1389031998le_alt > list_A1402527603le_alt > list_A1402527603le_alt,A_42: arrow_1389031998le_alt,List: list_A1402527603le_alt] :
( ( list_c1300280951le_alt @ F1_2 @ F2 @ ( cons_A1142416030le_alt @ A_42 @ List ) )
= ( F2 @ A_42 @ List ) ) ).
thf(fact_134_split__paired__Ex,axiom,
! [P_49: produc2069254453le_alt > $o] :
( ( ex2 @ P_49 )
<=> ? [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] : ( P_49 @ ( produc1014865963le_alt @ A_14 @ B_10 ) ) ) ).
thf(fact_135_split__paired__Ex,axiom,
! [P_49: produc1572197287le_alt > $o] :
( ( ex1 @ P_49 )
<=> ? [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] : ( P_49 @ ( produc897867031le_alt @ A_14 @ B_10 ) ) ) ).
thf(fact_136_splice_Osimps_I3_J,axiom,
! [X_105: arrow_1389031998le_alt,Xs_162: list_A1402527603le_alt,Y_39: arrow_1389031998le_alt,Ys_66: list_A1402527603le_alt] :
( ( splice287087809le_alt @ ( cons_A1142416030le_alt @ X_105 @ Xs_162 ) @ ( cons_A1142416030le_alt @ Y_39 @ Ys_66 ) )
= ( cons_A1142416030le_alt @ X_105 @ ( cons_A1142416030le_alt @ Y_39 @ ( splice287087809le_alt @ Xs_162 @ Ys_66 ) ) ) ) ).
thf(fact_137_splice_Osimps_I1_J,axiom,
! [Ys_65: list_A1402527603le_alt] :
( ( splice287087809le_alt @ nil_Ar52383470le_alt @ Ys_65 )
= Ys_65 ) ).
thf(fact_138_splice__Nil2,axiom,
! [Xs_161: list_A1402527603le_alt] :
( ( splice287087809le_alt @ Xs_161 @ nil_Ar52383470le_alt )
= Xs_161 ) ).
thf(fact_139_Pi__mem,axiom,
! [X_104: produc1572197287le_alt,F_19: produc1572197287le_alt > $o,A_41: produc1572197287le_alt > $o,B_33: produc1572197287le_alt > $o > $o] :
( ( member1241905979_alt_o @ F_19 @ ( pi_Pro418549519_alt_o @ A_41 @ B_33 ) )
=> ( ( member285112084le_alt @ X_104 @ A_41 )
=> ( member_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_140_Pi__mem,axiom,
! [X_104: produc1572197287le_alt,F_19: produc1572197287le_alt > nat,A_41: produc1572197287le_alt > $o,B_33: produc1572197287le_alt > nat > $o] :
( ( member1516223254lt_nat @ F_19 @ ( pi_Pro403816170lt_nat @ A_41 @ B_33 ) )
=> ( ( member285112084le_alt @ X_104 @ A_41 )
=> ( member_nat @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_141_Pi__mem,axiom,
! [X_104: produc1572197287le_alt,F_19: produc1572197287le_alt > produc2069254453le_alt,A_41: produc1572197287le_alt > $o,B_33: produc1572197287le_alt > produc2069254453le_alt > $o] :
( ( member707457599le_alt @ F_19 @ ( pi_Pro1816316757le_alt @ A_41 @ B_33 ) )
=> ( ( member285112084le_alt @ X_104 @ A_41 )
=> ( member735418658le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_142_Pi__mem,axiom,
! [X_104: produc1572197287le_alt,F_19: produc1572197287le_alt > arrow_1389031998le_alt,A_41: produc1572197287le_alt > $o,B_33: produc1572197287le_alt > arrow_1389031998le_alt > $o] :
( ( member1662126282le_alt @ F_19 @ ( pi_Pro39698462le_alt @ A_41 @ B_33 ) )
=> ( ( member285112084le_alt @ X_104 @ A_41 )
=> ( member998036369le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_143_Pi__mem,axiom,
! [X_104: produc1572197287le_alt,F_19: produc1572197287le_alt > arrow_1196572341e_indi,A_41: produc1572197287le_alt > $o,B_33: produc1572197287le_alt > arrow_1196572341e_indi > $o] :
( ( member1074431551e_indi @ F_19 @ ( pi_Pro1246947541e_indi @ A_41 @ B_33 ) )
=> ( ( member285112084le_alt @ X_104 @ A_41 )
=> ( member1818997282e_indi @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_144_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat,A_41: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_33: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat > $o] :
( ( member1278554994_o_nat @ F_19 @ ( pi_Arr1012822146_o_nat @ A_41 @ B_33 ) )
=> ( ( member822980838_alt_o @ X_104 @ A_41 )
=> ( member_nat @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_145_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt,A_41: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_33: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o] :
( ( member1883481315le_alt @ F_19 @ ( pi_Arr507332541le_alt @ A_41 @ B_33 ) )
=> ( ( member822980838_alt_o @ X_104 @ A_41 )
=> ( member735418658le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_146_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_41: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_33: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o] :
( ( member449992486le_alt @ F_19 @ ( pi_Arr1963576758le_alt @ A_41 @ B_33 ) )
=> ( ( member822980838_alt_o @ X_104 @ A_41 )
=> ( member998036369le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_147_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_41: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_33: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1186582243e_indi @ F_19 @ ( pi_Arr272777533e_indi @ A_41 @ B_33 ) )
=> ( ( member822980838_alt_o @ X_104 @ A_41 )
=> ( member1818997282e_indi @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_148_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_41: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_33: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o] :
( ( member1696373143lt_o_o @ F_19 @ ( pi_Arr1709554855lt_o_o @ A_41 @ B_33 ) )
=> ( ( member822980838_alt_o @ X_104 @ A_41 )
=> ( member_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_149_Pi__mem,axiom,
! [X_104: produc1572197287le_alt > $o,F_19: ( produc1572197287le_alt > $o ) > nat,A_41: ( produc1572197287le_alt > $o ) > $o,B_33: ( produc1572197287le_alt > $o ) > nat > $o] :
( ( member2133235421_o_nat @ F_19 @ ( pi_Pro1597367533_o_nat @ A_41 @ B_33 ) )
=> ( ( member1241905979_alt_o @ X_104 @ A_41 )
=> ( member_nat @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_150_Pi__mem,axiom,
! [X_104: produc1572197287le_alt > $o,F_19: ( produc1572197287le_alt > $o ) > produc2069254453le_alt,A_41: ( produc1572197287le_alt > $o ) > $o,B_33: ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o] :
( ( member1122245944le_alt @ F_19 @ ( pi_Pro216985362le_alt @ A_41 @ B_33 ) )
=> ( ( member1241905979_alt_o @ X_104 @ A_41 )
=> ( member735418658le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_151_Pi__mem,axiom,
! [X_104: produc1572197287le_alt > $o,F_19: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_41: ( produc1572197287le_alt > $o ) > $o,B_33: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o] :
( ( member376345105le_alt @ F_19 @ ( pi_Pro198875553le_alt @ A_41 @ B_33 ) )
=> ( ( member1241905979_alt_o @ X_104 @ A_41 )
=> ( member998036369le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_152_Pi__mem,axiom,
! [X_104: produc1572197287le_alt > $o,F_19: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_41: ( produc1572197287le_alt > $o ) > $o,B_33: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1830244024e_indi @ F_19 @ ( pi_Pro2039443474e_indi @ A_41 @ B_33 ) )
=> ( ( member1241905979_alt_o @ X_104 @ A_41 )
=> ( member1818997282e_indi @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_153_Pi__mem,axiom,
! [X_104: produc1572197287le_alt > $o,F_19: ( produc1572197287le_alt > $o ) > $o,A_41: ( produc1572197287le_alt > $o ) > $o,B_33: ( produc1572197287le_alt > $o ) > $o > $o] :
( ( member1925470338lt_o_o @ F_19 @ ( pi_Pro386796690lt_o_o @ A_41 @ B_33 ) )
=> ( ( member1241905979_alt_o @ X_104 @ A_41 )
=> ( member_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_154_Pi__mem,axiom,
! [X_104: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat,A_41: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_33: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat > $o] :
( ( member901499098_o_nat @ F_19 @ ( pi_Arr1985384878_o_nat @ A_41 @ B_33 ) )
=> ( ( member1425217232_alt_o @ X_104 @ A_41 )
=> ( member_nat @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_155_Pi__mem,axiom,
! [X_104: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt,A_41: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_33: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o] :
( ( member886874491le_alt @ F_19 @ ( pi_Arr634123665le_alt @ A_41 @ B_33 ) )
=> ( ( member1425217232_alt_o @ X_104 @ A_41 )
=> ( member735418658le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_156_Pi__mem,axiom,
! [X_104: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,A_41: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_33: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o] :
( ( member610734222le_alt @ F_19 @ ( pi_Arr620498146le_alt @ A_41 @ B_33 ) )
=> ( ( member1425217232_alt_o @ X_104 @ A_41 )
=> ( member998036369le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_157_Pi__mem,axiom,
! [X_104: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_41: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_33: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1539010427e_indi @ F_19 @ ( pi_Arr470535441e_indi @ A_41 @ B_33 ) )
=> ( ( member1425217232_alt_o @ X_104 @ A_41 )
=> ( member1818997282e_indi @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_158_Pi__mem,axiom,
! [X_104: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_41: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_33: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o] :
( ( member1346253567lt_o_o @ F_19 @ ( pi_Arr1865419731lt_o_o @ A_41 @ B_33 ) )
=> ( ( member1425217232_alt_o @ X_104 @ A_41 )
=> ( member_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_159_Pi__mem,axiom,
! [X_104: nat,F_19: nat > produc1572197287le_alt,A_41: nat > $o,B_33: nat > produc1572197287le_alt > $o] :
( ( member57786188le_alt @ F_19 @ ( pi_nat1240400806le_alt @ A_41 @ B_33 ) )
=> ( ( member_nat @ X_104 @ A_41 )
=> ( member285112084le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_160_Pi__mem,axiom,
! [X_104: produc2069254453le_alt,F_19: produc2069254453le_alt > produc1572197287le_alt,A_41: produc2069254453le_alt > $o,B_33: produc2069254453le_alt > produc1572197287le_alt > $o] :
( ( member41375167le_alt @ F_19 @ ( pi_Pro726541397le_alt @ A_41 @ B_33 ) )
=> ( ( member735418658le_alt @ X_104 @ A_41 )
=> ( member285112084le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_161_Pi__mem,axiom,
! [X_104: arrow_1389031998le_alt,F_19: arrow_1389031998le_alt > produc1572197287le_alt,A_41: arrow_1389031998le_alt > $o,B_33: arrow_1389031998le_alt > produc1572197287le_alt > $o] :
( ( member85184128le_alt @ F_19 @ ( pi_Arr564047834le_alt @ A_41 @ B_33 ) )
=> ( ( member998036369le_alt @ X_104 @ A_41 )
=> ( member285112084le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_162_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > produc1572197287le_alt,A_41: arrow_1196572341e_indi > $o,B_33: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member232085823le_alt @ F_19 @ ( pi_Arr1762714837le_alt @ A_41 @ B_33 ) )
=> ( ( member1818997282e_indi @ X_104 @ A_41 )
=> ( member285112084le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_163_Pi__mem,axiom,
! [X_104: $o,F_19: $o > produc1572197287le_alt,A_41: $o > $o,B_33: $o > produc1572197287le_alt > $o] :
( ( member1158049649le_alt @ F_19 @ ( pi_o_P728361163le_alt @ A_41 @ B_33 ) )
=> ( ( member_o @ X_104 @ A_41 )
=> ( member285112084le_alt @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_164_Pi__mem,axiom,
! [X_104: nat,F_19: nat > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_41: nat > $o,B_33: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1899388612_alt_o @ F_19 @ ( pi_nat1869411796_alt_o @ A_41 @ B_33 ) )
=> ( ( member_nat @ X_104 @ A_41 )
=> ( member822980838_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_165_Pi__mem,axiom,
! [X_104: produc2069254453le_alt,F_19: produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_41: produc2069254453le_alt > $o,B_33: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1452893329_alt_o @ F_19 @ ( pi_Pro1888753253_alt_o @ A_41 @ B_33 ) )
=> ( ( member735418658le_alt @ X_104 @ A_41 )
=> ( member822980838_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_166_Pi__mem,axiom,
! [X_104: arrow_1389031998le_alt,F_19: arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_41: arrow_1389031998le_alt > $o,B_33: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member1941085840_alt_o @ F_19 @ ( pi_Arr1349212320_alt_o @ A_41 @ B_33 ) )
=> ( ( member998036369le_alt @ X_104 @ A_41 )
=> ( member822980838_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_167_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_41: arrow_1196572341e_indi > $o,B_33: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2071265553_alt_o @ F_19 @ ( pi_Arr456308197_alt_o @ A_41 @ B_33 ) )
=> ( ( member1818997282e_indi @ X_104 @ A_41 )
=> ( member822980838_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_168_Pi__mem,axiom,
! [X_104: $o,F_19: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_41: $o > $o,B_33: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member984757343_alt_o @ F_19 @ ( pi_o_A1479825007_alt_o @ A_41 @ B_33 ) )
=> ( ( member_o @ X_104 @ A_41 )
=> ( member822980838_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_169_Pi__mem,axiom,
! [X_104: nat,F_19: nat > produc1572197287le_alt > $o,A_41: nat > $o,B_33: nat > ( produc1572197287le_alt > $o ) > $o] :
( ( member1425970457_alt_o @ F_19 @ ( pi_nat2104527145_alt_o @ A_41 @ B_33 ) )
=> ( ( member_nat @ X_104 @ A_41 )
=> ( member1241905979_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_170_Pi__mem,axiom,
! [X_104: produc2069254453le_alt,F_19: produc2069254453le_alt > produc1572197287le_alt > $o,A_41: produc2069254453le_alt > $o,B_33: produc2069254453le_alt > ( produc1572197287le_alt > $o ) > $o] :
( ( member1248875622_alt_o @ F_19 @ ( pi_Pro986808634_alt_o @ A_41 @ B_33 ) )
=> ( ( member735418658le_alt @ X_104 @ A_41 )
=> ( member1241905979_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_171_Pi__mem,axiom,
! [X_104: arrow_1389031998le_alt,F_19: arrow_1389031998le_alt > produc1572197287le_alt > $o,A_41: arrow_1389031998le_alt > $o,B_33: arrow_1389031998le_alt > ( produc1572197287le_alt > $o ) > $o] :
( ( member636776165_alt_o @ F_19 @ ( pi_Arr1480001013_alt_o @ A_41 @ B_33 ) )
=> ( ( member998036369le_alt @ X_104 @ A_41 )
=> ( member1241905979_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_172_Pi__mem,axiom,
! [X_104: $o,F_19: $o > produc1572197287le_alt > $o,A_41: $o > $o,B_33: $o > ( produc1572197287le_alt > $o ) > $o] :
( ( member1495989556_alt_o @ F_19 @ ( pi_o_P1417870404_alt_o @ A_41 @ B_33 ) )
=> ( ( member_o @ X_104 @ A_41 )
=> ( member1241905979_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_173_Pi__mem,axiom,
! [X_104: nat,F_19: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_41: nat > $o,B_33: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1908242824_alt_o @ F_19 @ ( pi_nat1912012898_alt_o @ A_41 @ B_33 ) )
=> ( ( member_nat @ X_104 @ A_41 )
=> ( member1425217232_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_174_Pi__mem,axiom,
! [X_104: produc2069254453le_alt,F_19: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_41: produc2069254453le_alt > $o,B_33: produc2069254453le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1082283899_alt_o @ F_19 @ ( pi_Pro1325670033_alt_o @ A_41 @ B_33 ) )
=> ( ( member735418658le_alt @ X_104 @ A_41 )
=> ( member1425217232_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_175_Pi__mem,axiom,
! [X_104: arrow_1389031998le_alt,F_19: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_41: arrow_1389031998le_alt > $o,B_33: arrow_1389031998le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member308341436_alt_o @ F_19 @ ( pi_Arr1191743126_alt_o @ A_41 @ B_33 ) )
=> ( ( member998036369le_alt @ X_104 @ A_41 )
=> ( member1425217232_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_176_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_41: arrow_1196572341e_indi > $o,B_33: arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1521294075_alt_o @ F_19 @ ( pi_Arr583278353_alt_o @ A_41 @ B_33 ) )
=> ( ( member1818997282e_indi @ X_104 @ A_41 )
=> ( member1425217232_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_177_Pi__mem,axiom,
! [X_104: $o,F_19: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_41: $o > $o,B_33: $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member161783341_alt_o @ F_19 @ ( pi_o_A1994447367_alt_o @ A_41 @ B_33 ) )
=> ( ( member_o @ X_104 @ A_41 )
=> ( member1425217232_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_178_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_41: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_33: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ F_19 @ ( pi_Arr1196397536_alt_o @ A_41 @ B_33 ) )
=> ( ( member822980838_alt_o @ X_104 @ A_41 )
=> ( member1241905979_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_179_Pi__mem,axiom,
! [X_104: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_41: arrow_1196572341e_indi > $o,B_33: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ F_19 @ ( pi_Arr1309696186_alt_o @ A_41 @ B_33 ) )
=> ( ( member1818997282e_indi @ X_104 @ A_41 )
=> ( member1241905979_alt_o @ ( F_19 @ X_104 ) @ ( B_33 @ X_104 ) ) ) ) ).
thf(fact_180_Pi__I,axiom,
! [F_18: produc1572197287le_alt > nat,B_32: produc1572197287le_alt > nat > $o,A_40: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_40 )
=> ( member_nat @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1516223254lt_nat @ F_18 @ ( pi_Pro403816170lt_nat @ A_40 @ B_32 ) ) ) ).
thf(fact_181_Pi__I,axiom,
! [F_18: produc1572197287le_alt > produc2069254453le_alt,B_32: produc1572197287le_alt > produc2069254453le_alt > $o,A_40: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_40 )
=> ( member735418658le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member707457599le_alt @ F_18 @ ( pi_Pro1816316757le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_182_Pi__I,axiom,
! [F_18: produc1572197287le_alt > arrow_1389031998le_alt,B_32: produc1572197287le_alt > arrow_1389031998le_alt > $o,A_40: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_40 )
=> ( member998036369le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1662126282le_alt @ F_18 @ ( pi_Pro39698462le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_183_Pi__I,axiom,
! [F_18: produc1572197287le_alt > arrow_1196572341e_indi,B_32: produc1572197287le_alt > arrow_1196572341e_indi > $o,A_40: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_40 )
=> ( member1818997282e_indi @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1074431551e_indi @ F_18 @ ( pi_Pro1246947541e_indi @ A_40 @ B_32 ) ) ) ).
thf(fact_184_Pi__I,axiom,
! [F_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat,B_32: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat > $o,A_40: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_40 )
=> ( member_nat @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1278554994_o_nat @ F_18 @ ( pi_Arr1012822146_o_nat @ A_40 @ B_32 ) ) ) ).
thf(fact_185_Pi__I,axiom,
! [F_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt,B_32: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o,A_40: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_40 )
=> ( member735418658le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1883481315le_alt @ F_18 @ ( pi_Arr507332541le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_186_Pi__I,axiom,
! [F_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_32: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o,A_40: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_40 )
=> ( member998036369le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member449992486le_alt @ F_18 @ ( pi_Arr1963576758le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_187_Pi__I,axiom,
! [F_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_32: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_40: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_40 )
=> ( member1818997282e_indi @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1186582243e_indi @ F_18 @ ( pi_Arr272777533e_indi @ A_40 @ B_32 ) ) ) ).
thf(fact_188_Pi__I,axiom,
! [F_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_32: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o,A_40: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_40 )
=> ( member_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1696373143lt_o_o @ F_18 @ ( pi_Arr1709554855lt_o_o @ A_40 @ B_32 ) ) ) ).
thf(fact_189_Pi__I,axiom,
! [F_18: ( produc1572197287le_alt > $o ) > nat,B_32: ( produc1572197287le_alt > $o ) > nat > $o,A_40: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_40 )
=> ( member_nat @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member2133235421_o_nat @ F_18 @ ( pi_Pro1597367533_o_nat @ A_40 @ B_32 ) ) ) ).
thf(fact_190_Pi__I,axiom,
! [F_18: ( produc1572197287le_alt > $o ) > produc2069254453le_alt,B_32: ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o,A_40: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_40 )
=> ( member735418658le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1122245944le_alt @ F_18 @ ( pi_Pro216985362le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_191_Pi__I,axiom,
! [F_18: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_32: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o,A_40: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_40 )
=> ( member998036369le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member376345105le_alt @ F_18 @ ( pi_Pro198875553le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_192_Pi__I,axiom,
! [F_18: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_32: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_40: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_40 )
=> ( member1818997282e_indi @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1830244024e_indi @ F_18 @ ( pi_Pro2039443474e_indi @ A_40 @ B_32 ) ) ) ).
thf(fact_193_Pi__I,axiom,
! [F_18: ( produc1572197287le_alt > $o ) > $o,B_32: ( produc1572197287le_alt > $o ) > $o > $o,A_40: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_40 )
=> ( member_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1925470338lt_o_o @ F_18 @ ( pi_Pro386796690lt_o_o @ A_40 @ B_32 ) ) ) ).
thf(fact_194_Pi__I,axiom,
! [F_18: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat,B_32: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat > $o,A_40: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_40 )
=> ( member_nat @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member901499098_o_nat @ F_18 @ ( pi_Arr1985384878_o_nat @ A_40 @ B_32 ) ) ) ).
thf(fact_195_Pi__I,axiom,
! [F_18: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt,B_32: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o,A_40: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_40 )
=> ( member735418658le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member886874491le_alt @ F_18 @ ( pi_Arr634123665le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_196_Pi__I,axiom,
! [F_18: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_32: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o,A_40: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_40 )
=> ( member998036369le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member610734222le_alt @ F_18 @ ( pi_Arr620498146le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_197_Pi__I,axiom,
! [F_18: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_32: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_40: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_40 )
=> ( member1818997282e_indi @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1539010427e_indi @ F_18 @ ( pi_Arr470535441e_indi @ A_40 @ B_32 ) ) ) ).
thf(fact_198_Pi__I,axiom,
! [F_18: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_32: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o,A_40: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_40 )
=> ( member_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1346253567lt_o_o @ F_18 @ ( pi_Arr1865419731lt_o_o @ A_40 @ B_32 ) ) ) ).
thf(fact_199_Pi__I,axiom,
! [F_18: nat > produc1572197287le_alt,B_32: nat > produc1572197287le_alt > $o,A_40: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_40 )
=> ( member285112084le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member57786188le_alt @ F_18 @ ( pi_nat1240400806le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_200_Pi__I,axiom,
! [F_18: produc2069254453le_alt > produc1572197287le_alt,B_32: produc2069254453le_alt > produc1572197287le_alt > $o,A_40: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_40 )
=> ( member285112084le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member41375167le_alt @ F_18 @ ( pi_Pro726541397le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_201_Pi__I,axiom,
! [F_18: arrow_1389031998le_alt > produc1572197287le_alt,B_32: arrow_1389031998le_alt > produc1572197287le_alt > $o,A_40: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_40 )
=> ( member285112084le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member85184128le_alt @ F_18 @ ( pi_Arr564047834le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_202_Pi__I,axiom,
! [F_18: arrow_1196572341e_indi > produc1572197287le_alt,B_32: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_40: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_40 )
=> ( member285112084le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member232085823le_alt @ F_18 @ ( pi_Arr1762714837le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_203_Pi__I,axiom,
! [F_18: $o > produc1572197287le_alt,B_32: $o > produc1572197287le_alt > $o,A_40: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_40 )
=> ( member285112084le_alt @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1158049649le_alt @ F_18 @ ( pi_o_P728361163le_alt @ A_40 @ B_32 ) ) ) ).
thf(fact_204_Pi__I,axiom,
! [F_18: nat > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_32: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_40: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_40 )
=> ( member822980838_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1899388612_alt_o @ F_18 @ ( pi_nat1869411796_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_205_Pi__I,axiom,
! [F_18: produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_32: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_40: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_40 )
=> ( member822980838_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1452893329_alt_o @ F_18 @ ( pi_Pro1888753253_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_206_Pi__I,axiom,
! [F_18: arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_32: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_40: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_40 )
=> ( member822980838_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1941085840_alt_o @ F_18 @ ( pi_Arr1349212320_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_207_Pi__I,axiom,
! [F_18: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_32: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_40: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_40 )
=> ( member822980838_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member2071265553_alt_o @ F_18 @ ( pi_Arr456308197_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_208_Pi__I,axiom,
! [F_18: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_32: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_40: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_40 )
=> ( member822980838_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member984757343_alt_o @ F_18 @ ( pi_o_A1479825007_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_209_Pi__I,axiom,
! [F_18: nat > produc1572197287le_alt > $o,B_32: nat > ( produc1572197287le_alt > $o ) > $o,A_40: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_40 )
=> ( member1241905979_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1425970457_alt_o @ F_18 @ ( pi_nat2104527145_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_210_Pi__I,axiom,
! [F_18: produc2069254453le_alt > produc1572197287le_alt > $o,B_32: produc2069254453le_alt > ( produc1572197287le_alt > $o ) > $o,A_40: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_40 )
=> ( member1241905979_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1248875622_alt_o @ F_18 @ ( pi_Pro986808634_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_211_Pi__I,axiom,
! [F_18: arrow_1389031998le_alt > produc1572197287le_alt > $o,B_32: arrow_1389031998le_alt > ( produc1572197287le_alt > $o ) > $o,A_40: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_40 )
=> ( member1241905979_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member636776165_alt_o @ F_18 @ ( pi_Arr1480001013_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_212_Pi__I,axiom,
! [F_18: $o > produc1572197287le_alt > $o,B_32: $o > ( produc1572197287le_alt > $o ) > $o,A_40: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_40 )
=> ( member1241905979_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1495989556_alt_o @ F_18 @ ( pi_o_P1417870404_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_213_Pi__I,axiom,
! [F_18: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_32: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_40: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_40 )
=> ( member1425217232_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1908242824_alt_o @ F_18 @ ( pi_nat1912012898_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_214_Pi__I,axiom,
! [F_18: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_32: produc2069254453le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_40: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_40 )
=> ( member1425217232_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1082283899_alt_o @ F_18 @ ( pi_Pro1325670033_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_215_Pi__I,axiom,
! [F_18: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_32: arrow_1389031998le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_40: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_40 )
=> ( member1425217232_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member308341436_alt_o @ F_18 @ ( pi_Arr1191743126_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_216_Pi__I,axiom,
! [F_18: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_32: arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_40: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_40 )
=> ( member1425217232_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1521294075_alt_o @ F_18 @ ( pi_Arr583278353_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_217_Pi__I,axiom,
! [F_18: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_32: $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_40: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_40 )
=> ( member1425217232_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member161783341_alt_o @ F_18 @ ( pi_o_A1994447367_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_218_Pi__I,axiom,
! [F_18: produc1572197287le_alt > $o,B_32: produc1572197287le_alt > $o > $o,A_40: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_40 )
=> ( member_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1241905979_alt_o @ F_18 @ ( pi_Pro418549519_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_219_Pi__I,axiom,
! [F_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_32: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o,A_40: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_40 )
=> ( member1241905979_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member1425217232_alt_o @ F_18 @ ( pi_Arr1196397536_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_220_Pi__I,axiom,
! [F_18: arrow_1196572341e_indi > produc1572197287le_alt > $o,B_32: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,A_40: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_40 )
=> ( member1241905979_alt_o @ ( F_18 @ X_1 ) @ ( B_32 @ X_1 ) ) )
=> ( member822980838_alt_o @ F_18 @ ( pi_Arr1309696186_alt_o @ A_40 @ B_32 ) ) ) ).
thf(fact_221_funcsetI,axiom,
! [F_17: produc1572197287le_alt > nat,B_31: nat > $o,A_39: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_39 )
=> ( member_nat @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1516223254lt_nat @ F_17
@ ( pi_Pro403816170lt_nat @ A_39
@ ^ [Uu: produc1572197287le_alt] : B_31 ) ) ) ).
thf(fact_222_funcsetI,axiom,
! [F_17: produc1572197287le_alt > produc2069254453le_alt,B_31: produc2069254453le_alt > $o,A_39: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_39 )
=> ( member735418658le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member707457599le_alt @ F_17
@ ( pi_Pro1816316757le_alt @ A_39
@ ^ [Uu: produc1572197287le_alt] : B_31 ) ) ) ).
thf(fact_223_funcsetI,axiom,
! [F_17: produc1572197287le_alt > arrow_1389031998le_alt,B_31: arrow_1389031998le_alt > $o,A_39: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_39 )
=> ( member998036369le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1662126282le_alt @ F_17
@ ( pi_Pro39698462le_alt @ A_39
@ ^ [Uu: produc1572197287le_alt] : B_31 ) ) ) ).
thf(fact_224_funcsetI,axiom,
! [F_17: produc1572197287le_alt > arrow_1196572341e_indi,B_31: arrow_1196572341e_indi > $o,A_39: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_39 )
=> ( member1818997282e_indi @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1074431551e_indi @ F_17
@ ( pi_Pro1246947541e_indi @ A_39
@ ^ [Uu: produc1572197287le_alt] : B_31 ) ) ) ).
thf(fact_225_funcsetI,axiom,
! [F_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat,B_31: nat > $o,A_39: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_39 )
=> ( member_nat @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1278554994_o_nat @ F_17
@ ( pi_Arr1012822146_o_nat @ A_39
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_226_funcsetI,axiom,
! [F_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt,B_31: produc2069254453le_alt > $o,A_39: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_39 )
=> ( member735418658le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1883481315le_alt @ F_17
@ ( pi_Arr507332541le_alt @ A_39
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_227_funcsetI,axiom,
! [F_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_31: arrow_1389031998le_alt > $o,A_39: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_39 )
=> ( member998036369le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member449992486le_alt @ F_17
@ ( pi_Arr1963576758le_alt @ A_39
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_228_funcsetI,axiom,
! [F_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_31: arrow_1196572341e_indi > $o,A_39: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_39 )
=> ( member1818997282e_indi @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1186582243e_indi @ F_17
@ ( pi_Arr272777533e_indi @ A_39
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_229_funcsetI,axiom,
! [F_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_31: $o > $o,A_39: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_39 )
=> ( member_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1696373143lt_o_o @ F_17
@ ( pi_Arr1709554855lt_o_o @ A_39
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_230_funcsetI,axiom,
! [F_17: ( produc1572197287le_alt > $o ) > nat,B_31: nat > $o,A_39: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_39 )
=> ( member_nat @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member2133235421_o_nat @ F_17
@ ( pi_Pro1597367533_o_nat @ A_39
@ ^ [Uu: produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_231_funcsetI,axiom,
! [F_17: ( produc1572197287le_alt > $o ) > produc2069254453le_alt,B_31: produc2069254453le_alt > $o,A_39: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_39 )
=> ( member735418658le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1122245944le_alt @ F_17
@ ( pi_Pro216985362le_alt @ A_39
@ ^ [Uu: produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_232_funcsetI,axiom,
! [F_17: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_31: arrow_1389031998le_alt > $o,A_39: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_39 )
=> ( member998036369le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member376345105le_alt @ F_17
@ ( pi_Pro198875553le_alt @ A_39
@ ^ [Uu: produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_233_funcsetI,axiom,
! [F_17: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_31: arrow_1196572341e_indi > $o,A_39: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_39 )
=> ( member1818997282e_indi @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1830244024e_indi @ F_17
@ ( pi_Pro2039443474e_indi @ A_39
@ ^ [Uu: produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_234_funcsetI,axiom,
! [F_17: ( produc1572197287le_alt > $o ) > $o,B_31: $o > $o,A_39: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_39 )
=> ( member_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1925470338lt_o_o @ F_17
@ ( pi_Pro386796690lt_o_o @ A_39
@ ^ [Uu: produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_235_funcsetI,axiom,
! [F_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat,B_31: nat > $o,A_39: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_39 )
=> ( member_nat @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member901499098_o_nat @ F_17
@ ( pi_Arr1985384878_o_nat @ A_39
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_236_funcsetI,axiom,
! [F_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt,B_31: produc2069254453le_alt > $o,A_39: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_39 )
=> ( member735418658le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member886874491le_alt @ F_17
@ ( pi_Arr634123665le_alt @ A_39
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_237_funcsetI,axiom,
! [F_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_31: arrow_1389031998le_alt > $o,A_39: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_39 )
=> ( member998036369le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member610734222le_alt @ F_17
@ ( pi_Arr620498146le_alt @ A_39
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_238_funcsetI,axiom,
! [F_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_31: arrow_1196572341e_indi > $o,A_39: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_39 )
=> ( member1818997282e_indi @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1539010427e_indi @ F_17
@ ( pi_Arr470535441e_indi @ A_39
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_239_funcsetI,axiom,
! [F_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_31: $o > $o,A_39: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_39 )
=> ( member_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1346253567lt_o_o @ F_17
@ ( pi_Arr1865419731lt_o_o @ A_39
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_240_funcsetI,axiom,
! [F_17: nat > produc1572197287le_alt,B_31: produc1572197287le_alt > $o,A_39: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_39 )
=> ( member285112084le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member57786188le_alt @ F_17
@ ( pi_nat1240400806le_alt @ A_39
@ ^ [Uu: nat] : B_31 ) ) ) ).
thf(fact_241_funcsetI,axiom,
! [F_17: produc2069254453le_alt > produc1572197287le_alt,B_31: produc1572197287le_alt > $o,A_39: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_39 )
=> ( member285112084le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member41375167le_alt @ F_17
@ ( pi_Pro726541397le_alt @ A_39
@ ^ [Uu: produc2069254453le_alt] : B_31 ) ) ) ).
thf(fact_242_funcsetI,axiom,
! [F_17: arrow_1389031998le_alt > produc1572197287le_alt,B_31: produc1572197287le_alt > $o,A_39: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_39 )
=> ( member285112084le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member85184128le_alt @ F_17
@ ( pi_Arr564047834le_alt @ A_39
@ ^ [Uu: arrow_1389031998le_alt] : B_31 ) ) ) ).
thf(fact_243_funcsetI,axiom,
! [F_17: arrow_1196572341e_indi > produc1572197287le_alt,B_31: produc1572197287le_alt > $o,A_39: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_39 )
=> ( member285112084le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member232085823le_alt @ F_17
@ ( pi_Arr1762714837le_alt @ A_39
@ ^ [Uu: arrow_1196572341e_indi] : B_31 ) ) ) ).
thf(fact_244_funcsetI,axiom,
! [F_17: $o > produc1572197287le_alt,B_31: produc1572197287le_alt > $o,A_39: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_39 )
=> ( member285112084le_alt @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1158049649le_alt @ F_17
@ ( pi_o_P728361163le_alt @ A_39
@ ^ [Uu: $o] : B_31 ) ) ) ).
thf(fact_245_funcsetI,axiom,
! [F_17: nat > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_39: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_39 )
=> ( member822980838_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1899388612_alt_o @ F_17
@ ( pi_nat1869411796_alt_o @ A_39
@ ^ [Uu: nat] : B_31 ) ) ) ).
thf(fact_246_funcsetI,axiom,
! [F_17: produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_39: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_39 )
=> ( member822980838_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1452893329_alt_o @ F_17
@ ( pi_Pro1888753253_alt_o @ A_39
@ ^ [Uu: produc2069254453le_alt] : B_31 ) ) ) ).
thf(fact_247_funcsetI,axiom,
! [F_17: arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_39: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_39 )
=> ( member822980838_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1941085840_alt_o @ F_17
@ ( pi_Arr1349212320_alt_o @ A_39
@ ^ [Uu: arrow_1389031998le_alt] : B_31 ) ) ) ).
thf(fact_248_funcsetI,axiom,
! [F_17: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_39: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_39 )
=> ( member822980838_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member2071265553_alt_o @ F_17
@ ( pi_Arr456308197_alt_o @ A_39
@ ^ [Uu: arrow_1196572341e_indi] : B_31 ) ) ) ).
thf(fact_249_funcsetI,axiom,
! [F_17: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_39: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_39 )
=> ( member822980838_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member984757343_alt_o @ F_17
@ ( pi_o_A1479825007_alt_o @ A_39
@ ^ [Uu: $o] : B_31 ) ) ) ).
thf(fact_250_funcsetI,axiom,
! [F_17: nat > produc1572197287le_alt > $o,B_31: ( produc1572197287le_alt > $o ) > $o,A_39: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_39 )
=> ( member1241905979_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1425970457_alt_o @ F_17
@ ( pi_nat2104527145_alt_o @ A_39
@ ^ [Uu: nat] : B_31 ) ) ) ).
thf(fact_251_funcsetI,axiom,
! [F_17: produc2069254453le_alt > produc1572197287le_alt > $o,B_31: ( produc1572197287le_alt > $o ) > $o,A_39: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_39 )
=> ( member1241905979_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1248875622_alt_o @ F_17
@ ( pi_Pro986808634_alt_o @ A_39
@ ^ [Uu: produc2069254453le_alt] : B_31 ) ) ) ).
thf(fact_252_funcsetI,axiom,
! [F_17: arrow_1389031998le_alt > produc1572197287le_alt > $o,B_31: ( produc1572197287le_alt > $o ) > $o,A_39: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_39 )
=> ( member1241905979_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member636776165_alt_o @ F_17
@ ( pi_Arr1480001013_alt_o @ A_39
@ ^ [Uu: arrow_1389031998le_alt] : B_31 ) ) ) ).
thf(fact_253_funcsetI,axiom,
! [F_17: $o > produc1572197287le_alt > $o,B_31: ( produc1572197287le_alt > $o ) > $o,A_39: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_39 )
=> ( member1241905979_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1495989556_alt_o @ F_17
@ ( pi_o_P1417870404_alt_o @ A_39
@ ^ [Uu: $o] : B_31 ) ) ) ).
thf(fact_254_funcsetI,axiom,
! [F_17: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_31: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_39: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_39 )
=> ( member1425217232_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1908242824_alt_o @ F_17
@ ( pi_nat1912012898_alt_o @ A_39
@ ^ [Uu: nat] : B_31 ) ) ) ).
thf(fact_255_funcsetI,axiom,
! [F_17: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_31: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_39: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_39 )
=> ( member1425217232_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1082283899_alt_o @ F_17
@ ( pi_Pro1325670033_alt_o @ A_39
@ ^ [Uu: produc2069254453le_alt] : B_31 ) ) ) ).
thf(fact_256_funcsetI,axiom,
! [F_17: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_31: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_39: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_39 )
=> ( member1425217232_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member308341436_alt_o @ F_17
@ ( pi_Arr1191743126_alt_o @ A_39
@ ^ [Uu: arrow_1389031998le_alt] : B_31 ) ) ) ).
thf(fact_257_funcsetI,axiom,
! [F_17: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_31: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_39: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_39 )
=> ( member1425217232_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1521294075_alt_o @ F_17
@ ( pi_Arr583278353_alt_o @ A_39
@ ^ [Uu: arrow_1196572341e_indi] : B_31 ) ) ) ).
thf(fact_258_funcsetI,axiom,
! [F_17: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_31: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_39: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_39 )
=> ( member1425217232_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member161783341_alt_o @ F_17
@ ( pi_o_A1994447367_alt_o @ A_39
@ ^ [Uu: $o] : B_31 ) ) ) ).
thf(fact_259_funcsetI,axiom,
! [F_17: produc1572197287le_alt > $o,B_31: $o > $o,A_39: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_39 )
=> ( member_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1241905979_alt_o @ F_17
@ ( pi_Pro418549519_alt_o @ A_39
@ ^ [Uu: produc1572197287le_alt] : B_31 ) ) ) ).
thf(fact_260_funcsetI,axiom,
! [F_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_31: ( produc1572197287le_alt > $o ) > $o,A_39: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_39 )
=> ( member1241905979_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member1425217232_alt_o @ F_17
@ ( pi_Arr1196397536_alt_o @ A_39
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_31 ) ) ) ).
thf(fact_261_funcsetI,axiom,
! [F_17: arrow_1196572341e_indi > produc1572197287le_alt > $o,B_31: ( produc1572197287le_alt > $o ) > $o,A_39: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_39 )
=> ( member1241905979_alt_o @ ( F_17 @ X_1 ) @ B_31 ) )
=> ( member822980838_alt_o @ F_17
@ ( pi_Arr1309696186_alt_o @ A_39
@ ^ [Uu: arrow_1196572341e_indi] : B_31 ) ) ) ).
thf(fact_262_Pi__I_H,axiom,
! [F_16: produc1572197287le_alt > nat,B_30: produc1572197287le_alt > nat > $o,A_38: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_38 )
=> ( member_nat @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1516223254lt_nat @ F_16 @ ( pi_Pro403816170lt_nat @ A_38 @ B_30 ) ) ) ).
thf(fact_263_Pi__I_H,axiom,
! [F_16: produc1572197287le_alt > produc2069254453le_alt,B_30: produc1572197287le_alt > produc2069254453le_alt > $o,A_38: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_38 )
=> ( member735418658le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member707457599le_alt @ F_16 @ ( pi_Pro1816316757le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_264_Pi__I_H,axiom,
! [F_16: produc1572197287le_alt > arrow_1389031998le_alt,B_30: produc1572197287le_alt > arrow_1389031998le_alt > $o,A_38: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_38 )
=> ( member998036369le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1662126282le_alt @ F_16 @ ( pi_Pro39698462le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_265_Pi__I_H,axiom,
! [F_16: produc1572197287le_alt > arrow_1196572341e_indi,B_30: produc1572197287le_alt > arrow_1196572341e_indi > $o,A_38: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_38 )
=> ( member1818997282e_indi @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1074431551e_indi @ F_16 @ ( pi_Pro1246947541e_indi @ A_38 @ B_30 ) ) ) ).
thf(fact_266_Pi__I_H,axiom,
! [F_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat,B_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > nat > $o,A_38: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_38 )
=> ( member_nat @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1278554994_o_nat @ F_16 @ ( pi_Arr1012822146_o_nat @ A_38 @ B_30 ) ) ) ).
thf(fact_267_Pi__I_H,axiom,
! [F_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt,B_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o,A_38: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_38 )
=> ( member735418658le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1883481315le_alt @ F_16 @ ( pi_Arr507332541le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_268_Pi__I_H,axiom,
! [F_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o,A_38: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_38 )
=> ( member998036369le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member449992486le_alt @ F_16 @ ( pi_Arr1963576758le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_269_Pi__I_H,axiom,
! [F_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_38: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_38 )
=> ( member1818997282e_indi @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1186582243e_indi @ F_16 @ ( pi_Arr272777533e_indi @ A_38 @ B_30 ) ) ) ).
thf(fact_270_Pi__I_H,axiom,
! [F_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o,A_38: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_38 )
=> ( member_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1696373143lt_o_o @ F_16 @ ( pi_Arr1709554855lt_o_o @ A_38 @ B_30 ) ) ) ).
thf(fact_271_Pi__I_H,axiom,
! [F_16: ( produc1572197287le_alt > $o ) > nat,B_30: ( produc1572197287le_alt > $o ) > nat > $o,A_38: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_38 )
=> ( member_nat @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member2133235421_o_nat @ F_16 @ ( pi_Pro1597367533_o_nat @ A_38 @ B_30 ) ) ) ).
thf(fact_272_Pi__I_H,axiom,
! [F_16: ( produc1572197287le_alt > $o ) > produc2069254453le_alt,B_30: ( produc1572197287le_alt > $o ) > produc2069254453le_alt > $o,A_38: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_38 )
=> ( member735418658le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1122245944le_alt @ F_16 @ ( pi_Pro216985362le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_273_Pi__I_H,axiom,
! [F_16: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_30: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o,A_38: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_38 )
=> ( member998036369le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member376345105le_alt @ F_16 @ ( pi_Pro198875553le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_274_Pi__I_H,axiom,
! [F_16: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_30: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_38: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_38 )
=> ( member1818997282e_indi @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1830244024e_indi @ F_16 @ ( pi_Pro2039443474e_indi @ A_38 @ B_30 ) ) ) ).
thf(fact_275_Pi__I_H,axiom,
! [F_16: ( produc1572197287le_alt > $o ) > $o,B_30: ( produc1572197287le_alt > $o ) > $o > $o,A_38: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_38 )
=> ( member_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1925470338lt_o_o @ F_16 @ ( pi_Pro386796690lt_o_o @ A_38 @ B_30 ) ) ) ).
thf(fact_276_Pi__I_H,axiom,
! [F_16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat,B_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > nat > $o,A_38: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_38 )
=> ( member_nat @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member901499098_o_nat @ F_16 @ ( pi_Arr1985384878_o_nat @ A_38 @ B_30 ) ) ) ).
thf(fact_277_Pi__I_H,axiom,
! [F_16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt,B_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > produc2069254453le_alt > $o,A_38: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_38 )
=> ( member735418658le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member886874491le_alt @ F_16 @ ( pi_Arr634123665le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_278_Pi__I_H,axiom,
! [F_16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt,B_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt > $o,A_38: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_38 )
=> ( member998036369le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member610734222le_alt @ F_16 @ ( pi_Arr620498146le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_279_Pi__I_H,axiom,
! [F_16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_38: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_38 )
=> ( member1818997282e_indi @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1539010427e_indi @ F_16 @ ( pi_Arr470535441e_indi @ A_38 @ B_30 ) ) ) ).
thf(fact_280_Pi__I_H,axiom,
! [F_16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o,A_38: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ A_38 )
=> ( member_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1346253567lt_o_o @ F_16 @ ( pi_Arr1865419731lt_o_o @ A_38 @ B_30 ) ) ) ).
thf(fact_281_Pi__I_H,axiom,
! [F_16: nat > produc1572197287le_alt,B_30: nat > produc1572197287le_alt > $o,A_38: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_38 )
=> ( member285112084le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member57786188le_alt @ F_16 @ ( pi_nat1240400806le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_282_Pi__I_H,axiom,
! [F_16: produc2069254453le_alt > produc1572197287le_alt,B_30: produc2069254453le_alt > produc1572197287le_alt > $o,A_38: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_38 )
=> ( member285112084le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member41375167le_alt @ F_16 @ ( pi_Pro726541397le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_283_Pi__I_H,axiom,
! [F_16: arrow_1389031998le_alt > produc1572197287le_alt,B_30: arrow_1389031998le_alt > produc1572197287le_alt > $o,A_38: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_38 )
=> ( member285112084le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member85184128le_alt @ F_16 @ ( pi_Arr564047834le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_284_Pi__I_H,axiom,
! [F_16: arrow_1196572341e_indi > produc1572197287le_alt,B_30: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_38: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_38 )
=> ( member285112084le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member232085823le_alt @ F_16 @ ( pi_Arr1762714837le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_285_Pi__I_H,axiom,
! [F_16: $o > produc1572197287le_alt,B_30: $o > produc1572197287le_alt > $o,A_38: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_38 )
=> ( member285112084le_alt @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1158049649le_alt @ F_16 @ ( pi_o_P728361163le_alt @ A_38 @ B_30 ) ) ) ).
thf(fact_286_Pi__I_H,axiom,
! [F_16: nat > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_30: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_38: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_38 )
=> ( member822980838_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1899388612_alt_o @ F_16 @ ( pi_nat1869411796_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_287_Pi__I_H,axiom,
! [F_16: produc2069254453le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_30: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_38: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_38 )
=> ( member822980838_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1452893329_alt_o @ F_16 @ ( pi_Pro1888753253_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_288_Pi__I_H,axiom,
! [F_16: arrow_1389031998le_alt > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_30: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_38: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_38 )
=> ( member822980838_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1941085840_alt_o @ F_16 @ ( pi_Arr1349212320_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_289_Pi__I_H,axiom,
! [F_16: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_30: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_38: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_38 )
=> ( member822980838_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member2071265553_alt_o @ F_16 @ ( pi_Arr456308197_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_290_Pi__I_H,axiom,
! [F_16: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_30: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_38: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_38 )
=> ( member822980838_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member984757343_alt_o @ F_16 @ ( pi_o_A1479825007_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_291_Pi__I_H,axiom,
! [F_16: nat > produc1572197287le_alt > $o,B_30: nat > ( produc1572197287le_alt > $o ) > $o,A_38: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_38 )
=> ( member1241905979_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1425970457_alt_o @ F_16 @ ( pi_nat2104527145_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_292_Pi__I_H,axiom,
! [F_16: produc2069254453le_alt > produc1572197287le_alt > $o,B_30: produc2069254453le_alt > ( produc1572197287le_alt > $o ) > $o,A_38: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_38 )
=> ( member1241905979_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1248875622_alt_o @ F_16 @ ( pi_Pro986808634_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_293_Pi__I_H,axiom,
! [F_16: arrow_1389031998le_alt > produc1572197287le_alt > $o,B_30: arrow_1389031998le_alt > ( produc1572197287le_alt > $o ) > $o,A_38: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_38 )
=> ( member1241905979_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member636776165_alt_o @ F_16 @ ( pi_Arr1480001013_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_294_Pi__I_H,axiom,
! [F_16: $o > produc1572197287le_alt > $o,B_30: $o > ( produc1572197287le_alt > $o ) > $o,A_38: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_38 )
=> ( member1241905979_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1495989556_alt_o @ F_16 @ ( pi_o_P1417870404_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_295_Pi__I_H,axiom,
! [F_16: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_30: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_38: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_38 )
=> ( member1425217232_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1908242824_alt_o @ F_16 @ ( pi_nat1912012898_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_296_Pi__I_H,axiom,
! [F_16: produc2069254453le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_30: produc2069254453le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_38: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ A_38 )
=> ( member1425217232_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1082283899_alt_o @ F_16 @ ( pi_Pro1325670033_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_297_Pi__I_H,axiom,
! [F_16: arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_30: arrow_1389031998le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_38: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ A_38 )
=> ( member1425217232_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member308341436_alt_o @ F_16 @ ( pi_Arr1191743126_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_298_Pi__I_H,axiom,
! [F_16: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_30: arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_38: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_38 )
=> ( member1425217232_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1521294075_alt_o @ F_16 @ ( pi_Arr583278353_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_299_Pi__I_H,axiom,
! [F_16: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_30: $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_38: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_38 )
=> ( member1425217232_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member161783341_alt_o @ F_16 @ ( pi_o_A1994447367_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_300_Pi__I_H,axiom,
! [F_16: produc1572197287le_alt > $o,B_30: produc1572197287le_alt > $o > $o,A_38: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_38 )
=> ( member_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1241905979_alt_o @ F_16 @ ( pi_Pro418549519_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_301_Pi__I_H,axiom,
! [F_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o,A_38: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_38 )
=> ( member1241905979_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member1425217232_alt_o @ F_16 @ ( pi_Arr1196397536_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_302_Pi__I_H,axiom,
! [F_16: arrow_1196572341e_indi > produc1572197287le_alt > $o,B_30: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,A_38: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_38 )
=> ( member1241905979_alt_o @ ( F_16 @ X_1 ) @ ( B_30 @ X_1 ) ) )
=> ( member822980838_alt_o @ F_16 @ ( pi_Arr1309696186_alt_o @ A_38 @ B_30 ) ) ) ).
thf(fact_303_Pi__cong,axiom,
! [B_29: produc1572197287le_alt > $o > $o,G_3: produc1572197287le_alt > $o,F_15: produc1572197287le_alt > $o,A_37: produc1572197287le_alt > $o] :
( ! [W: produc1572197287le_alt] :
( ( member285112084le_alt @ W @ A_37 )
=> ( ( F_15 @ W )
<=> ( G_3 @ W ) ) )
=> ( ( member1241905979_alt_o @ F_15 @ ( pi_Pro418549519_alt_o @ A_37 @ B_29 ) )
<=> ( member1241905979_alt_o @ G_3 @ ( pi_Pro418549519_alt_o @ A_37 @ B_29 ) ) ) ) ).
thf(fact_304_Pi__cong,axiom,
! [B_29: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o,F_15: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,G_3: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_37: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [W: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ W @ A_37 )
=> ( ( F_15 @ W )
= ( G_3 @ W ) ) )
=> ( ( member1425217232_alt_o @ F_15 @ ( pi_Arr1196397536_alt_o @ A_37 @ B_29 ) )
<=> ( member1425217232_alt_o @ G_3 @ ( pi_Arr1196397536_alt_o @ A_37 @ B_29 ) ) ) ) ).
thf(fact_305_Pi__cong,axiom,
! [B_29: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,F_15: arrow_1196572341e_indi > produc1572197287le_alt > $o,G_3: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_37: arrow_1196572341e_indi > $o] :
( ! [W: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ W @ A_37 )
=> ( ( F_15 @ W )
= ( G_3 @ W ) ) )
=> ( ( member822980838_alt_o @ F_15 @ ( pi_Arr1309696186_alt_o @ A_37 @ B_29 ) )
<=> ( member822980838_alt_o @ G_3 @ ( pi_Arr1309696186_alt_o @ A_37 @ B_29 ) ) ) ) ).
thf(fact_306_PairE,axiom,
! [P_48: produc2069254453le_alt] :
~ ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( P_48
!= ( produc1014865963le_alt @ X_1 @ Y_10 ) ) ).
thf(fact_307_PairE,axiom,
! [P_48: produc1572197287le_alt] :
~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( P_48
!= ( produc897867031le_alt @ X_1 @ Y_10 ) ) ).
thf(fact_308_prod_Oexhaust,axiom,
! [Y_38: produc2069254453le_alt] :
~ ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] :
( Y_38
!= ( produc1014865963le_alt @ A_14 @ B_10 ) ) ).
thf(fact_309_prod_Oexhaust,axiom,
! [Y_38: produc1572197287le_alt] :
~ ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( Y_38
!= ( produc897867031le_alt @ A_14 @ B_10 ) ) ).
thf(fact_310_pred__equals__eq2,axiom,
! [S_4: produc2069254453le_alt > $o,R_64: produc2069254453le_alt > $o] :
( ! [X_1: list_A1402527603le_alt,Xa: list_A1402527603le_alt] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Xa ) @ R_64 )
<=> ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_64 = S_4 ) ) ).
thf(fact_311_pred__equals__eq2,axiom,
! [S_4: produc1572197287le_alt > $o,R_64: produc1572197287le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt,Xa: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Xa ) @ R_64 )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Xa ) @ S_4 ) )
<=> ( R_64 = S_4 ) ) ).
thf(fact_312_insert__Nil,axiom,
! [X_103: arrow_1389031998le_alt] :
( ( insert886756100le_alt @ X_103 @ nil_Ar52383470le_alt )
= ( cons_A1142416030le_alt @ X_103 @ nil_Ar52383470le_alt ) ) ).
thf(fact_313_list__nonempty__induct,axiom,
! [P_47: list_A1402527603le_alt > $o,Xs_160: list_A1402527603le_alt] :
( ( Xs_160 != nil_Ar52383470le_alt )
=> ( ! [X_1: arrow_1389031998le_alt] : ( P_47 @ ( cons_A1142416030le_alt @ X_1 @ nil_Ar52383470le_alt ) )
=> ( ! [X_1: arrow_1389031998le_alt,Xs_71: list_A1402527603le_alt] :
( ( Xs_71 != nil_Ar52383470le_alt )
=> ( ( P_47 @ Xs_71 )
=> ( P_47 @ ( cons_A1142416030le_alt @ X_1 @ Xs_71 ) ) ) )
=> ( P_47 @ Xs_160 ) ) ) ) ).
thf(fact_314_mem__def,axiom,
! [X_102: nat,A_36: nat > $o] :
( ( member_nat @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_315_mem__def,axiom,
! [X_102: produc2069254453le_alt,A_36: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_316_mem__def,axiom,
! [X_102: arrow_1389031998le_alt,A_36: arrow_1389031998le_alt > $o] :
( ( member998036369le_alt @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_317_mem__def,axiom,
! [X_102: arrow_1196572341e_indi,A_36: arrow_1196572341e_indi > $o] :
( ( member1818997282e_indi @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_318_mem__def,axiom,
! [X_102: $o,A_36: $o > $o] :
( ( member_o @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_319_mem__def,axiom,
! [X_102: produc1572197287le_alt,A_36: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_320_mem__def,axiom,
! [X_102: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_36: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_321_mem__def,axiom,
! [X_102: produc1572197287le_alt > $o,A_36: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_322_mem__def,axiom,
! [X_102: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_36: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(fact_323_Collect__def,axiom,
! [P_46: nat > $o] :
( ( collect_nat @ P_46 )
= P_46 ) ).
thf(fact_324_Collect__def,axiom,
! [P_46: arrow_1389031998le_alt > $o] :
( ( collec1655747795le_alt @ P_46 )
= P_46 ) ).
thf(fact_325_Collect__def,axiom,
! [P_46: arrow_1196572341e_indi > $o] :
( ( collec1936859488e_indi @ P_46 )
= P_46 ) ).
thf(fact_326_Collect__def,axiom,
! [P_46: ( produc1572197287le_alt > $o ) > $o] :
( ( collec958969213_alt_o @ P_46 )
= P_46 ) ).
thf(fact_327_curry__def,axiom,
! [X_1: produc1572197287le_alt > $o,Xa: arrow_1389031998le_alt,Xb_1: arrow_1389031998le_alt] :
( ( produc1084757966_alt_o @ X_1 @ Xa @ Xb_1 )
<=> ( X_1 @ ( produc897867031le_alt @ Xa @ Xb_1 ) ) ) ).
thf(fact_328_curryI,axiom,
! [F_14: produc2069254453le_alt > $o,A_35: list_A1402527603le_alt,B_28: list_A1402527603le_alt] :
( ( F_14 @ ( produc1014865963le_alt @ A_35 @ B_28 ) )
=> ( produc28228666_alt_o @ F_14 @ A_35 @ B_28 ) ) ).
thf(fact_329_curryI,axiom,
! [F_14: produc1572197287le_alt > $o,A_35: arrow_1389031998le_alt,B_28: arrow_1389031998le_alt] :
( ( F_14 @ ( produc897867031le_alt @ A_35 @ B_28 ) )
=> ( produc1084757966_alt_o @ F_14 @ A_35 @ B_28 ) ) ).
thf(fact_330_curryE,axiom,
! [F_13: produc2069254453le_alt > $o,A_34: list_A1402527603le_alt,B_27: list_A1402527603le_alt] :
( ( produc28228666_alt_o @ F_13 @ A_34 @ B_27 )
=> ( F_13 @ ( produc1014865963le_alt @ A_34 @ B_27 ) ) ) ).
thf(fact_331_curryE,axiom,
! [F_13: produc1572197287le_alt > $o,A_34: arrow_1389031998le_alt,B_27: arrow_1389031998le_alt] :
( ( produc1084757966_alt_o @ F_13 @ A_34 @ B_27 )
=> ( F_13 @ ( produc897867031le_alt @ A_34 @ B_27 ) ) ) ).
thf(fact_332_curryD,axiom,
! [F_12: produc2069254453le_alt > $o,A_33: list_A1402527603le_alt,B_26: list_A1402527603le_alt] :
( ( produc28228666_alt_o @ F_12 @ A_33 @ B_26 )
=> ( F_12 @ ( produc1014865963le_alt @ A_33 @ B_26 ) ) ) ).
thf(fact_333_curryD,axiom,
! [F_12: produc1572197287le_alt > $o,A_33: arrow_1389031998le_alt,B_26: arrow_1389031998le_alt] :
( ( produc1084757966_alt_o @ F_12 @ A_33 @ B_26 )
=> ( F_12 @ ( produc897867031le_alt @ A_33 @ B_26 ) ) ) ).
thf(fact_334_distinct__insert,axiom,
! [X_101: arrow_1389031998le_alt,Xs_159: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ Xs_159 )
=> ( distin1149997281le_alt @ ( insert886756100le_alt @ X_101 @ Xs_159 ) ) ) ).
thf(fact_335_curry__conv,axiom,
! [F_11: produc1572197287le_alt > $o,A_32: arrow_1389031998le_alt,B_25: arrow_1389031998le_alt] :
( ( produc1084757966_alt_o @ F_11 @ A_32 @ B_25 )
<=> ( F_11 @ ( produc897867031le_alt @ A_32 @ B_25 ) ) ) ).
thf(fact_336_null__rec_I2_J,axiom,
null_A287154422le_alt @ nil_Ar52383470le_alt ).
thf(fact_337_List_Onull__def,axiom,
! [Xs_158: list_A1402527603le_alt] :
( ( null_A287154422le_alt @ Xs_158 )
<=> ( Xs_158 = nil_Ar52383470le_alt ) ) ).
thf(fact_338_eq__Nil__null,axiom,
! [Xs_157: list_A1402527603le_alt] :
( ( Xs_157 = nil_Ar52383470le_alt )
<=> ( null_A287154422le_alt @ Xs_157 ) ) ).
thf(fact_339_null__rec_I1_J,axiom,
! [X_100: arrow_1389031998le_alt,Xs_156: list_A1402527603le_alt] :
~ ( null_A287154422le_alt @ ( cons_A1142416030le_alt @ X_100 @ Xs_156 ) ) ).
thf(fact_340_Prof__def,axiom,
( arrow_1647925946e_Prof
= ( pi_Arr1309696186_alt_o @ top_to54564308indi_o
@ ^ [Uu: arrow_1196572341e_indi] : arrow_1982173296le_Lin ) ) ).
thf(fact_341_lexord__cons__cons,axiom,
! [A_31: list_A1402527603le_alt,X_99: list_l1230899348le_alt,B_24: list_A1402527603le_alt,Y_37: list_l1230899348le_alt,R_63: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ ( cons_l2069870355le_alt @ A_31 @ X_99 ) @ ( cons_l2069870355le_alt @ B_24 @ Y_37 ) ) @ ( lexord1904689174le_alt @ R_63 ) )
<=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ A_31 @ B_24 ) @ R_63 )
| ( ( A_31 = B_24 )
& ( member104660884le_alt @ ( produc110512663le_alt @ X_99 @ Y_37 ) @ ( lexord1904689174le_alt @ R_63 ) ) ) ) ) ).
thf(fact_342_lexord__cons__cons,axiom,
! [A_31: arrow_1389031998le_alt,X_99: list_A1402527603le_alt,B_24: arrow_1389031998le_alt,Y_37: list_A1402527603le_alt,R_63: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ A_31 @ X_99 ) @ ( cons_A1142416030le_alt @ B_24 @ Y_37 ) ) @ ( lexord1871768411le_alt @ R_63 ) )
<=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_31 @ B_24 ) @ R_63 )
| ( ( A_31 = B_24 )
& ( member735418658le_alt @ ( produc1014865963le_alt @ X_99 @ Y_37 ) @ ( lexord1871768411le_alt @ R_63 ) ) ) ) ) ).
thf(fact_343_distinct__butlast,axiom,
! [Xs_155: list_A1402527603le_alt] :
( ( Xs_155 != nil_Ar52383470le_alt )
=> ( ( distin1149997281le_alt @ Xs_155 )
=> ( distin1149997281le_alt @ ( butlas1188620858le_alt @ Xs_155 ) ) ) ) ).
thf(fact_344_last_Osimps,axiom,
! [X_98: arrow_1389031998le_alt,Xs_154: list_A1402527603le_alt] :
( ( ( Xs_154 = nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( cons_A1142416030le_alt @ X_98 @ Xs_154 ) )
= X_98 ) )
& ( ( Xs_154 != nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( cons_A1142416030le_alt @ X_98 @ Xs_154 ) )
= ( last_A2130988295le_alt @ Xs_154 ) ) ) ) ).
thf(fact_345_top1I,axiom,
! [X_97: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( top_to1492351398lt_o_o @ X_97 ) ).
thf(fact_346_top1I,axiom,
! [X_97: produc1572197287le_alt > $o] : ( top_to1806834203lt_o_o @ X_97 ) ).
thf(fact_347_top1I,axiom,
! [X_97: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( top_to732317616lt_o_o @ X_97 ) ).
thf(fact_348_top1I,axiom,
! [X_97: produc1572197287le_alt] : ( top_to558618722_alt_o @ X_97 ) ).
thf(fact_349_top1I,axiom,
! [X_97: arrow_1196572341e_indi] : ( top_to54564308indi_o @ X_97 ) ).
thf(fact_350_top1I,axiom,
! [X_97: arrow_1389031998le_alt] : ( top_to1031852101_alt_o @ X_97 ) ).
thf(fact_351_Pi__UNIV,axiom,
! [A_30: produc1572197287le_alt > $o] :
( ( pi_Pro418549519_alt_o @ A_30
@ ^ [Uu: produc1572197287le_alt] : top_top_o_o )
= top_to1806834203lt_o_o ) ).
thf(fact_352_Pi__UNIV,axiom,
! [A_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( pi_Arr1196397536_alt_o @ A_30
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : top_to1806834203lt_o_o )
= top_to1492351398lt_o_o ) ).
thf(fact_353_Pi__UNIV,axiom,
! [A_30: arrow_1196572341e_indi > $o] :
( ( pi_Arr1309696186_alt_o @ A_30
@ ^ [Uu: arrow_1196572341e_indi] : top_to1806834203lt_o_o )
= top_to732317616lt_o_o ) ).
thf(fact_354_butlast_Osimps_I1_J,axiom,
( ( butlas1188620858le_alt @ nil_Ar52383470le_alt )
= nil_Ar52383470le_alt ) ).
thf(fact_355_lexord__Nil__right,axiom,
! [X_96: list_A1402527603le_alt,R_62: produc1572197287le_alt > $o] :
~ ( member735418658le_alt @ ( produc1014865963le_alt @ X_96 @ nil_Ar52383470le_alt ) @ ( lexord1871768411le_alt @ R_62 ) ) ).
thf(fact_356_butlast_Osimps_I2_J,axiom,
! [X_95: arrow_1389031998le_alt,Xs_153: list_A1402527603le_alt] :
( ( ( Xs_153 = nil_Ar52383470le_alt )
=> ( ( butlas1188620858le_alt @ ( cons_A1142416030le_alt @ X_95 @ Xs_153 ) )
= nil_Ar52383470le_alt ) )
& ( ( Xs_153 != nil_Ar52383470le_alt )
=> ( ( butlas1188620858le_alt @ ( cons_A1142416030le_alt @ X_95 @ Xs_153 ) )
= ( cons_A1142416030le_alt @ X_95 @ ( butlas1188620858le_alt @ Xs_153 ) ) ) ) ) ).
thf(fact_357_last__ConsL,axiom,
! [X_94: arrow_1389031998le_alt,Xs_152: list_A1402527603le_alt] :
( ( Xs_152 = nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( cons_A1142416030le_alt @ X_94 @ Xs_152 ) )
= X_94 ) ) ).
thf(fact_358_last__ConsR,axiom,
! [X_93: arrow_1389031998le_alt,Xs_151: list_A1402527603le_alt] :
( ( Xs_151 != nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( cons_A1142416030le_alt @ X_93 @ Xs_151 ) )
= ( last_A2130988295le_alt @ Xs_151 ) ) ) ).
thf(fact_359_lexord__Nil__left,axiom,
! [Y_36: list_A1402527603le_alt,R_61: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ nil_Ar52383470le_alt @ Y_36 ) @ ( lexord1871768411le_alt @ R_61 ) )
<=> ? [A_14: arrow_1389031998le_alt,X_1: list_A1402527603le_alt] :
( Y_36
= ( cons_A1142416030le_alt @ A_14 @ X_1 ) ) ) ).
thf(fact_360_lexord__linear,axiom,
! [X_92: list_l1230899348le_alt,Y_35: list_l1230899348le_alt,R_60: produc2069254453le_alt > $o] :
( ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_14 @ B_10 ) @ R_60 )
| ( A_14 = B_10 )
| ( member735418658le_alt @ ( produc1014865963le_alt @ B_10 @ A_14 ) @ R_60 ) )
=> ( ( member104660884le_alt @ ( produc110512663le_alt @ X_92 @ Y_35 ) @ ( lexord1904689174le_alt @ R_60 ) )
| ( X_92 = Y_35 )
| ( member104660884le_alt @ ( produc110512663le_alt @ Y_35 @ X_92 ) @ ( lexord1904689174le_alt @ R_60 ) ) ) ) ).
thf(fact_361_lexord__linear,axiom,
! [X_92: list_A1402527603le_alt,Y_35: list_A1402527603le_alt,R_60: produc1572197287le_alt > $o] :
( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ R_60 )
| ( A_14 = B_10 )
| ( member285112084le_alt @ ( produc897867031le_alt @ B_10 @ A_14 ) @ R_60 ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ X_92 @ Y_35 ) @ ( lexord1871768411le_alt @ R_60 ) )
| ( X_92 = Y_35 )
| ( member735418658le_alt @ ( produc1014865963le_alt @ Y_35 @ X_92 ) @ ( lexord1871768411le_alt @ R_60 ) ) ) ) ).
thf(fact_362_lexord__irreflexive,axiom,
! [Xs_150: list_l1230899348le_alt,R_59: produc2069254453le_alt > $o] :
( ! [X_1: list_A1402527603le_alt] :
~ ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ X_1 ) @ R_59 )
=> ~ ( member104660884le_alt @ ( produc110512663le_alt @ Xs_150 @ Xs_150 ) @ ( lexord1904689174le_alt @ R_59 ) ) ) ).
thf(fact_363_lexord__irreflexive,axiom,
! [Xs_150: list_A1402527603le_alt,R_59: produc1572197287le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] :
~ ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ X_1 ) @ R_59 )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_150 @ Xs_150 ) @ ( lexord1871768411le_alt @ R_59 ) ) ) ).
thf(fact_364_iso__tuple__UNIV__I,axiom,
! [X_91: nat] : ( member_nat @ X_91 @ top_top_nat_o ) ).
thf(fact_365_iso__tuple__UNIV__I,axiom,
! [X_91: produc2069254453le_alt] : ( member735418658le_alt @ X_91 @ top_to1489741524_alt_o ) ).
thf(fact_366_iso__tuple__UNIV__I,axiom,
! [X_91: $o] : ( member_o @ X_91 @ top_top_o_o ) ).
thf(fact_367_iso__tuple__UNIV__I,axiom,
! [X_91: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_91 @ top_to54564308indi_o ) ).
thf(fact_368_iso__tuple__UNIV__I,axiom,
! [X_91: arrow_1389031998le_alt] : ( member998036369le_alt @ X_91 @ top_to1031852101_alt_o ) ).
thf(fact_369_iso__tuple__UNIV__I,axiom,
! [X_91: produc1572197287le_alt] : ( member285112084le_alt @ X_91 @ top_to558618722_alt_o ) ).
thf(fact_370_iso__tuple__UNIV__I,axiom,
! [X_91: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( member822980838_alt_o @ X_91 @ top_to732317616lt_o_o ) ).
thf(fact_371_iso__tuple__UNIV__I,axiom,
! [X_91: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ X_91 @ top_to1806834203lt_o_o ) ).
thf(fact_372_iso__tuple__UNIV__I,axiom,
! [X_91: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( member1425217232_alt_o @ X_91 @ top_to1492351398lt_o_o ) ).
thf(fact_373_UNIV__I,axiom,
! [X_90: nat] : ( member_nat @ X_90 @ top_top_nat_o ) ).
thf(fact_374_UNIV__I,axiom,
! [X_90: produc2069254453le_alt] : ( member735418658le_alt @ X_90 @ top_to1489741524_alt_o ) ).
thf(fact_375_UNIV__I,axiom,
! [X_90: $o] : ( member_o @ X_90 @ top_top_o_o ) ).
thf(fact_376_UNIV__I,axiom,
! [X_90: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_90 @ top_to54564308indi_o ) ).
thf(fact_377_UNIV__I,axiom,
! [X_90: arrow_1389031998le_alt] : ( member998036369le_alt @ X_90 @ top_to1031852101_alt_o ) ).
thf(fact_378_UNIV__I,axiom,
! [X_90: produc1572197287le_alt] : ( member285112084le_alt @ X_90 @ top_to558618722_alt_o ) ).
thf(fact_379_UNIV__I,axiom,
! [X_90: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( member822980838_alt_o @ X_90 @ top_to732317616lt_o_o ) ).
thf(fact_380_UNIV__I,axiom,
! [X_90: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ X_90 @ top_to1806834203lt_o_o ) ).
thf(fact_381_UNIV__I,axiom,
! [X_90: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( member1425217232_alt_o @ X_90 @ top_to1492351398lt_o_o ) ).
thf(fact_382_top__apply,axiom,
! [X_89: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( top_to1492351398lt_o_o @ X_89 )
<=> top_top_o ) ).
thf(fact_383_top__apply,axiom,
! [X_89: produc1572197287le_alt > $o] :
( ( top_to1806834203lt_o_o @ X_89 )
<=> top_top_o ) ).
thf(fact_384_top__apply,axiom,
! [X_89: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( top_to732317616lt_o_o @ X_89 )
<=> top_top_o ) ).
thf(fact_385_top__apply,axiom,
! [X_89: produc1572197287le_alt] :
( ( top_to558618722_alt_o @ X_89 )
<=> top_top_o ) ).
thf(fact_386_top__apply,axiom,
! [X_89: arrow_1196572341e_indi] :
( ( top_to54564308indi_o @ X_89 )
<=> top_top_o ) ).
thf(fact_387_top__apply,axiom,
! [X_89: arrow_1389031998le_alt] :
( ( top_to1031852101_alt_o @ X_89 )
<=> top_top_o ) ).
thf(fact_388_takeWhile__not__last,axiom,
! [Xs_149: list_A1402527603le_alt] :
( ( Xs_149 != nil_Ar52383470le_alt )
=> ( ( distin1149997281le_alt @ Xs_149 )
=> ( ( takeWh462480871le_alt
@ ^ [Y_10: arrow_1389031998le_alt] :
( (~)
@ ( Y_10
= ( last_A2130988295le_alt @ Xs_149 ) ) )
@ Xs_149 )
= ( butlas1188620858le_alt @ Xs_149 ) ) ) ) ).
thf(fact_389_equal__Nil__null,axiom,
! [Xs_148: list_A1402527603le_alt] :
( ( equal_1919384209le_alt @ Xs_148 @ nil_Ar52383470le_alt )
<=> ( null_A287154422le_alt @ Xs_148 ) ) ).
thf(fact_390_partition_Osimps_I1_J,axiom,
! [P_45: arrow_1389031998le_alt > $o] :
( ( partit253767143le_alt @ P_45 @ nil_Ar52383470le_alt )
= ( produc1014865963le_alt @ nil_Ar52383470le_alt @ nil_Ar52383470le_alt ) ) ).
thf(fact_391_append__butlast__last__id,axiom,
! [Xs_147: list_A1402527603le_alt] :
( ( Xs_147 != nil_Ar52383470le_alt )
=> ( ( append1092755459le_alt @ ( butlas1188620858le_alt @ Xs_147 ) @ ( cons_A1142416030le_alt @ ( last_A2130988295le_alt @ Xs_147 ) @ nil_Ar52383470le_alt ) )
= Xs_147 ) ) ).
thf(fact_392_takeWhile__tail,axiom,
! [Xs_146: list_A1402527603le_alt,L_3: list_A1402527603le_alt,P_44: arrow_1389031998le_alt > $o,X_88: arrow_1389031998le_alt] :
( ~ ( P_44 @ X_88 )
=> ( ( takeWh462480871le_alt @ P_44 @ ( append1092755459le_alt @ Xs_146 @ ( cons_A1142416030le_alt @ X_88 @ L_3 ) ) )
= ( takeWh462480871le_alt @ P_44 @ Xs_146 ) ) ) ).
thf(fact_393_append__eq__appendI,axiom,
! [Ys_64: list_A1402527603le_alt,Us_3: list_A1402527603le_alt,Xs_145: list_A1402527603le_alt,Xs1_1: list_A1402527603le_alt,Zs_10: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Xs_145 @ Xs1_1 )
= Zs_10 )
=> ( ( Ys_64
= ( append1092755459le_alt @ Xs1_1 @ Us_3 ) )
=> ( ( append1092755459le_alt @ Xs_145 @ Ys_64 )
= ( append1092755459le_alt @ Zs_10 @ Us_3 ) ) ) ) ).
thf(fact_394_append__same__eq,axiom,
! [Ys_63: list_A1402527603le_alt,Xs_144: list_A1402527603le_alt,Zs_9: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Ys_63 @ Xs_144 )
= ( append1092755459le_alt @ Zs_9 @ Xs_144 ) )
<=> ( Ys_63 = Zs_9 ) ) ).
thf(fact_395_same__append__eq,axiom,
! [Xs_143: list_A1402527603le_alt,Ys_62: list_A1402527603le_alt,Zs_8: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Xs_143 @ Ys_62 )
= ( append1092755459le_alt @ Xs_143 @ Zs_8 ) )
<=> ( Ys_62 = Zs_8 ) ) ).
thf(fact_396_append__eq__append__conv2,axiom,
! [Xs_142: list_A1402527603le_alt,Ys_61: list_A1402527603le_alt,Zs_7: list_A1402527603le_alt,Ts: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Xs_142 @ Ys_61 )
= ( append1092755459le_alt @ Zs_7 @ Ts ) )
<=> ? [Us: list_A1402527603le_alt] :
( ( ( Xs_142
= ( append1092755459le_alt @ Zs_7 @ Us ) )
& ( ( append1092755459le_alt @ Us @ Ys_61 )
= Ts ) )
| ( ( ( append1092755459le_alt @ Xs_142 @ Us )
= Zs_7 )
& ( Ys_61
= ( append1092755459le_alt @ Us @ Ts ) ) ) ) ) ).
thf(fact_397_append__assoc,axiom,
! [Xs_141: list_A1402527603le_alt,Ys_60: list_A1402527603le_alt,Zs_6: list_A1402527603le_alt] :
( ( append1092755459le_alt @ ( append1092755459le_alt @ Xs_141 @ Ys_60 ) @ Zs_6 )
= ( append1092755459le_alt @ Xs_141 @ ( append1092755459le_alt @ Ys_60 @ Zs_6 ) ) ) ).
thf(fact_398_equal__list__def,axiom,
! [X_87: list_A1402527603le_alt,Y_34: list_A1402527603le_alt] :
( ( equal_1919384209le_alt @ X_87 @ Y_34 )
<=> ( X_87 = Y_34 ) ) ).
thf(fact_399_append__Cons,axiom,
! [X_86: arrow_1389031998le_alt,Xs_140: list_A1402527603le_alt,Ys_59: list_A1402527603le_alt] :
( ( append1092755459le_alt @ ( cons_A1142416030le_alt @ X_86 @ Xs_140 ) @ Ys_59 )
= ( cons_A1142416030le_alt @ X_86 @ ( append1092755459le_alt @ Xs_140 @ Ys_59 ) ) ) ).
thf(fact_400_Cons__eq__appendI,axiom,
! [Xs_139: list_A1402527603le_alt,Zs_5: list_A1402527603le_alt,X_85: arrow_1389031998le_alt,Xs1: list_A1402527603le_alt,Ys_58: list_A1402527603le_alt] :
( ( ( cons_A1142416030le_alt @ X_85 @ Xs1 )
= Ys_58 )
=> ( ( Xs_139
= ( append1092755459le_alt @ Xs1 @ Zs_5 ) )
=> ( ( cons_A1142416030le_alt @ X_85 @ Xs_139 )
= ( append1092755459le_alt @ Ys_58 @ Zs_5 ) ) ) ) ).
thf(fact_401_append__Nil,axiom,
! [Ys_57: list_A1402527603le_alt] :
( ( append1092755459le_alt @ nil_Ar52383470le_alt @ Ys_57 )
= Ys_57 ) ).
thf(fact_402_Nil__is__append__conv,axiom,
! [Xs_138: list_A1402527603le_alt,Ys_56: list_A1402527603le_alt] :
( ( nil_Ar52383470le_alt
= ( append1092755459le_alt @ Xs_138 @ Ys_56 ) )
<=> ( ( Xs_138 = nil_Ar52383470le_alt )
& ( Ys_56 = nil_Ar52383470le_alt ) ) ) ).
thf(fact_403_append__Nil2,axiom,
! [Xs_137: list_A1402527603le_alt] :
( ( append1092755459le_alt @ Xs_137 @ nil_Ar52383470le_alt )
= Xs_137 ) ).
thf(fact_404_self__append__conv,axiom,
! [Xs_136: list_A1402527603le_alt,Ys_55: list_A1402527603le_alt] :
( ( Xs_136
= ( append1092755459le_alt @ Xs_136 @ Ys_55 ) )
<=> ( Ys_55 = nil_Ar52383470le_alt ) ) ).
thf(fact_405_self__append__conv2,axiom,
! [Ys_54: list_A1402527603le_alt,Xs_135: list_A1402527603le_alt] :
( ( Ys_54
= ( append1092755459le_alt @ Xs_135 @ Ys_54 ) )
<=> ( Xs_135 = nil_Ar52383470le_alt ) ) ).
thf(fact_406_append__is__Nil__conv,axiom,
! [Xs_134: list_A1402527603le_alt,Ys_53: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Xs_134 @ Ys_53 )
= nil_Ar52383470le_alt )
<=> ( ( Xs_134 = nil_Ar52383470le_alt )
& ( Ys_53 = nil_Ar52383470le_alt ) ) ) ).
thf(fact_407_append__self__conv,axiom,
! [Xs_133: list_A1402527603le_alt,Ys_52: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Xs_133 @ Ys_52 )
= Xs_133 )
<=> ( Ys_52 = nil_Ar52383470le_alt ) ) ).
thf(fact_408_append__self__conv2,axiom,
! [Xs_132: list_A1402527603le_alt,Ys_51: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Xs_132 @ Ys_51 )
= Ys_51 )
<=> ( Xs_132 = nil_Ar52383470le_alt ) ) ).
thf(fact_409_eq__Nil__appendI,axiom,
! [Xs_131: list_A1402527603le_alt,Ys_50: list_A1402527603le_alt] :
( ( Xs_131 = Ys_50 )
=> ( Xs_131
= ( append1092755459le_alt @ nil_Ar52383470le_alt @ Ys_50 ) ) ) ).
thf(fact_410_takeWhile_Osimps_I1_J,axiom,
! [P_43: arrow_1389031998le_alt > $o] :
( ( takeWh462480871le_alt @ P_43 @ nil_Ar52383470le_alt )
= nil_Ar52383470le_alt ) ).
thf(fact_411_distinct__takeWhile,axiom,
! [P_42: arrow_1389031998le_alt > $o,Xs_130: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ Xs_130 )
=> ( distin1149997281le_alt @ ( takeWh462480871le_alt @ P_42 @ Xs_130 ) ) ) ).
thf(fact_412_append__eq__Cons__conv,axiom,
! [Ys_49: list_A1402527603le_alt,Zs_4: list_A1402527603le_alt,X_84: arrow_1389031998le_alt,Xs_129: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Ys_49 @ Zs_4 )
= ( cons_A1142416030le_alt @ X_84 @ Xs_129 ) )
<=> ( ( ( Ys_49 = nil_Ar52383470le_alt )
& ( Zs_4
= ( cons_A1142416030le_alt @ X_84 @ Xs_129 ) ) )
| ? [Ys_48: list_A1402527603le_alt] :
( ( Ys_49
= ( cons_A1142416030le_alt @ X_84 @ Ys_48 ) )
& ( ( append1092755459le_alt @ Ys_48 @ Zs_4 )
= Xs_129 ) ) ) ) ).
thf(fact_413_Cons__eq__append__conv,axiom,
! [X_83: arrow_1389031998le_alt,Xs_128: list_A1402527603le_alt,Ys_47: list_A1402527603le_alt,Zs_3: list_A1402527603le_alt] :
( ( ( cons_A1142416030le_alt @ X_83 @ Xs_128 )
= ( append1092755459le_alt @ Ys_47 @ Zs_3 ) )
<=> ( ( ( Ys_47 = nil_Ar52383470le_alt )
& ( ( cons_A1142416030le_alt @ X_83 @ Xs_128 )
= Zs_3 ) )
| ? [Ys_48: list_A1402527603le_alt] :
( ( ( cons_A1142416030le_alt @ X_83 @ Ys_48 )
= Ys_47 )
& ( Xs_128
= ( append1092755459le_alt @ Ys_48 @ Zs_3 ) ) ) ) ) ).
thf(fact_414_append1__eq__conv,axiom,
! [Xs_127: list_A1402527603le_alt,X_82: arrow_1389031998le_alt,Ys_46: list_A1402527603le_alt,Y_33: arrow_1389031998le_alt] :
( ( ( append1092755459le_alt @ Xs_127 @ ( cons_A1142416030le_alt @ X_82 @ nil_Ar52383470le_alt ) )
= ( append1092755459le_alt @ Ys_46 @ ( cons_A1142416030le_alt @ Y_33 @ nil_Ar52383470le_alt ) ) )
<=> ( ( Xs_127 = Ys_46 )
& ( X_82 = Y_33 ) ) ) ).
thf(fact_415_butlast__append,axiom,
! [Xs_126: list_A1402527603le_alt,Ys_45: list_A1402527603le_alt] :
( ( ( Ys_45 = nil_Ar52383470le_alt )
=> ( ( butlas1188620858le_alt @ ( append1092755459le_alt @ Xs_126 @ Ys_45 ) )
= ( butlas1188620858le_alt @ Xs_126 ) ) )
& ( ( Ys_45 != nil_Ar52383470le_alt )
=> ( ( butlas1188620858le_alt @ ( append1092755459le_alt @ Xs_126 @ Ys_45 ) )
= ( append1092755459le_alt @ Xs_126 @ ( butlas1188620858le_alt @ Ys_45 ) ) ) ) ) ).
thf(fact_416_last__appendL,axiom,
! [Xs_125: list_A1402527603le_alt,Ys_44: list_A1402527603le_alt] :
( ( Ys_44 = nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( append1092755459le_alt @ Xs_125 @ Ys_44 ) )
= ( last_A2130988295le_alt @ Xs_125 ) ) ) ).
thf(fact_417_last__appendR,axiom,
! [Xs_124: list_A1402527603le_alt,Ys_43: list_A1402527603le_alt] :
( ( Ys_43 != nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( append1092755459le_alt @ Xs_124 @ Ys_43 ) )
= ( last_A2130988295le_alt @ Ys_43 ) ) ) ).
thf(fact_418_last__append,axiom,
! [Xs_123: list_A1402527603le_alt,Ys_42: list_A1402527603le_alt] :
( ( ( Ys_42 = nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( append1092755459le_alt @ Xs_123 @ Ys_42 ) )
= ( last_A2130988295le_alt @ Xs_123 ) ) )
& ( ( Ys_42 != nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( append1092755459le_alt @ Xs_123 @ Ys_42 ) )
= ( last_A2130988295le_alt @ Ys_42 ) ) ) ) ).
thf(fact_419_lexord__append__leftI,axiom,
! [X_81: list_A1402527603le_alt,U_2: list_A1402527603le_alt,V_3: list_A1402527603le_alt,R_58: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ U_2 @ V_3 ) @ ( lexord1871768411le_alt @ R_58 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ ( append1092755459le_alt @ X_81 @ U_2 ) @ ( append1092755459le_alt @ X_81 @ V_3 ) ) @ ( lexord1871768411le_alt @ R_58 ) ) ) ).
thf(fact_420_takeWhile_Osimps_I2_J,axiom,
! [Xs_122: list_A1402527603le_alt,P_41: arrow_1389031998le_alt > $o,X_80: arrow_1389031998le_alt] :
( ( ( P_41 @ X_80 )
=> ( ( takeWh462480871le_alt @ P_41 @ ( cons_A1142416030le_alt @ X_80 @ Xs_122 ) )
= ( cons_A1142416030le_alt @ X_80 @ ( takeWh462480871le_alt @ P_41 @ Xs_122 ) ) ) )
& ( ~ ( P_41 @ X_80 )
=> ( ( takeWh462480871le_alt @ P_41 @ ( cons_A1142416030le_alt @ X_80 @ Xs_122 ) )
= nil_Ar52383470le_alt ) ) ) ).
thf(fact_421_maps__simps_I1_J,axiom,
! [F_10: arrow_1389031998le_alt > list_A1402527603le_alt,X_79: arrow_1389031998le_alt,Xs_121: list_A1402527603le_alt] :
( ( maps_A2106577089le_alt @ F_10 @ ( cons_A1142416030le_alt @ X_79 @ Xs_121 ) )
= ( append1092755459le_alt @ ( F_10 @ X_79 ) @ ( maps_A2106577089le_alt @ F_10 @ Xs_121 ) ) ) ).
thf(fact_422_butlast__snoc,axiom,
! [Xs_120: list_A1402527603le_alt,X_78: arrow_1389031998le_alt] :
( ( butlas1188620858le_alt @ ( append1092755459le_alt @ Xs_120 @ ( cons_A1142416030le_alt @ X_78 @ nil_Ar52383470le_alt ) ) )
= Xs_120 ) ).
thf(fact_423_last__snoc,axiom,
! [Xs_119: list_A1402527603le_alt,X_77: arrow_1389031998le_alt] :
( ( last_A2130988295le_alt @ ( append1092755459le_alt @ Xs_119 @ ( cons_A1142416030le_alt @ X_77 @ nil_Ar52383470le_alt ) ) )
= X_77 ) ).
thf(fact_424_UNIV__def,axiom,
( top_top_nat_o
= ( collect_nat
@ ^ [X_1: nat] : $true ) ) ).
thf(fact_425_UNIV__def,axiom,
( top_to1492351398lt_o_o
= ( collec670126350_alt_o
@ ^ [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : $true ) ) ).
thf(fact_426_UNIV__def,axiom,
( top_to732317616lt_o_o
= ( collec979749928_alt_o
@ ^ [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] : $true ) ) ).
thf(fact_427_UNIV__def,axiom,
( top_to558618722_alt_o
= ( collec940901970le_alt
@ ^ [X_1: produc1572197287le_alt] : $true ) ) ).
thf(fact_428_UNIV__def,axiom,
( top_to54564308indi_o
= ( collec1936859488e_indi
@ ^ [X_1: arrow_1196572341e_indi] : $true ) ) ).
thf(fact_429_UNIV__def,axiom,
( top_to1031852101_alt_o
= ( collec1655747795le_alt
@ ^ [X_1: arrow_1389031998le_alt] : $true ) ) ).
thf(fact_430_UNIV__def,axiom,
( top_to1806834203lt_o_o
= ( collec958969213_alt_o
@ ^ [X_1: produc1572197287le_alt > $o] : $true ) ) ).
thf(fact_431_lexord__append__left__rightI,axiom,
! [U_1: list_l1230899348le_alt,X_76: list_l1230899348le_alt,Y_32: list_l1230899348le_alt,A_29: list_A1402527603le_alt,B_23: list_A1402527603le_alt,R_57: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_29 @ B_23 ) @ R_57 )
=> ( member104660884le_alt @ ( produc110512663le_alt @ ( append453290350le_alt @ U_1 @ ( cons_l2069870355le_alt @ A_29 @ X_76 ) ) @ ( append453290350le_alt @ U_1 @ ( cons_l2069870355le_alt @ B_23 @ Y_32 ) ) ) @ ( lexord1904689174le_alt @ R_57 ) ) ) ).
thf(fact_432_lexord__append__left__rightI,axiom,
! [U_1: list_A1402527603le_alt,X_76: list_A1402527603le_alt,Y_32: list_A1402527603le_alt,A_29: arrow_1389031998le_alt,B_23: arrow_1389031998le_alt,R_57: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_29 @ B_23 ) @ R_57 )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ ( append1092755459le_alt @ U_1 @ ( cons_A1142416030le_alt @ A_29 @ X_76 ) ) @ ( append1092755459le_alt @ U_1 @ ( cons_A1142416030le_alt @ B_23 @ Y_32 ) ) ) @ ( lexord1871768411le_alt @ R_57 ) ) ) ).
thf(fact_433_snoc__eq__iff__butlast,axiom,
! [Xs_118: list_A1402527603le_alt,X_75: arrow_1389031998le_alt,Ys_41: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Xs_118 @ ( cons_A1142416030le_alt @ X_75 @ nil_Ar52383470le_alt ) )
= Ys_41 )
<=> ( ( Ys_41 != nil_Ar52383470le_alt )
& ( ( butlas1188620858le_alt @ Ys_41 )
= Xs_118 )
& ( ( last_A2130988295le_alt @ Ys_41 )
= X_75 ) ) ) ).
thf(fact_434_lexord__append__rightI,axiom,
! [X_74: list_A1402527603le_alt,R_56: produc1572197287le_alt > $o,Y_31: list_A1402527603le_alt] :
( ? [B_10: arrow_1389031998le_alt,Z_4: list_A1402527603le_alt] :
( Y_31
= ( cons_A1142416030le_alt @ B_10 @ Z_4 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ X_74 @ ( append1092755459le_alt @ X_74 @ Y_31 ) ) @ ( lexord1871768411le_alt @ R_56 ) ) ) ).
thf(fact_435_lexord__append__leftD,axiom,
! [X_73: list_l1230899348le_alt,U: list_l1230899348le_alt,V_2: list_l1230899348le_alt,R_55: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ ( append453290350le_alt @ X_73 @ U ) @ ( append453290350le_alt @ X_73 @ V_2 ) ) @ ( lexord1904689174le_alt @ R_55 ) )
=> ( ! [A_14: list_A1402527603le_alt] :
~ ( member735418658le_alt @ ( produc1014865963le_alt @ A_14 @ A_14 ) @ R_55 )
=> ( member104660884le_alt @ ( produc110512663le_alt @ U @ V_2 ) @ ( lexord1904689174le_alt @ R_55 ) ) ) ) ).
thf(fact_436_lexord__append__leftD,axiom,
! [X_73: list_A1402527603le_alt,U: list_A1402527603le_alt,V_2: list_A1402527603le_alt,R_55: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ ( append1092755459le_alt @ X_73 @ U ) @ ( append1092755459le_alt @ X_73 @ V_2 ) ) @ ( lexord1871768411le_alt @ R_55 ) )
=> ( ! [A_14: arrow_1389031998le_alt] :
~ ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ A_14 ) @ R_55 )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ U @ V_2 ) @ ( lexord1871768411le_alt @ R_55 ) ) ) ) ).
thf(fact_437_rev__induct,axiom,
! [Xs_117: list_A1402527603le_alt,P_40: list_A1402527603le_alt > $o] :
( ( P_40 @ nil_Ar52383470le_alt )
=> ( ! [X_1: arrow_1389031998le_alt,Xs_71: list_A1402527603le_alt] :
( ( P_40 @ Xs_71 )
=> ( P_40 @ ( append1092755459le_alt @ Xs_71 @ ( cons_A1142416030le_alt @ X_1 @ nil_Ar52383470le_alt ) ) ) )
=> ( P_40 @ Xs_117 ) ) ) ).
thf(fact_438_rev__cases,axiom,
! [Xs_116: list_A1402527603le_alt] :
( ( Xs_116 != nil_Ar52383470le_alt )
=> ~ ! [Ys: list_A1402527603le_alt,Y_10: arrow_1389031998le_alt] :
( Xs_116
!= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ Y_10 @ nil_Ar52383470le_alt ) ) ) ) ).
thf(fact_439_snoc__listrel1__snoc__iff,axiom,
! [Xs_115: list_l1230899348le_alt,X_72: list_A1402527603le_alt,Ys_40: list_l1230899348le_alt,Y_30: list_A1402527603le_alt,R_54: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ ( append453290350le_alt @ Xs_115 @ ( cons_l2069870355le_alt @ X_72 @ nil_li1194575555le_alt ) ) @ ( append453290350le_alt @ Ys_40 @ ( cons_l2069870355le_alt @ Y_30 @ nil_li1194575555le_alt ) ) ) @ ( listre2055328042le_alt @ R_54 ) )
<=> ( ( ( member104660884le_alt @ ( produc110512663le_alt @ Xs_115 @ Ys_40 ) @ ( listre2055328042le_alt @ R_54 ) )
& ( X_72 = Y_30 ) )
| ( ( Xs_115 = Ys_40 )
& ( member735418658le_alt @ ( produc1014865963le_alt @ X_72 @ Y_30 ) @ R_54 ) ) ) ) ).
thf(fact_440_snoc__listrel1__snoc__iff,axiom,
! [Xs_115: list_A1402527603le_alt,X_72: arrow_1389031998le_alt,Ys_40: list_A1402527603le_alt,Y_30: arrow_1389031998le_alt,R_54: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ ( append1092755459le_alt @ Xs_115 @ ( cons_A1142416030le_alt @ X_72 @ nil_Ar52383470le_alt ) ) @ ( append1092755459le_alt @ Ys_40 @ ( cons_A1142416030le_alt @ Y_30 @ nil_Ar52383470le_alt ) ) ) @ ( listre830192455le_alt @ R_54 ) )
<=> ( ( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_115 @ Ys_40 ) @ ( listre830192455le_alt @ R_54 ) )
& ( X_72 = Y_30 ) )
| ( ( Xs_115 = Ys_40 )
& ( member285112084le_alt @ ( produc897867031le_alt @ X_72 @ Y_30 ) @ R_54 ) ) ) ) ).
thf(fact_441_rotate1__def,axiom,
! [Xs_114: list_A1402527603le_alt] :
( ( rotate1249022267le_alt @ Xs_114 )
= ( list_c1300280951le_alt @ nil_Ar52383470le_alt
@ ^ [X_1: arrow_1389031998le_alt,Xs_71: list_A1402527603le_alt] : ( append1092755459le_alt @ Xs_71 @ ( cons_A1142416030le_alt @ X_1 @ nil_Ar52383470le_alt ) )
@ Xs_114 ) ) ).
thf(fact_442_rotate__simps,axiom,
! [X_71: arrow_1389031998le_alt,Xs_113: list_A1402527603le_alt] :
( ( ( rotate1249022267le_alt @ nil_Ar52383470le_alt )
= nil_Ar52383470le_alt )
& ( ( rotate1249022267le_alt @ ( cons_A1142416030le_alt @ X_71 @ Xs_113 ) )
= ( append1092755459le_alt @ Xs_113 @ ( cons_A1142416030le_alt @ X_71 @ nil_Ar52383470le_alt ) ) ) ) ).
thf(fact_443_UNIV__witness,axiom,
? [X_1: nat] : ( member_nat @ X_1 @ top_top_nat_o ) ).
thf(fact_444_UNIV__witness,axiom,
? [X_1: produc2069254453le_alt] : ( member735418658le_alt @ X_1 @ top_to1489741524_alt_o ) ).
thf(fact_445_UNIV__witness,axiom,
? [X_1: $o] : ( member_o @ X_1 @ top_top_o_o ) ).
thf(fact_446_UNIV__witness,axiom,
? [X_1: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_1 @ top_to54564308indi_o ) ).
thf(fact_447_UNIV__witness,axiom,
? [X_1: arrow_1389031998le_alt] : ( member998036369le_alt @ X_1 @ top_to1031852101_alt_o ) ).
thf(fact_448_UNIV__witness,axiom,
? [X_1: produc1572197287le_alt] : ( member285112084le_alt @ X_1 @ top_to558618722_alt_o ) ).
thf(fact_449_UNIV__witness,axiom,
? [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( member822980838_alt_o @ X_1 @ top_to732317616lt_o_o ) ).
thf(fact_450_UNIV__witness,axiom,
? [X_1: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ X_1 @ top_to1806834203lt_o_o ) ).
thf(fact_451_UNIV__witness,axiom,
? [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( member1425217232_alt_o @ X_1 @ top_to1492351398lt_o_o ) ).
thf(fact_452_UNIV__eq__I,axiom,
! [A_28: nat > $o] :
( ! [X_1: nat] : ( member_nat @ X_1 @ A_28 )
=> ( top_top_nat_o = A_28 ) ) ).
thf(fact_453_UNIV__eq__I,axiom,
! [A_28: produc2069254453le_alt > $o] :
( ! [X_1: produc2069254453le_alt] : ( member735418658le_alt @ X_1 @ A_28 )
=> ( top_to1489741524_alt_o = A_28 ) ) ).
thf(fact_454_UNIV__eq__I,axiom,
! [A_28: $o > $o] :
( ! [X_1: $o] : ( member_o @ X_1 @ A_28 )
=> ( top_top_o_o = A_28 ) ) ).
thf(fact_455_UNIV__eq__I,axiom,
! [A_28: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_1 @ A_28 )
=> ( top_to54564308indi_o = A_28 ) ) ).
thf(fact_456_UNIV__eq__I,axiom,
! [A_28: arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] : ( member998036369le_alt @ X_1 @ A_28 )
=> ( top_to1031852101_alt_o = A_28 ) ) ).
thf(fact_457_UNIV__eq__I,axiom,
! [A_28: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] : ( member285112084le_alt @ X_1 @ A_28 )
=> ( top_to558618722_alt_o = A_28 ) ) ).
thf(fact_458_UNIV__eq__I,axiom,
! [A_28: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( member822980838_alt_o @ X_1 @ A_28 )
=> ( top_to732317616lt_o_o = A_28 ) ) ).
thf(fact_459_UNIV__eq__I,axiom,
! [A_28: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ X_1 @ A_28 )
=> ( top_to1806834203lt_o_o = A_28 ) ) ).
thf(fact_460_UNIV__eq__I,axiom,
! [A_28: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( member1425217232_alt_o @ X_1 @ A_28 )
=> ( top_to1492351398lt_o_o = A_28 ) ) ).
thf(fact_461_rotate1__is__Nil__conv,axiom,
! [Xs_112: list_A1402527603le_alt] :
( ( ( rotate1249022267le_alt @ Xs_112 )
= nil_Ar52383470le_alt )
<=> ( Xs_112 = nil_Ar52383470le_alt ) ) ).
thf(fact_462_distinct1__rotate,axiom,
! [Xs_111: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ ( rotate1249022267le_alt @ Xs_111 ) )
<=> ( distin1149997281le_alt @ Xs_111 ) ) ).
thf(fact_463_listrel1I2,axiom,
! [X_70: arrow_1389031998le_alt,Xs_110: list_A1402527603le_alt,Ys_39: list_A1402527603le_alt,R_53: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_110 @ Ys_39 ) @ ( listre830192455le_alt @ R_53 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_70 @ Xs_110 ) @ ( cons_A1142416030le_alt @ X_70 @ Ys_39 ) ) @ ( listre830192455le_alt @ R_53 ) ) ) ).
thf(fact_464_not__listrel1__Nil,axiom,
! [Xs_109: list_A1402527603le_alt,R_52: produc1572197287le_alt > $o] :
~ ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_109 @ nil_Ar52383470le_alt ) @ ( listre830192455le_alt @ R_52 ) ) ).
thf(fact_465_not__Nil__listrel1,axiom,
! [Xs_108: list_A1402527603le_alt,R_51: produc1572197287le_alt > $o] :
~ ( member735418658le_alt @ ( produc1014865963le_alt @ nil_Ar52383470le_alt @ Xs_108 ) @ ( listre830192455le_alt @ R_51 ) ) ).
thf(fact_466_append__listrel1I,axiom,
! [Us_2: list_A1402527603le_alt,Vs_2: list_A1402527603le_alt,Xs_107: list_A1402527603le_alt,Ys_38: list_A1402527603le_alt,R_50: produc1572197287le_alt > $o] :
( ( ( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_107 @ Ys_38 ) @ ( listre830192455le_alt @ R_50 ) )
& ( Us_2 = Vs_2 ) )
| ( ( Xs_107 = Ys_38 )
& ( member735418658le_alt @ ( produc1014865963le_alt @ Us_2 @ Vs_2 ) @ ( listre830192455le_alt @ R_50 ) ) ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ ( append1092755459le_alt @ Xs_107 @ Us_2 ) @ ( append1092755459le_alt @ Ys_38 @ Vs_2 ) ) @ ( listre830192455le_alt @ R_50 ) ) ) ).
thf(fact_467_Cons__listrel1__Cons,axiom,
! [X_69: list_A1402527603le_alt,Xs_106: list_l1230899348le_alt,Y_29: list_A1402527603le_alt,Ys_37: list_l1230899348le_alt,R_49: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ ( cons_l2069870355le_alt @ X_69 @ Xs_106 ) @ ( cons_l2069870355le_alt @ Y_29 @ Ys_37 ) ) @ ( listre2055328042le_alt @ R_49 ) )
<=> ( ( ( member735418658le_alt @ ( produc1014865963le_alt @ X_69 @ Y_29 ) @ R_49 )
& ( Xs_106 = Ys_37 ) )
| ( ( X_69 = Y_29 )
& ( member104660884le_alt @ ( produc110512663le_alt @ Xs_106 @ Ys_37 ) @ ( listre2055328042le_alt @ R_49 ) ) ) ) ) ).
thf(fact_468_Cons__listrel1__Cons,axiom,
! [X_69: arrow_1389031998le_alt,Xs_106: list_A1402527603le_alt,Y_29: arrow_1389031998le_alt,Ys_37: list_A1402527603le_alt,R_49: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_69 @ Xs_106 ) @ ( cons_A1142416030le_alt @ Y_29 @ Ys_37 ) ) @ ( listre830192455le_alt @ R_49 ) )
<=> ( ( ( member285112084le_alt @ ( produc897867031le_alt @ X_69 @ Y_29 ) @ R_49 )
& ( Xs_106 = Ys_37 ) )
| ( ( X_69 = Y_29 )
& ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_106 @ Ys_37 ) @ ( listre830192455le_alt @ R_49 ) ) ) ) ) ).
thf(fact_469_listrel1I1,axiom,
! [Xs_105: list_l1230899348le_alt,X_68: list_A1402527603le_alt,Y_28: list_A1402527603le_alt,R_48: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_68 @ Y_28 ) @ R_48 )
=> ( member104660884le_alt @ ( produc110512663le_alt @ ( cons_l2069870355le_alt @ X_68 @ Xs_105 ) @ ( cons_l2069870355le_alt @ Y_28 @ Xs_105 ) ) @ ( listre2055328042le_alt @ R_48 ) ) ) ).
thf(fact_470_listrel1I1,axiom,
! [Xs_105: list_A1402527603le_alt,X_68: arrow_1389031998le_alt,Y_28: arrow_1389031998le_alt,R_48: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_68 @ Y_28 ) @ R_48 )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_68 @ Xs_105 ) @ ( cons_A1142416030le_alt @ Y_28 @ Xs_105 ) ) @ ( listre830192455le_alt @ R_48 ) ) ) ).
thf(fact_471_listrel1I,axiom,
! [Ys_36: list_l1230899348le_alt,Xs_104: list_l1230899348le_alt,Us_1: list_l1230899348le_alt,Vs_1: list_l1230899348le_alt,X_67: list_A1402527603le_alt,Y_27: list_A1402527603le_alt,R_47: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_67 @ Y_27 ) @ R_47 )
=> ( ( Xs_104
= ( append453290350le_alt @ Us_1 @ ( cons_l2069870355le_alt @ X_67 @ Vs_1 ) ) )
=> ( ( Ys_36
= ( append453290350le_alt @ Us_1 @ ( cons_l2069870355le_alt @ Y_27 @ Vs_1 ) ) )
=> ( member104660884le_alt @ ( produc110512663le_alt @ Xs_104 @ Ys_36 ) @ ( listre2055328042le_alt @ R_47 ) ) ) ) ) ).
thf(fact_472_listrel1I,axiom,
! [Ys_36: list_A1402527603le_alt,Xs_104: list_A1402527603le_alt,Us_1: list_A1402527603le_alt,Vs_1: list_A1402527603le_alt,X_67: arrow_1389031998le_alt,Y_27: arrow_1389031998le_alt,R_47: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_67 @ Y_27 ) @ R_47 )
=> ( ( Xs_104
= ( append1092755459le_alt @ Us_1 @ ( cons_A1142416030le_alt @ X_67 @ Vs_1 ) ) )
=> ( ( Ys_36
= ( append1092755459le_alt @ Us_1 @ ( cons_A1142416030le_alt @ Y_27 @ Vs_1 ) ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_104 @ Ys_36 ) @ ( listre830192455le_alt @ R_47 ) ) ) ) ) ).
thf(fact_473_listrel1E,axiom,
! [Xs_103: list_l1230899348le_alt,Ys_35: list_l1230899348le_alt,R_46: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ Xs_103 @ Ys_35 ) @ ( listre2055328042le_alt @ R_46 ) )
=> ~ ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Y_10 ) @ R_46 )
=> ! [Us: list_l1230899348le_alt,Vs: list_l1230899348le_alt] :
( ( Xs_103
= ( append453290350le_alt @ Us @ ( cons_l2069870355le_alt @ X_1 @ Vs ) ) )
=> ( Ys_35
!= ( append453290350le_alt @ Us @ ( cons_l2069870355le_alt @ Y_10 @ Vs ) ) ) ) ) ) ).
thf(fact_474_listrel1E,axiom,
! [Xs_103: list_A1402527603le_alt,Ys_35: list_A1402527603le_alt,R_46: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_103 @ Ys_35 ) @ ( listre830192455le_alt @ R_46 ) )
=> ~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Y_10 ) @ R_46 )
=> ! [Us: list_A1402527603le_alt,Vs: list_A1402527603le_alt] :
( ( Xs_103
= ( append1092755459le_alt @ Us @ ( cons_A1142416030le_alt @ X_1 @ Vs ) ) )
=> ( Ys_35
!= ( append1092755459le_alt @ Us @ ( cons_A1142416030le_alt @ Y_10 @ Vs ) ) ) ) ) ) ).
thf(fact_475_Cons__listrel1E1,axiom,
! [X_66: list_A1402527603le_alt,Xs_102: list_l1230899348le_alt,Ys_34: list_l1230899348le_alt,R_45: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ ( cons_l2069870355le_alt @ X_66 @ Xs_102 ) @ Ys_34 ) @ ( listre2055328042le_alt @ R_45 ) )
=> ( ! [Y_10: list_A1402527603le_alt] :
( ( Ys_34
= ( cons_l2069870355le_alt @ Y_10 @ Xs_102 ) )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ X_66 @ Y_10 ) @ R_45 ) )
=> ~ ! [Zs: list_l1230899348le_alt] :
( ( Ys_34
= ( cons_l2069870355le_alt @ X_66 @ Zs ) )
=> ~ ( member104660884le_alt @ ( produc110512663le_alt @ Xs_102 @ Zs ) @ ( listre2055328042le_alt @ R_45 ) ) ) ) ) ).
thf(fact_476_Cons__listrel1E1,axiom,
! [X_66: arrow_1389031998le_alt,Xs_102: list_A1402527603le_alt,Ys_34: list_A1402527603le_alt,R_45: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_66 @ Xs_102 ) @ Ys_34 ) @ ( listre830192455le_alt @ R_45 ) )
=> ( ! [Y_10: arrow_1389031998le_alt] :
( ( Ys_34
= ( cons_A1142416030le_alt @ Y_10 @ Xs_102 ) )
=> ~ ( member285112084le_alt @ ( produc897867031le_alt @ X_66 @ Y_10 ) @ R_45 ) )
=> ~ ! [Zs: list_A1402527603le_alt] :
( ( Ys_34
= ( cons_A1142416030le_alt @ X_66 @ Zs ) )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_102 @ Zs ) @ ( listre830192455le_alt @ R_45 ) ) ) ) ) ).
thf(fact_477_Cons__listrel1E2,axiom,
! [Xs_101: list_l1230899348le_alt,Y_26: list_A1402527603le_alt,Ys_33: list_l1230899348le_alt,R_44: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ Xs_101 @ ( cons_l2069870355le_alt @ Y_26 @ Ys_33 ) ) @ ( listre2055328042le_alt @ R_44 ) )
=> ( ! [X_1: list_A1402527603le_alt] :
( ( Xs_101
= ( cons_l2069870355le_alt @ X_1 @ Ys_33 ) )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Y_26 ) @ R_44 ) )
=> ~ ! [Zs: list_l1230899348le_alt] :
( ( Xs_101
= ( cons_l2069870355le_alt @ Y_26 @ Zs ) )
=> ~ ( member104660884le_alt @ ( produc110512663le_alt @ Zs @ Ys_33 ) @ ( listre2055328042le_alt @ R_44 ) ) ) ) ) ).
thf(fact_478_Cons__listrel1E2,axiom,
! [Xs_101: list_A1402527603le_alt,Y_26: arrow_1389031998le_alt,Ys_33: list_A1402527603le_alt,R_44: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_101 @ ( cons_A1142416030le_alt @ Y_26 @ Ys_33 ) ) @ ( listre830192455le_alt @ R_44 ) )
=> ( ! [X_1: arrow_1389031998le_alt] :
( ( Xs_101
= ( cons_A1142416030le_alt @ X_1 @ Ys_33 ) )
=> ~ ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Y_26 ) @ R_44 ) )
=> ~ ! [Zs: list_A1402527603le_alt] :
( ( Xs_101
= ( cons_A1142416030le_alt @ Y_26 @ Zs ) )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ Zs @ Ys_33 ) @ ( listre830192455le_alt @ R_44 ) ) ) ) ) ).
thf(fact_479_Lin__def,axiom,
( arrow_1982173296le_Lin
= ( collec958969213_alt_o @ ( order_762106470le_alt @ top_to1031852101_alt_o ) ) ) ).
thf(fact_480_dropWhile__eq__Cons__conv,axiom,
! [P_39: arrow_1389031998le_alt > $o,Xs_100: list_A1402527603le_alt,Y_25: arrow_1389031998le_alt,Ys_32: list_A1402527603le_alt] :
( ( ( dropWh82971279le_alt @ P_39 @ Xs_100 )
= ( cons_A1142416030le_alt @ Y_25 @ Ys_32 ) )
<=> ( ( Xs_100
= ( append1092755459le_alt @ ( takeWh462480871le_alt @ P_39 @ Xs_100 ) @ ( cons_A1142416030le_alt @ Y_25 @ Ys_32 ) ) )
& ~ ( P_39 @ Y_25 ) ) ) ).
thf(fact_481_Nil2__notin__lex,axiom,
! [Xs_99: list_A1402527603le_alt,R_43: produc1572197287le_alt > $o] :
~ ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_99 @ nil_Ar52383470le_alt ) @ ( lex_Ar181706578le_alt @ R_43 ) ) ).
thf(fact_482_Nil__notin__lex,axiom,
! [Ys_31: list_A1402527603le_alt,R_42: produc1572197287le_alt > $o] :
~ ( member735418658le_alt @ ( produc1014865963le_alt @ nil_Ar52383470le_alt @ Ys_31 ) @ ( lex_Ar181706578le_alt @ R_42 ) ) ).
thf(fact_483_partition_Osimps_I2_J,axiom,
! [P_38: arrow_1389031998le_alt > $o,X_65: arrow_1389031998le_alt,Xs_98: list_A1402527603le_alt] :
( ( partit253767143le_alt @ P_38 @ ( cons_A1142416030le_alt @ X_65 @ Xs_98 ) )
= ( produc1712983243le_alt
@ ^ [Yes_1: list_A1402527603le_alt,No_1: list_A1402527603le_alt] : ( if_Pro1021494213le_alt @ ( P_38 @ X_65 ) @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_65 @ Yes_1 ) @ No_1 ) @ ( produc1014865963le_alt @ Yes_1 @ ( cons_A1142416030le_alt @ X_65 @ No_1 ) ) )
@ ( partit253767143le_alt @ P_38 @ Xs_98 ) ) ) ).
thf(fact_484_split__weak__cong,axiom,
! [C_15: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,P_37: produc1572197287le_alt,Q_5: produc1572197287le_alt] :
( ( P_37 = Q_5 )
=> ( ( produc536934701_alt_o @ C_15 @ P_37 )
<=> ( produc536934701_alt_o @ C_15 @ Q_5 ) ) ) ).
thf(fact_485_split__weak__cong,axiom,
! [C_15: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt,P_37: produc2069254453le_alt,Q_5: produc2069254453le_alt] :
( ( P_37 = Q_5 )
=> ( ( produc1712983243le_alt @ C_15 @ P_37 )
= ( produc1712983243le_alt @ C_15 @ Q_5 ) ) ) ).
thf(fact_486_prod_Osimps_I2_J,axiom,
! [F1_1: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt,A_27: list_A1402527603le_alt,B_22: list_A1402527603le_alt] :
( ( produc1712983243le_alt @ F1_1 @ ( produc1014865963le_alt @ A_27 @ B_22 ) )
= ( F1_1 @ A_27 @ B_22 ) ) ).
thf(fact_487_prod_Osimps_I2_J,axiom,
! [F1_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_27: arrow_1389031998le_alt,B_22: arrow_1389031998le_alt] :
( ( produc536934701_alt_o @ F1_1 @ ( produc897867031le_alt @ A_27 @ B_22 ) )
<=> ( F1_1 @ A_27 @ B_22 ) ) ).
thf(fact_488_split__conv,axiom,
! [F_9: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt,A_26: list_A1402527603le_alt,B_21: list_A1402527603le_alt] :
( ( produc1712983243le_alt @ F_9 @ ( produc1014865963le_alt @ A_26 @ B_21 ) )
= ( F_9 @ A_26 @ B_21 ) ) ).
thf(fact_489_split__conv,axiom,
! [F_9: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_26: arrow_1389031998le_alt,B_21: arrow_1389031998le_alt] :
( ( produc536934701_alt_o @ F_9 @ ( produc897867031le_alt @ A_26 @ B_21 ) )
<=> ( F_9 @ A_26 @ B_21 ) ) ).
thf(fact_490_dropWhile_Osimps_I2_J,axiom,
! [Xs_97: list_A1402527603le_alt,P_36: arrow_1389031998le_alt > $o,X_64: arrow_1389031998le_alt] :
( ( ( P_36 @ X_64 )
=> ( ( dropWh82971279le_alt @ P_36 @ ( cons_A1142416030le_alt @ X_64 @ Xs_97 ) )
= ( dropWh82971279le_alt @ P_36 @ Xs_97 ) ) )
& ( ~ ( P_36 @ X_64 )
=> ( ( dropWh82971279le_alt @ P_36 @ ( cons_A1142416030le_alt @ X_64 @ Xs_97 ) )
= ( cons_A1142416030le_alt @ X_64 @ Xs_97 ) ) ) ) ).
thf(fact_491_dropWhile_Osimps_I1_J,axiom,
! [P_35: arrow_1389031998le_alt > $o] :
( ( dropWh82971279le_alt @ P_35 @ nil_Ar52383470le_alt )
= nil_Ar52383470le_alt ) ).
thf(fact_492_distinct__dropWhile,axiom,
! [P_34: arrow_1389031998le_alt > $o,Xs_96: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ Xs_96 )
=> ( distin1149997281le_alt @ ( dropWh82971279le_alt @ P_34 @ Xs_96 ) ) ) ).
thf(fact_493_split__eta,axiom,
! [F_8: produc2069254453le_alt > produc2069254453le_alt] :
( ( produc1712983243le_alt
@ ^ [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] : ( F_8 @ ( produc1014865963le_alt @ X_1 @ Y_10 ) ) )
= F_8 ) ).
thf(fact_494_split__eta,axiom,
! [F_8: produc1572197287le_alt > $o] :
( ( produc536934701_alt_o
@ ^ [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] : ( F_8 @ ( produc897867031le_alt @ X_1 @ Y_10 ) ) )
= F_8 ) ).
thf(fact_495_split__curry,axiom,
! [F_7: produc1572197287le_alt > $o] :
( ( produc536934701_alt_o @ ( produc1084757966_alt_o @ F_7 ) )
= F_7 ) ).
thf(fact_496_split__curry,axiom,
! [F_7: produc2069254453le_alt > produc2069254453le_alt] :
( ( produc1712983243le_alt @ ( produc1300022634le_alt @ F_7 ) )
= F_7 ) ).
thf(fact_497_curry__split,axiom,
! [F_6: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( produc1084757966_alt_o @ ( produc536934701_alt_o @ F_6 ) )
= F_6 ) ).
thf(fact_498_curry__split,axiom,
! [F_6: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt] :
( ( produc1300022634le_alt @ ( produc1712983243le_alt @ F_6 ) )
= F_6 ) ).
thf(fact_499_internal__split__def,axiom,
produc403413048_alt_o = produc536934701_alt_o ).
thf(fact_500_internal__split__def,axiom,
produc1014699392le_alt = produc1712983243le_alt ).
thf(fact_501_takeWhile__dropWhile__id,axiom,
! [P_33: arrow_1389031998le_alt > $o,Xs_95: list_A1402527603le_alt] :
( ( append1092755459le_alt @ ( takeWh462480871le_alt @ P_33 @ Xs_95 ) @ ( dropWh82971279le_alt @ P_33 @ Xs_95 ) )
= Xs_95 ) ).
thf(fact_502_cond__split__eta,axiom,
! [F_5: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt,G_2: produc2069254453le_alt > produc2069254453le_alt] :
( ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( F_5 @ X_1 @ Y_10 )
= ( G_2 @ ( produc1014865963le_alt @ X_1 @ Y_10 ) ) )
=> ( ( produc1712983243le_alt @ F_5 )
= G_2 ) ) ).
thf(fact_503_cond__split__eta,axiom,
! [G_2: produc1572197287le_alt > $o,F_5: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( F_5 @ X_1 @ Y_10 )
<=> ( G_2 @ ( produc897867031le_alt @ X_1 @ Y_10 ) ) )
=> ( ( produc536934701_alt_o @ F_5 )
= G_2 ) ) ).
thf(fact_504_splitE2,axiom,
! [Q_4: produc2069254453le_alt > $o,P_32: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt,Z_8: produc2069254453le_alt] :
( ( Q_4 @ ( produc1712983243le_alt @ P_32 @ Z_8 ) )
=> ~ ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( Z_8
= ( produc1014865963le_alt @ X_1 @ Y_10 ) )
=> ~ ( Q_4 @ ( P_32 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_505_splitE2,axiom,
! [Q_4: $o > $o,P_32: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Z_8: produc1572197287le_alt] :
( ( Q_4 @ ( produc536934701_alt_o @ P_32 @ Z_8 ) )
=> ~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( Z_8
= ( produc897867031le_alt @ X_1 @ Y_10 ) )
=> ~ ( Q_4 @ ( P_32 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_506_split__cong,axiom,
! [P_31: produc2069254453le_alt,F_4: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt,G_1: list_A1402527603le_alt > list_A1402527603le_alt > produc2069254453le_alt,Q_3: produc2069254453le_alt] :
( ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( ( produc1014865963le_alt @ X_1 @ Y_10 )
= Q_3 )
=> ( ( F_4 @ X_1 @ Y_10 )
= ( G_1 @ X_1 @ Y_10 ) ) )
=> ( ( P_31 = Q_3 )
=> ( ( produc1712983243le_alt @ F_4 @ P_31 )
= ( produc1712983243le_alt @ G_1 @ Q_3 ) ) ) ) ).
thf(fact_507_split__cong,axiom,
! [P_31: produc1572197287le_alt,G_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_4: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Q_3: produc1572197287le_alt] :
( ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( ( produc897867031le_alt @ X_1 @ Y_10 )
= Q_3 )
=> ( ( F_4 @ X_1 @ Y_10 )
<=> ( G_1 @ X_1 @ Y_10 ) ) )
=> ( ( P_31 = Q_3 )
=> ( ( produc536934701_alt_o @ F_4 @ P_31 )
<=> ( produc536934701_alt_o @ G_1 @ Q_3 ) ) ) ) ).
thf(fact_508_Cons__in__lex,axiom,
! [X_63: list_A1402527603le_alt,Xs_94: list_l1230899348le_alt,Y_24: list_A1402527603le_alt,Ys_30: list_l1230899348le_alt,R_41: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ ( cons_l2069870355le_alt @ X_63 @ Xs_94 ) @ ( cons_l2069870355le_alt @ Y_24 @ Ys_30 ) ) @ ( lex_li2097910111le_alt @ R_41 ) )
<=> ( ( ( member735418658le_alt @ ( produc1014865963le_alt @ X_63 @ Y_24 ) @ R_41 )
& ( ( size_s1667586986le_alt @ Xs_94 )
= ( size_s1667586986le_alt @ Ys_30 ) ) )
| ( ( X_63 = Y_24 )
& ( member104660884le_alt @ ( produc110512663le_alt @ Xs_94 @ Ys_30 ) @ ( lex_li2097910111le_alt @ R_41 ) ) ) ) ) ).
thf(fact_509_Cons__in__lex,axiom,
! [X_63: arrow_1389031998le_alt,Xs_94: list_A1402527603le_alt,Y_24: arrow_1389031998le_alt,Ys_30: list_A1402527603le_alt,R_41: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_63 @ Xs_94 ) @ ( cons_A1142416030le_alt @ Y_24 @ Ys_30 ) ) @ ( lex_Ar181706578le_alt @ R_41 ) )
<=> ( ( ( member285112084le_alt @ ( produc897867031le_alt @ X_63 @ Y_24 ) @ R_41 )
& ( ( size_s1146069981le_alt @ Xs_94 )
= ( size_s1146069981le_alt @ Ys_30 ) ) )
| ( ( X_63 = Y_24 )
& ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_94 @ Ys_30 ) @ ( lex_Ar181706578le_alt @ R_41 ) ) ) ) ) ).
thf(fact_510_not__distinct__decomp,axiom,
! [Ws: list_A1402527603le_alt] :
( ~ ( distin1149997281le_alt @ Ws )
=> ? [Xs_71: list_A1402527603le_alt,Ys: list_A1402527603le_alt,Zs: list_A1402527603le_alt,Y_10: arrow_1389031998le_alt] :
( Ws
= ( append1092755459le_alt @ Xs_71 @ ( append1092755459le_alt @ ( cons_A1142416030le_alt @ Y_10 @ nil_Ar52383470le_alt ) @ ( append1092755459le_alt @ Ys @ ( append1092755459le_alt @ ( cons_A1142416030le_alt @ Y_10 @ nil_Ar52383470le_alt ) @ Zs ) ) ) ) ) ) ).
thf(fact_511_listrel_OCons,axiom,
! [Xs_93: list_l1230899348le_alt,Ys_29: list_l1230899348le_alt,X_62: list_A1402527603le_alt,Y_23: list_A1402527603le_alt,R_40: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_62 @ Y_23 ) @ R_40 )
=> ( ( member104660884le_alt @ ( produc110512663le_alt @ Xs_93 @ Ys_29 ) @ ( listre2057938843le_alt @ R_40 ) )
=> ( member104660884le_alt @ ( produc110512663le_alt @ ( cons_l2069870355le_alt @ X_62 @ Xs_93 ) @ ( cons_l2069870355le_alt @ Y_23 @ Ys_29 ) ) @ ( listre2057938843le_alt @ R_40 ) ) ) ) ).
thf(fact_512_listrel_OCons,axiom,
! [Xs_93: list_A1402527603le_alt,Ys_29: list_A1402527603le_alt,X_62: arrow_1389031998le_alt,Y_23: arrow_1389031998le_alt,R_40: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_62 @ Y_23 ) @ R_40 )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_93 @ Ys_29 ) @ ( listre686844950le_alt @ R_40 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_62 @ Xs_93 ) @ ( cons_A1142416030le_alt @ Y_23 @ Ys_29 ) ) @ ( listre686844950le_alt @ R_40 ) ) ) ) ).
thf(fact_513_tl__append,axiom,
! [Xs_92: list_A1402527603le_alt,Ys_28: list_A1402527603le_alt] :
( ( tl_Arr1379124165le_alt @ ( append1092755459le_alt @ Xs_92 @ Ys_28 ) )
= ( list_c1300280951le_alt @ ( tl_Arr1379124165le_alt @ Ys_28 )
@ ^ [Z_4: arrow_1389031998le_alt,Zs: list_A1402527603le_alt] : ( append1092755459le_alt @ Zs @ Ys_28 )
@ Xs_92 ) ) ).
thf(fact_514_equal,axiom,
equal_1919384209le_alt = fequal68576820le_alt ).
thf(fact_515_splitI,axiom,
! [F_3: list_A1402527603le_alt > list_A1402527603le_alt > $o,A_25: list_A1402527603le_alt,B_20: list_A1402527603le_alt] :
( ( F_3 @ A_25 @ B_20 )
=> ( produc236889881_alt_o @ F_3 @ ( produc1014865963le_alt @ A_25 @ B_20 ) ) ) ).
thf(fact_516_splitI,axiom,
! [F_3: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_25: arrow_1389031998le_alt,B_20: arrow_1389031998le_alt] :
( ( F_3 @ A_25 @ B_20 )
=> ( produc536934701_alt_o @ F_3 @ ( produc897867031le_alt @ A_25 @ B_20 ) ) ) ).
thf(fact_517_prod__caseI,axiom,
! [F1: list_A1402527603le_alt > list_A1402527603le_alt > $o,A_24: list_A1402527603le_alt,B_19: list_A1402527603le_alt] :
( ( F1 @ A_24 @ B_19 )
=> ( produc236889881_alt_o @ F1 @ ( produc1014865963le_alt @ A_24 @ B_19 ) ) ) ).
thf(fact_518_prod__caseI,axiom,
! [F1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_24: arrow_1389031998le_alt,B_19: arrow_1389031998le_alt] :
( ( F1 @ A_24 @ B_19 )
=> ( produc536934701_alt_o @ F1 @ ( produc897867031le_alt @ A_24 @ B_19 ) ) ) ).
thf(fact_519_mem__splitI,axiom,
! [Z_7: nat,C_14: arrow_1389031998le_alt > arrow_1389031998le_alt > nat > $o,A_23: arrow_1389031998le_alt,B_18: arrow_1389031998le_alt] :
( ( member_nat @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member_nat @ Z_7 @ ( produc147560437_nat_o @ C_14 @ ( produc897867031le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_520_mem__splitI,axiom,
! [Z_7: produc2069254453le_alt,C_14: arrow_1389031998le_alt > arrow_1389031998le_alt > produc2069254453le_alt > $o,A_23: arrow_1389031998le_alt,B_18: arrow_1389031998le_alt] :
( ( member735418658le_alt @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member735418658le_alt @ Z_7 @ ( produc1563188184_alt_o @ C_14 @ ( produc897867031le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_521_mem__splitI,axiom,
! [Z_7: arrow_1389031998le_alt,C_14: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_23: arrow_1389031998le_alt,B_18: arrow_1389031998le_alt] :
( ( member998036369le_alt @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member998036369le_alt @ Z_7 @ ( produc1662252097_alt_o @ C_14 @ ( produc897867031le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_522_mem__splitI,axiom,
! [Z_7: arrow_1196572341e_indi,C_14: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1196572341e_indi > $o,A_23: arrow_1389031998le_alt,B_18: arrow_1389031998le_alt] :
( ( member1818997282e_indi @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member1818997282e_indi @ Z_7 @ ( produc1718776024indi_o @ C_14 @ ( produc897867031le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_523_mem__splitI,axiom,
! [Z_7: $o,C_14: arrow_1389031998le_alt > arrow_1389031998le_alt > $o > $o,A_23: arrow_1389031998le_alt,B_18: arrow_1389031998le_alt] :
( ( member_o @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member_o @ Z_7 @ ( produc443852560lt_o_o @ C_14 @ ( produc897867031le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_524_mem__splitI,axiom,
! [Z_7: produc1572197287le_alt,C_14: list_A1402527603le_alt > list_A1402527603le_alt > produc1572197287le_alt > $o,A_23: list_A1402527603le_alt,B_18: list_A1402527603le_alt] :
( ( member285112084le_alt @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member285112084le_alt @ Z_7 @ ( produc2042681170_alt_o @ C_14 @ ( produc1014865963le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_525_mem__splitI,axiom,
! [Z_7: arrow_1196572341e_indi > produc1572197287le_alt > $o,C_14: list_A1402527603le_alt > list_A1402527603le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_23: list_A1402527603le_alt,B_18: list_A1402527603le_alt] :
( ( member822980838_alt_o @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member822980838_alt_o @ Z_7 @ ( produc1882479808lt_o_o @ C_14 @ ( produc1014865963le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_526_mem__splitI,axiom,
! [Z_7: produc1572197287le_alt > $o,C_14: list_A1402527603le_alt > list_A1402527603le_alt > ( produc1572197287le_alt > $o ) > $o,A_23: list_A1402527603le_alt,B_18: list_A1402527603le_alt] :
( ( member1241905979_alt_o @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member1241905979_alt_o @ Z_7 @ ( produc123184939lt_o_o @ C_14 @ ( produc1014865963le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_527_mem__splitI,axiom,
! [Z_7: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,C_14: list_A1402527603le_alt > list_A1402527603le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_23: list_A1402527603le_alt,B_18: list_A1402527603le_alt] :
( ( member1425217232_alt_o @ Z_7 @ ( C_14 @ A_23 @ B_18 ) )
=> ( member1425217232_alt_o @ Z_7 @ ( produc1628065942lt_o_o @ C_14 @ ( produc1014865963le_alt @ A_23 @ B_18 ) ) ) ) ).
thf(fact_528_listrel__Nil2,axiom,
! [Xs_91: list_A1402527603le_alt,R_39: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_91 @ nil_Ar52383470le_alt ) @ ( listre686844950le_alt @ R_39 ) )
=> ( Xs_91 = nil_Ar52383470le_alt ) ) ).
thf(fact_529_listrel__Nil1,axiom,
! [Xs_90: list_A1402527603le_alt,R_38: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ nil_Ar52383470le_alt @ Xs_90 ) @ ( listre686844950le_alt @ R_38 ) )
=> ( Xs_90 = nil_Ar52383470le_alt ) ) ).
thf(fact_530_neq__if__length__neq,axiom,
! [Xs_89: list_A1402527603le_alt,Ys_27: list_A1402527603le_alt] :
( ( ( size_s1146069981le_alt @ Xs_89 )
!= ( size_s1146069981le_alt @ Ys_27 ) )
=> ( Xs_89 != Ys_27 ) ) ).
thf(fact_531_listrel__eq__len,axiom,
! [Xs_88: list_A1402527603le_alt,Ys_26: list_A1402527603le_alt,R_37: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_88 @ Ys_26 ) @ ( listre686844950le_alt @ R_37 ) )
=> ( ( size_s1146069981le_alt @ Xs_88 )
= ( size_s1146069981le_alt @ Ys_26 ) ) ) ).
thf(fact_532_splitD,axiom,
! [F_2: list_A1402527603le_alt > list_A1402527603le_alt > $o,A_22: list_A1402527603le_alt,B_17: list_A1402527603le_alt] :
( ( produc236889881_alt_o @ F_2 @ ( produc1014865963le_alt @ A_22 @ B_17 ) )
=> ( F_2 @ A_22 @ B_17 ) ) ).
thf(fact_533_splitD,axiom,
! [F_2: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_22: arrow_1389031998le_alt,B_17: arrow_1389031998le_alt] :
( ( produc536934701_alt_o @ F_2 @ ( produc897867031le_alt @ A_22 @ B_17 ) )
=> ( F_2 @ A_22 @ B_17 ) ) ).
thf(fact_534_length__rotate1,axiom,
! [Xs_87: list_A1402527603le_alt] :
( ( size_s1146069981le_alt @ ( rotate1249022267le_alt @ Xs_87 ) )
= ( size_s1146069981le_alt @ Xs_87 ) ) ).
thf(fact_535_tl_Osimps_I2_J,axiom,
! [X_61: arrow_1389031998le_alt,Xs_86: list_A1402527603le_alt] :
( ( tl_Arr1379124165le_alt @ ( cons_A1142416030le_alt @ X_61 @ Xs_86 ) )
= Xs_86 ) ).
thf(fact_536_tl_Osimps_I1_J,axiom,
( ( tl_Arr1379124165le_alt @ nil_Ar52383470le_alt )
= nil_Ar52383470le_alt ) ).
thf(fact_537_distinct__tl,axiom,
! [Xs_85: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ Xs_85 )
=> ( distin1149997281le_alt @ ( tl_Arr1379124165le_alt @ Xs_85 ) ) ) ).
thf(fact_538_listrel1__eq__len,axiom,
! [Xs_84: list_A1402527603le_alt,Ys_25: list_A1402527603le_alt,R_36: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_84 @ Ys_25 ) @ ( listre830192455le_alt @ R_36 ) )
=> ( ( size_s1146069981le_alt @ Xs_84 )
= ( size_s1146069981le_alt @ Ys_25 ) ) ) ).
thf(fact_539_listrel_ONil,axiom,
! [R_35: produc1572197287le_alt > $o] : ( member735418658le_alt @ ( produc1014865963le_alt @ nil_Ar52383470le_alt @ nil_Ar52383470le_alt ) @ ( listre686844950le_alt @ R_35 ) ) ).
thf(fact_540_tl__append2,axiom,
! [Ys_24: list_A1402527603le_alt,Xs_83: list_A1402527603le_alt] :
( ( Xs_83 != nil_Ar52383470le_alt )
=> ( ( tl_Arr1379124165le_alt @ ( append1092755459le_alt @ Xs_83 @ Ys_24 ) )
= ( append1092755459le_alt @ ( tl_Arr1379124165le_alt @ Xs_83 ) @ Ys_24 ) ) ) ).
thf(fact_541_lexord__lex,axiom,
! [X_60: list_A1402527603le_alt,Y_22: list_A1402527603le_alt,R_34: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_60 @ Y_22 ) @ ( lex_Ar181706578le_alt @ R_34 ) )
<=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ X_60 @ Y_22 ) @ ( lexord1871768411le_alt @ R_34 ) )
& ( ( size_s1146069981le_alt @ X_60 )
= ( size_s1146069981le_alt @ Y_22 ) ) ) ) ).
thf(fact_542_eq__equal,axiom,
fequal68576820le_alt = equal_1919384209le_alt ).
thf(fact_543_equal__eq,axiom,
! [X_59: list_A1402527603le_alt,Y_21: list_A1402527603le_alt] :
( ( equal_1919384209le_alt @ X_59 @ Y_21 )
<=> ( X_59 = Y_21 ) ) ).
thf(fact_544_equal__refl,axiom,
! [X_58: list_A1402527603le_alt] : ( equal_1919384209le_alt @ X_58 @ X_58 ) ).
thf(fact_545_listrel__Cons2,axiom,
! [Xs_82: list_l1230899348le_alt,Y_20: list_A1402527603le_alt,Ys_23: list_l1230899348le_alt,R_33: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ Xs_82 @ ( cons_l2069870355le_alt @ Y_20 @ Ys_23 ) ) @ ( listre2057938843le_alt @ R_33 ) )
=> ~ ! [X_1: list_A1402527603le_alt,Xs_71: list_l1230899348le_alt] :
( ( Xs_82
= ( cons_l2069870355le_alt @ X_1 @ Xs_71 ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Y_20 ) @ R_33 )
=> ~ ( member104660884le_alt @ ( produc110512663le_alt @ Xs_71 @ Ys_23 ) @ ( listre2057938843le_alt @ R_33 ) ) ) ) ) ).
thf(fact_546_listrel__Cons2,axiom,
! [Xs_82: list_A1402527603le_alt,Y_20: arrow_1389031998le_alt,Ys_23: list_A1402527603le_alt,R_33: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_82 @ ( cons_A1142416030le_alt @ Y_20 @ Ys_23 ) ) @ ( listre686844950le_alt @ R_33 ) )
=> ~ ! [X_1: arrow_1389031998le_alt,Xs_71: list_A1402527603le_alt] :
( ( Xs_82
= ( cons_A1142416030le_alt @ X_1 @ Xs_71 ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Y_20 ) @ R_33 )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_71 @ Ys_23 ) @ ( listre686844950le_alt @ R_33 ) ) ) ) ) ).
thf(fact_547_listrel__Cons1,axiom,
! [Y_19: list_A1402527603le_alt,Ys_22: list_l1230899348le_alt,Xs_81: list_l1230899348le_alt,R_32: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ ( cons_l2069870355le_alt @ Y_19 @ Ys_22 ) @ Xs_81 ) @ ( listre2057938843le_alt @ R_32 ) )
=> ~ ! [Y_10: list_A1402527603le_alt,Ys: list_l1230899348le_alt] :
( ( Xs_81
= ( cons_l2069870355le_alt @ Y_10 @ Ys ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Y_19 @ Y_10 ) @ R_32 )
=> ~ ( member104660884le_alt @ ( produc110512663le_alt @ Ys_22 @ Ys ) @ ( listre2057938843le_alt @ R_32 ) ) ) ) ) ).
thf(fact_548_listrel__Cons1,axiom,
! [Y_19: arrow_1389031998le_alt,Ys_22: list_A1402527603le_alt,Xs_81: list_A1402527603le_alt,R_32: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ Y_19 @ Ys_22 ) @ Xs_81 ) @ ( listre686844950le_alt @ R_32 ) )
=> ~ ! [Y_10: arrow_1389031998le_alt,Ys: list_A1402527603le_alt] :
( ( Xs_81
= ( cons_A1142416030le_alt @ Y_10 @ Ys ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ Y_19 @ Y_10 ) @ R_32 )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ Ys_22 @ Ys ) @ ( listre686844950le_alt @ R_32 ) ) ) ) ) ).
thf(fact_549_list__induct2,axiom,
! [P_30: list_A1402527603le_alt > list_A1402527603le_alt > $o,Xs_80: list_A1402527603le_alt,Ys_21: list_A1402527603le_alt] :
( ( ( size_s1146069981le_alt @ Xs_80 )
= ( size_s1146069981le_alt @ Ys_21 ) )
=> ( ( P_30 @ nil_Ar52383470le_alt @ nil_Ar52383470le_alt )
=> ( ! [X_1: arrow_1389031998le_alt,Xs_71: list_A1402527603le_alt,Y_10: arrow_1389031998le_alt,Ys: list_A1402527603le_alt] :
( ( ( size_s1146069981le_alt @ Xs_71 )
= ( size_s1146069981le_alt @ Ys ) )
=> ( ( P_30 @ Xs_71 @ Ys )
=> ( P_30 @ ( cons_A1142416030le_alt @ X_1 @ Xs_71 ) @ ( cons_A1142416030le_alt @ Y_10 @ Ys ) ) ) )
=> ( P_30 @ Xs_80 @ Ys_21 ) ) ) ) ).
thf(fact_550_splitI2,axiom,
! [C_13: list_A1402527603le_alt > list_A1402527603le_alt > $o,P_29: produc2069254453le_alt] :
( ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] :
( ( P_29
= ( produc1014865963le_alt @ A_14 @ B_10 ) )
=> ( C_13 @ A_14 @ B_10 ) )
=> ( produc236889881_alt_o @ C_13 @ P_29 ) ) ).
thf(fact_551_splitI2,axiom,
! [C_13: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,P_29: produc1572197287le_alt] :
( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( P_29
= ( produc897867031le_alt @ A_14 @ B_10 ) )
=> ( C_13 @ A_14 @ B_10 ) )
=> ( produc536934701_alt_o @ C_13 @ P_29 ) ) ).
thf(fact_552_splitE,axiom,
! [C_12: list_A1402527603le_alt > list_A1402527603le_alt > $o,P_28: produc2069254453le_alt] :
( ( produc236889881_alt_o @ C_12 @ P_28 )
=> ~ ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( P_28
= ( produc1014865963le_alt @ X_1 @ Y_10 ) )
=> ~ ( C_12 @ X_1 @ Y_10 ) ) ) ).
thf(fact_553_splitE,axiom,
! [C_12: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,P_28: produc1572197287le_alt] :
( ( produc536934701_alt_o @ C_12 @ P_28 )
=> ~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( P_28
= ( produc897867031le_alt @ X_1 @ Y_10 ) )
=> ~ ( C_12 @ X_1 @ Y_10 ) ) ) ).
thf(fact_554_mem__splitI2,axiom,
! [Z_6: nat,C_11: arrow_1389031998le_alt > arrow_1389031998le_alt > nat > $o,P_27: produc1572197287le_alt] :
( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( P_27
= ( produc897867031le_alt @ A_14 @ B_10 ) )
=> ( member_nat @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member_nat @ Z_6 @ ( produc147560437_nat_o @ C_11 @ P_27 ) ) ) ).
thf(fact_555_mem__splitI2,axiom,
! [Z_6: produc2069254453le_alt,C_11: arrow_1389031998le_alt > arrow_1389031998le_alt > produc2069254453le_alt > $o,P_27: produc1572197287le_alt] :
( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( P_27
= ( produc897867031le_alt @ A_14 @ B_10 ) )
=> ( member735418658le_alt @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member735418658le_alt @ Z_6 @ ( produc1563188184_alt_o @ C_11 @ P_27 ) ) ) ).
thf(fact_556_mem__splitI2,axiom,
! [Z_6: arrow_1389031998le_alt,C_11: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,P_27: produc1572197287le_alt] :
( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( P_27
= ( produc897867031le_alt @ A_14 @ B_10 ) )
=> ( member998036369le_alt @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member998036369le_alt @ Z_6 @ ( produc1662252097_alt_o @ C_11 @ P_27 ) ) ) ).
thf(fact_557_mem__splitI2,axiom,
! [Z_6: arrow_1196572341e_indi,C_11: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1196572341e_indi > $o,P_27: produc1572197287le_alt] :
( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( P_27
= ( produc897867031le_alt @ A_14 @ B_10 ) )
=> ( member1818997282e_indi @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member1818997282e_indi @ Z_6 @ ( produc1718776024indi_o @ C_11 @ P_27 ) ) ) ).
thf(fact_558_mem__splitI2,axiom,
! [Z_6: $o,C_11: arrow_1389031998le_alt > arrow_1389031998le_alt > $o > $o,P_27: produc1572197287le_alt] :
( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( P_27
= ( produc897867031le_alt @ A_14 @ B_10 ) )
=> ( member_o @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member_o @ Z_6 @ ( produc443852560lt_o_o @ C_11 @ P_27 ) ) ) ).
thf(fact_559_mem__splitI2,axiom,
! [Z_6: produc1572197287le_alt,C_11: list_A1402527603le_alt > list_A1402527603le_alt > produc1572197287le_alt > $o,P_27: produc2069254453le_alt] :
( ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] :
( ( P_27
= ( produc1014865963le_alt @ A_14 @ B_10 ) )
=> ( member285112084le_alt @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member285112084le_alt @ Z_6 @ ( produc2042681170_alt_o @ C_11 @ P_27 ) ) ) ).
thf(fact_560_mem__splitI2,axiom,
! [Z_6: arrow_1196572341e_indi > produc1572197287le_alt > $o,C_11: list_A1402527603le_alt > list_A1402527603le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,P_27: produc2069254453le_alt] :
( ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] :
( ( P_27
= ( produc1014865963le_alt @ A_14 @ B_10 ) )
=> ( member822980838_alt_o @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member822980838_alt_o @ Z_6 @ ( produc1882479808lt_o_o @ C_11 @ P_27 ) ) ) ).
thf(fact_561_mem__splitI2,axiom,
! [Z_6: produc1572197287le_alt > $o,C_11: list_A1402527603le_alt > list_A1402527603le_alt > ( produc1572197287le_alt > $o ) > $o,P_27: produc2069254453le_alt] :
( ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] :
( ( P_27
= ( produc1014865963le_alt @ A_14 @ B_10 ) )
=> ( member1241905979_alt_o @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member1241905979_alt_o @ Z_6 @ ( produc123184939lt_o_o @ C_11 @ P_27 ) ) ) ).
thf(fact_562_mem__splitI2,axiom,
! [Z_6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,C_11: list_A1402527603le_alt > list_A1402527603le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,P_27: produc2069254453le_alt] :
( ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] :
( ( P_27
= ( produc1014865963le_alt @ A_14 @ B_10 ) )
=> ( member1425217232_alt_o @ Z_6 @ ( C_11 @ A_14 @ B_10 ) ) )
=> ( member1425217232_alt_o @ Z_6 @ ( produc1628065942lt_o_o @ C_11 @ P_27 ) ) ) ).
thf(fact_563_mem__splitE,axiom,
! [Z_5: nat,C_10: arrow_1389031998le_alt > arrow_1389031998le_alt > nat > $o,P_26: produc1572197287le_alt] :
( ( member_nat @ Z_5 @ ( produc147560437_nat_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( P_26
= ( produc897867031le_alt @ X_1 @ Y_10 ) )
=> ~ ( member_nat @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_564_mem__splitE,axiom,
! [Z_5: produc2069254453le_alt,C_10: arrow_1389031998le_alt > arrow_1389031998le_alt > produc2069254453le_alt > $o,P_26: produc1572197287le_alt] :
( ( member735418658le_alt @ Z_5 @ ( produc1563188184_alt_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( P_26
= ( produc897867031le_alt @ X_1 @ Y_10 ) )
=> ~ ( member735418658le_alt @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_565_mem__splitE,axiom,
! [Z_5: arrow_1389031998le_alt,C_10: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,P_26: produc1572197287le_alt] :
( ( member998036369le_alt @ Z_5 @ ( produc1662252097_alt_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( P_26
= ( produc897867031le_alt @ X_1 @ Y_10 ) )
=> ~ ( member998036369le_alt @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_566_mem__splitE,axiom,
! [Z_5: arrow_1196572341e_indi,C_10: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1196572341e_indi > $o,P_26: produc1572197287le_alt] :
( ( member1818997282e_indi @ Z_5 @ ( produc1718776024indi_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( P_26
= ( produc897867031le_alt @ X_1 @ Y_10 ) )
=> ~ ( member1818997282e_indi @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_567_mem__splitE,axiom,
! [Z_5: $o,C_10: arrow_1389031998le_alt > arrow_1389031998le_alt > $o > $o,P_26: produc1572197287le_alt] :
( ( member_o @ Z_5 @ ( produc443852560lt_o_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt] :
( ( P_26
= ( produc897867031le_alt @ X_1 @ Y_10 ) )
=> ~ ( member_o @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_568_mem__splitE,axiom,
! [Z_5: produc1572197287le_alt,C_10: list_A1402527603le_alt > list_A1402527603le_alt > produc1572197287le_alt > $o,P_26: produc2069254453le_alt] :
( ( member285112084le_alt @ Z_5 @ ( produc2042681170_alt_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( P_26
= ( produc1014865963le_alt @ X_1 @ Y_10 ) )
=> ~ ( member285112084le_alt @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_569_mem__splitE,axiom,
! [Z_5: arrow_1196572341e_indi > produc1572197287le_alt > $o,C_10: list_A1402527603le_alt > list_A1402527603le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,P_26: produc2069254453le_alt] :
( ( member822980838_alt_o @ Z_5 @ ( produc1882479808lt_o_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( P_26
= ( produc1014865963le_alt @ X_1 @ Y_10 ) )
=> ~ ( member822980838_alt_o @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_570_mem__splitE,axiom,
! [Z_5: produc1572197287le_alt > $o,C_10: list_A1402527603le_alt > list_A1402527603le_alt > ( produc1572197287le_alt > $o ) > $o,P_26: produc2069254453le_alt] :
( ( member1241905979_alt_o @ Z_5 @ ( produc123184939lt_o_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( P_26
= ( produc1014865963le_alt @ X_1 @ Y_10 ) )
=> ~ ( member1241905979_alt_o @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_571_mem__splitE,axiom,
! [Z_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,C_10: list_A1402527603le_alt > list_A1402527603le_alt > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,P_26: produc2069254453le_alt] :
( ( member1425217232_alt_o @ Z_5 @ ( produc1628065942lt_o_o @ C_10 @ P_26 ) )
=> ~ ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] :
( ( P_26
= ( produc1014865963le_alt @ X_1 @ Y_10 ) )
=> ~ ( member1425217232_alt_o @ Z_5 @ ( C_10 @ X_1 @ Y_10 ) ) ) ) ).
thf(fact_572_split__part,axiom,
! [P_25: $o,Q_2: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_1: produc1572197287le_alt] :
( ( produc536934701_alt_o
@ ^ [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] : ( (&) @ P_25 @ ( Q_2 @ A_14 @ B_10 ) )
@ X_1 )
<=> ( P_25
& ( produc536934701_alt_o @ Q_2 @ X_1 ) ) ) ).
thf(fact_573_listrelp__listrel__eq,axiom,
! [R_31: produc2069254453le_alt > $o,X_1: list_l1230899348le_alt,Xa: list_l1230899348le_alt] :
( ( listre103969769le_alt
@ ^ [Y_10: list_A1402527603le_alt,Z_4: list_A1402527603le_alt] : ( member735418658le_alt @ ( produc1014865963le_alt @ Y_10 @ Z_4 ) @ R_31 )
@ X_1
@ Xa )
<=> ( member104660884le_alt @ ( produc110512663le_alt @ X_1 @ Xa ) @ ( listre2057938843le_alt @ R_31 ) ) ) ).
thf(fact_574_listrelp__listrel__eq,axiom,
! [R_31: produc1572197287le_alt > $o,X_1: list_A1402527603le_alt,Xa: list_A1402527603le_alt] :
( ( listre2126835016le_alt
@ ^ [Y_10: arrow_1389031998le_alt,Z_4: arrow_1389031998le_alt] : ( member285112084le_alt @ ( produc897867031le_alt @ Y_10 @ Z_4 ) @ R_31 )
@ X_1
@ Xa )
<=> ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Xa ) @ ( listre686844950le_alt @ R_31 ) ) ) ).
thf(fact_575_rotate1__hd__tl,axiom,
! [Xs_79: list_A1402527603le_alt] :
( ( Xs_79 != nil_Ar52383470le_alt )
=> ( ( rotate1249022267le_alt @ Xs_79 )
= ( append1092755459le_alt @ ( tl_Arr1379124165le_alt @ Xs_79 ) @ ( cons_A1142416030le_alt @ ( hd_Arr731872705le_alt @ Xs_79 ) @ nil_Ar52383470le_alt ) ) ) ) ).
thf(fact_576_listrel_Osimps,axiom,
! [A1_2: list_l1230899348le_alt,A2_2: list_l1230899348le_alt,R_30: produc2069254453le_alt > $o] :
( ( member104660884le_alt @ ( produc110512663le_alt @ A1_2 @ A2_2 ) @ ( listre2057938843le_alt @ R_30 ) )
<=> ( ( ( A1_2 = nil_li1194575555le_alt )
& ( A2_2 = nil_li1194575555le_alt ) )
| ? [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt,Xs_71: list_l1230899348le_alt,Ys: list_l1230899348le_alt] :
( ( A1_2
= ( cons_l2069870355le_alt @ X_1 @ Xs_71 ) )
& ( A2_2
= ( cons_l2069870355le_alt @ Y_10 @ Ys ) )
& ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Y_10 ) @ R_30 )
& ( member104660884le_alt @ ( produc110512663le_alt @ Xs_71 @ Ys ) @ ( listre2057938843le_alt @ R_30 ) ) ) ) ) ).
thf(fact_577_listrel_Osimps,axiom,
! [A1_2: list_A1402527603le_alt,A2_2: list_A1402527603le_alt,R_30: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A1_2 @ A2_2 ) @ ( listre686844950le_alt @ R_30 ) )
<=> ( ( ( A1_2 = nil_Ar52383470le_alt )
& ( A2_2 = nil_Ar52383470le_alt ) )
| ? [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt,Xs_71: list_A1402527603le_alt,Ys: list_A1402527603le_alt] :
( ( A1_2
= ( cons_A1142416030le_alt @ X_1 @ Xs_71 ) )
& ( A2_2
= ( cons_A1142416030le_alt @ Y_10 @ Ys ) )
& ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Y_10 ) @ R_30 )
& ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_71 @ Ys ) @ ( listre686844950le_alt @ R_30 ) ) ) ) ) ).
thf(fact_578_lexn__length,axiom,
! [Xs_78: list_A1402527603le_alt,Ys_20: list_A1402527603le_alt,R_29: produc1572197287le_alt > $o,N_17: nat] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_78 @ Ys_20 ) @ ( lexn_A1084034446le_alt @ R_29 @ N_17 ) )
=> ( ( ( size_s1146069981le_alt @ Xs_78 )
= N_17 )
& ( ( size_s1146069981le_alt @ Ys_20 )
= N_17 ) ) ) ).
thf(fact_579_Ex__list__of__length,axiom,
! [N_16: nat] :
? [Xs_71: list_A1402527603le_alt] :
( ( size_s1146069981le_alt @ Xs_71 )
= N_16 ) ).
thf(fact_580_replicate__append__same,axiom,
! [I_11: nat,X_57: arrow_1389031998le_alt] :
( ( append1092755459le_alt @ ( replic277728168le_alt @ I_11 @ X_57 ) @ ( cons_A1142416030le_alt @ X_57 @ nil_Ar52383470le_alt ) )
= ( cons_A1142416030le_alt @ X_57 @ ( replic277728168le_alt @ I_11 @ X_57 ) ) ) ).
thf(fact_581_length__replicate,axiom,
! [N_15: nat,X_56: arrow_1389031998le_alt] :
( ( size_s1146069981le_alt @ ( replic277728168le_alt @ N_15 @ X_56 ) )
= N_15 ) ).
thf(fact_582_append__replicate__commute,axiom,
! [N_14: nat,X_55: arrow_1389031998le_alt,K_5: nat] :
( ( append1092755459le_alt @ ( replic277728168le_alt @ N_14 @ X_55 ) @ ( replic277728168le_alt @ K_5 @ X_55 ) )
= ( append1092755459le_alt @ ( replic277728168le_alt @ K_5 @ X_55 ) @ ( replic277728168le_alt @ N_14 @ X_55 ) ) ) ).
thf(fact_583_hd_Osimps,axiom,
! [X_54: arrow_1389031998le_alt,Xs_77: list_A1402527603le_alt] :
( ( hd_Arr731872705le_alt @ ( cons_A1142416030le_alt @ X_54 @ Xs_77 ) )
= X_54 ) ).
thf(fact_584_replicate__app__Cons__same,axiom,
! [N_13: nat,X_53: arrow_1389031998le_alt,Xs_76: list_A1402527603le_alt] :
( ( append1092755459le_alt @ ( replic277728168le_alt @ N_13 @ X_53 ) @ ( cons_A1142416030le_alt @ X_53 @ Xs_76 ) )
= ( cons_A1142416030le_alt @ X_53 @ ( append1092755459le_alt @ ( replic277728168le_alt @ N_13 @ X_53 ) @ Xs_76 ) ) ) ).
thf(fact_585_listrelp_OCons,axiom,
! [Xs_75: list_A1402527603le_alt,Ys_19: list_A1402527603le_alt,R_28: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_52: arrow_1389031998le_alt,Y_18: arrow_1389031998le_alt] :
( ( R_28 @ X_52 @ Y_18 )
=> ( ( listre2126835016le_alt @ R_28 @ Xs_75 @ Ys_19 )
=> ( listre2126835016le_alt @ R_28 @ ( cons_A1142416030le_alt @ X_52 @ Xs_75 ) @ ( cons_A1142416030le_alt @ Y_18 @ Ys_19 ) ) ) ) ).
thf(fact_586_listrelp_ONil,axiom,
! [R_27: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] : ( listre2126835016le_alt @ R_27 @ nil_Ar52383470le_alt @ nil_Ar52383470le_alt ) ).
thf(fact_587_hd__append,axiom,
! [Ys_18: list_A1402527603le_alt,Xs_74: list_A1402527603le_alt] :
( ( ( Xs_74 = nil_Ar52383470le_alt )
=> ( ( hd_Arr731872705le_alt @ ( append1092755459le_alt @ Xs_74 @ Ys_18 ) )
= ( hd_Arr731872705le_alt @ Ys_18 ) ) )
& ( ( Xs_74 != nil_Ar52383470le_alt )
=> ( ( hd_Arr731872705le_alt @ ( append1092755459le_alt @ Xs_74 @ Ys_18 ) )
= ( hd_Arr731872705le_alt @ Xs_74 ) ) ) ) ).
thf(fact_588_hd__append2,axiom,
! [Ys_17: list_A1402527603le_alt,Xs_73: list_A1402527603le_alt] :
( ( Xs_73 != nil_Ar52383470le_alt )
=> ( ( hd_Arr731872705le_alt @ ( append1092755459le_alt @ Xs_73 @ Ys_17 ) )
= ( hd_Arr731872705le_alt @ Xs_73 ) ) ) ).
thf(fact_589_hd__dropWhile,axiom,
! [P_24: arrow_1389031998le_alt > $o,Xs_72: list_A1402527603le_alt] :
( ( ( dropWh82971279le_alt @ P_24 @ Xs_72 )
!= nil_Ar52383470le_alt )
=> ~ ( P_24 @ ( hd_Arr731872705le_alt @ ( dropWh82971279le_alt @ P_24 @ Xs_72 ) ) ) ) ).
thf(fact_590_listrelp_Osimps,axiom,
! [R_26: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A1_1: list_A1402527603le_alt,A2_1: list_A1402527603le_alt] :
( ( listre2126835016le_alt @ R_26 @ A1_1 @ A2_1 )
<=> ( ( ( A1_1 = nil_Ar52383470le_alt )
& ( A2_1 = nil_Ar52383470le_alt ) )
| ? [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt,Xs_71: list_A1402527603le_alt,Ys: list_A1402527603le_alt] :
( ( A1_1
= ( cons_A1142416030le_alt @ X_1 @ Xs_71 ) )
& ( A2_1
= ( cons_A1142416030le_alt @ Y_10 @ Ys ) )
& ( R_26 @ X_1 @ Y_10 )
& ( listre2126835016le_alt @ R_26 @ Xs_71 @ Ys ) ) ) ) ).
thf(fact_591_last__rev,axiom,
! [Xs_70: list_A1402527603le_alt] :
( ( Xs_70 != nil_Ar52383470le_alt )
=> ( ( last_A2130988295le_alt @ ( rev_Ar2020079950le_alt @ Xs_70 ) )
= ( hd_Arr731872705le_alt @ Xs_70 ) ) ) ).
thf(fact_592_hd__rev,axiom,
! [Xs_69: list_A1402527603le_alt] :
( ( Xs_69 != nil_Ar52383470le_alt )
=> ( ( hd_Arr731872705le_alt @ ( rev_Ar2020079950le_alt @ Xs_69 ) )
= ( last_A2130988295le_alt @ Xs_69 ) ) ) ).
thf(fact_593_dropWhile__eq__drop,axiom,
! [P_23: arrow_1389031998le_alt > $o,Xs_68: list_A1402527603le_alt] :
( ( dropWh82971279le_alt @ P_23 @ Xs_68 )
= ( drop_A112899118le_alt @ ( size_s1146069981le_alt @ ( takeWh462480871le_alt @ P_23 @ Xs_68 ) ) @ Xs_68 ) ) ).
thf(fact_594_list__update__length,axiom,
! [Xs_67: list_A1402527603le_alt,X_51: arrow_1389031998le_alt,Ys_16: list_A1402527603le_alt,Y_17: arrow_1389031998le_alt] :
( ( list_u976150870le_alt @ ( append1092755459le_alt @ Xs_67 @ ( cons_A1142416030le_alt @ X_51 @ Ys_16 ) ) @ ( size_s1146069981le_alt @ Xs_67 ) @ Y_17 )
= ( append1092755459le_alt @ Xs_67 @ ( cons_A1142416030le_alt @ Y_17 @ Ys_16 ) ) ) ).
thf(fact_595_map__pair__def,axiom,
! [F_1: list_A1402527603le_alt > list_A1402527603le_alt,G: list_A1402527603le_alt > list_A1402527603le_alt] :
( ( produc1315215393le_alt @ F_1 @ G )
= ( produc1712983243le_alt
@ ^ [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt] : ( produc1014865963le_alt @ ( F_1 @ X_1 ) @ ( G @ Y_10 ) ) ) ) ).
thf(fact_596_rtrancl__listrel1__if__listrel,axiom,
! [Xs_66: list_A1402527603le_alt,Ys_15: list_A1402527603le_alt,R_25: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_66 @ Ys_15 ) @ ( listre686844950le_alt @ R_25 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_66 @ Ys_15 ) @ ( transi264395782le_alt @ ( listre830192455le_alt @ R_25 ) ) ) ) ).
thf(fact_597_listrel__rtrancl__refl,axiom,
! [Xs_65: list_A1402527603le_alt,R_24: produc1572197287le_alt > $o] : ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_65 @ Xs_65 ) @ ( listre686844950le_alt @ ( transi1182735211le_alt @ R_24 ) ) ) ).
thf(fact_598_list__update__swap,axiom,
! [Xs_64: list_A1402527603le_alt,X_50: arrow_1389031998le_alt,X_49: arrow_1389031998le_alt,I_10: nat,I_9: nat] :
( ( I_10 != I_9 )
=> ( ( list_u976150870le_alt @ ( list_u976150870le_alt @ Xs_64 @ I_10 @ X_50 ) @ I_9 @ X_49 )
= ( list_u976150870le_alt @ ( list_u976150870le_alt @ Xs_64 @ I_9 @ X_49 ) @ I_10 @ X_50 ) ) ) ).
thf(fact_599_list__update__overwrite,axiom,
! [Xs_63: list_A1402527603le_alt,I_8: nat,X_48: arrow_1389031998le_alt,Y_16: arrow_1389031998le_alt] :
( ( list_u976150870le_alt @ ( list_u976150870le_alt @ Xs_63 @ I_8 @ X_48 ) @ I_8 @ Y_16 )
= ( list_u976150870le_alt @ Xs_63 @ I_8 @ Y_16 ) ) ).
thf(fact_600_rev__is__rev__conv,axiom,
! [Xs_62: list_A1402527603le_alt,Ys_14: list_A1402527603le_alt] :
( ( ( rev_Ar2020079950le_alt @ Xs_62 )
= ( rev_Ar2020079950le_alt @ Ys_14 ) )
<=> ( Xs_62 = Ys_14 ) ) ).
thf(fact_601_rev__swap,axiom,
! [Xs_61: list_A1402527603le_alt,Ys_13: list_A1402527603le_alt] :
( ( ( rev_Ar2020079950le_alt @ Xs_61 )
= Ys_13 )
<=> ( Xs_61
= ( rev_Ar2020079950le_alt @ Ys_13 ) ) ) ).
thf(fact_602_rev__rev__ident,axiom,
! [Xs_60: list_A1402527603le_alt] :
( ( rev_Ar2020079950le_alt @ ( rev_Ar2020079950le_alt @ Xs_60 ) )
= Xs_60 ) ).
thf(fact_603_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [R_23: produc1572197287le_alt > $o] :
( ( listre686844950le_alt @ ( transi1182735211le_alt @ R_23 ) )
= ( transi264395782le_alt @ ( listre830192455le_alt @ R_23 ) ) ) ).
thf(fact_604_drop__Nil,axiom,
! [N_12: nat] :
( ( drop_A112899118le_alt @ N_12 @ nil_Ar52383470le_alt )
= nil_Ar52383470le_alt ) ).
thf(fact_605_rev_Osimps_I1_J,axiom,
( ( rev_Ar2020079950le_alt @ nil_Ar52383470le_alt )
= nil_Ar52383470le_alt ) ).
thf(fact_606_Nil__is__rev__conv,axiom,
! [Xs_59: list_A1402527603le_alt] :
( ( nil_Ar52383470le_alt
= ( rev_Ar2020079950le_alt @ Xs_59 ) )
<=> ( Xs_59 = nil_Ar52383470le_alt ) ) ).
thf(fact_607_rev__is__Nil__conv,axiom,
! [Xs_58: list_A1402527603le_alt] :
( ( ( rev_Ar2020079950le_alt @ Xs_58 )
= nil_Ar52383470le_alt )
<=> ( Xs_58 = nil_Ar52383470le_alt ) ) ).
thf(fact_608_length__rev,axiom,
! [Xs_57: list_A1402527603le_alt] :
( ( size_s1146069981le_alt @ ( rev_Ar2020079950le_alt @ Xs_57 ) )
= ( size_s1146069981le_alt @ Xs_57 ) ) ).
thf(fact_609_rev__append,axiom,
! [Xs_56: list_A1402527603le_alt,Ys_12: list_A1402527603le_alt] :
( ( rev_Ar2020079950le_alt @ ( append1092755459le_alt @ Xs_56 @ Ys_12 ) )
= ( append1092755459le_alt @ ( rev_Ar2020079950le_alt @ Ys_12 ) @ ( rev_Ar2020079950le_alt @ Xs_56 ) ) ) ).
thf(fact_610_distinct__drop,axiom,
! [I_7: nat,Xs_55: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ Xs_55 )
=> ( distin1149997281le_alt @ ( drop_A112899118le_alt @ I_7 @ Xs_55 ) ) ) ).
thf(fact_611_list__update__nonempty,axiom,
! [Xs_54: list_A1402527603le_alt,K_4: nat,X_47: arrow_1389031998le_alt] :
( ( ( list_u976150870le_alt @ Xs_54 @ K_4 @ X_47 )
= nil_Ar52383470le_alt )
<=> ( Xs_54 = nil_Ar52383470le_alt ) ) ).
thf(fact_612_list__update_Osimps_I1_J,axiom,
! [I_6: nat,V_1: arrow_1389031998le_alt] :
( ( list_u976150870le_alt @ nil_Ar52383470le_alt @ I_6 @ V_1 )
= nil_Ar52383470le_alt ) ).
thf(fact_613_list__update__code_I1_J,axiom,
! [I_5: nat,Y_15: arrow_1389031998le_alt] :
( ( list_u976150870le_alt @ nil_Ar52383470le_alt @ I_5 @ Y_15 )
= nil_Ar52383470le_alt ) ).
thf(fact_614_length__list__update,axiom,
! [Xs_53: list_A1402527603le_alt,I_4: nat,X_46: arrow_1389031998le_alt] :
( ( size_s1146069981le_alt @ ( list_u976150870le_alt @ Xs_53 @ I_4 @ X_46 ) )
= ( size_s1146069981le_alt @ Xs_53 ) ) ).
thf(fact_615_distinct__rev,axiom,
! [Xs_52: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ ( rev_Ar2020079950le_alt @ Xs_52 ) )
<=> ( distin1149997281le_alt @ Xs_52 ) ) ).
thf(fact_616_rev__replicate,axiom,
! [N_11: nat,X_45: arrow_1389031998le_alt] :
( ( rev_Ar2020079950le_alt @ ( replic277728168le_alt @ N_11 @ X_45 ) )
= ( replic277728168le_alt @ N_11 @ X_45 ) ) ).
thf(fact_617_drop__butlast,axiom,
! [N_10: nat,Xs_51: list_A1402527603le_alt] :
( ( drop_A112899118le_alt @ N_10 @ ( butlas1188620858le_alt @ Xs_51 ) )
= ( butlas1188620858le_alt @ ( drop_A112899118le_alt @ N_10 @ Xs_51 ) ) ) ).
thf(fact_618_butlast__drop,axiom,
! [N_9: nat,Xs_50: list_A1402527603le_alt] :
( ( butlas1188620858le_alt @ ( drop_A112899118le_alt @ N_9 @ Xs_50 ) )
= ( drop_A112899118le_alt @ N_9 @ ( butlas1188620858le_alt @ Xs_50 ) ) ) ).
thf(fact_619_drop__tl,axiom,
! [N_8: nat,Xs_49: list_A1402527603le_alt] :
( ( drop_A112899118le_alt @ N_8 @ ( tl_Arr1379124165le_alt @ Xs_49 ) )
= ( tl_Arr1379124165le_alt @ ( drop_A112899118le_alt @ N_8 @ Xs_49 ) ) ) ).
thf(fact_620_tl__drop,axiom,
! [N_7: nat,Xs_48: list_A1402527603le_alt] :
( ( tl_Arr1379124165le_alt @ ( drop_A112899118le_alt @ N_7 @ Xs_48 ) )
= ( drop_A112899118le_alt @ N_7 @ ( tl_Arr1379124165le_alt @ Xs_48 ) ) ) ).
thf(fact_621_rtrancl__listrel1__ConsI2,axiom,
! [Xs_47: list_A1402527603le_alt,Ys_11: list_A1402527603le_alt,X_44: arrow_1389031998le_alt,Y_14: arrow_1389031998le_alt,R_22: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_44 @ Y_14 ) @ ( transi1182735211le_alt @ R_22 ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_47 @ Ys_11 ) @ ( transi264395782le_alt @ ( listre830192455le_alt @ R_22 ) ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_44 @ Xs_47 ) @ ( cons_A1142416030le_alt @ Y_14 @ Ys_11 ) ) @ ( transi264395782le_alt @ ( listre830192455le_alt @ R_22 ) ) ) ) ) ).
thf(fact_622_rtrancl__listrel1__ConsI2,axiom,
! [Xs_47: list_l1230899348le_alt,Ys_11: list_l1230899348le_alt,X_44: list_A1402527603le_alt,Y_14: list_A1402527603le_alt,R_22: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_44 @ Y_14 ) @ ( transi264395782le_alt @ R_22 ) )
=> ( ( member104660884le_alt @ ( produc110512663le_alt @ Xs_47 @ Ys_11 ) @ ( transi452343361le_alt @ ( listre2055328042le_alt @ R_22 ) ) )
=> ( member104660884le_alt @ ( produc110512663le_alt @ ( cons_l2069870355le_alt @ X_44 @ Xs_47 ) @ ( cons_l2069870355le_alt @ Y_14 @ Ys_11 ) ) @ ( transi452343361le_alt @ ( listre2055328042le_alt @ R_22 ) ) ) ) ) ).
thf(fact_623_rev__singleton__conv,axiom,
! [Xs_46: list_A1402527603le_alt,X_43: arrow_1389031998le_alt] :
( ( ( rev_Ar2020079950le_alt @ Xs_46 )
= ( cons_A1142416030le_alt @ X_43 @ nil_Ar52383470le_alt ) )
<=> ( Xs_46
= ( cons_A1142416030le_alt @ X_43 @ nil_Ar52383470le_alt ) ) ) ).
thf(fact_624_singleton__rev__conv,axiom,
! [X_42: arrow_1389031998le_alt,Xs_45: list_A1402527603le_alt] :
( ( ( cons_A1142416030le_alt @ X_42 @ nil_Ar52383470le_alt )
= ( rev_Ar2020079950le_alt @ Xs_45 ) )
<=> ( Xs_45
= ( cons_A1142416030le_alt @ X_42 @ nil_Ar52383470le_alt ) ) ) ).
thf(fact_625_listrel__rtrancl__trans,axiom,
! [Zs_2: list_A1402527603le_alt,Xs_44: list_A1402527603le_alt,Ys_10: list_A1402527603le_alt,R_21: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_44 @ Ys_10 ) @ ( listre686844950le_alt @ ( transi1182735211le_alt @ R_21 ) ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Ys_10 @ Zs_2 ) @ ( listre686844950le_alt @ ( transi1182735211le_alt @ R_21 ) ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_44 @ Zs_2 ) @ ( listre686844950le_alt @ ( transi1182735211le_alt @ R_21 ) ) ) ) ) ).
thf(fact_626_rtrancl__listrel1__ConsI1,axiom,
! [X_41: arrow_1389031998le_alt,Xs_43: list_A1402527603le_alt,Ys_9: list_A1402527603le_alt,R_20: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_43 @ Ys_9 ) @ ( transi264395782le_alt @ ( listre830192455le_alt @ R_20 ) ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ ( cons_A1142416030le_alt @ X_41 @ Xs_43 ) @ ( cons_A1142416030le_alt @ X_41 @ Ys_9 ) ) @ ( transi264395782le_alt @ ( listre830192455le_alt @ R_20 ) ) ) ) ).
thf(fact_627_rtrancl__listrel1__eq__len,axiom,
! [X_40: list_A1402527603le_alt,Y_13: list_A1402527603le_alt,R_19: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_40 @ Y_13 ) @ ( transi264395782le_alt @ ( listre830192455le_alt @ R_19 ) ) )
=> ( ( size_s1146069981le_alt @ X_40 )
= ( size_s1146069981le_alt @ Y_13 ) ) ) ).
thf(fact_628_rev_Osimps_I2_J,axiom,
! [X_39: arrow_1389031998le_alt,Xs_42: list_A1402527603le_alt] :
( ( rev_Ar2020079950le_alt @ ( cons_A1142416030le_alt @ X_39 @ Xs_42 ) )
= ( append1092755459le_alt @ ( rev_Ar2020079950le_alt @ Xs_42 ) @ ( cons_A1142416030le_alt @ X_39 @ nil_Ar52383470le_alt ) ) ) ).
thf(fact_629_rev__eq__Cons__iff,axiom,
! [Xs_41: list_A1402527603le_alt,Y_12: arrow_1389031998le_alt,Ys_8: list_A1402527603le_alt] :
( ( ( rev_Ar2020079950le_alt @ Xs_41 )
= ( cons_A1142416030le_alt @ Y_12 @ Ys_8 ) )
<=> ( Xs_41
= ( append1092755459le_alt @ ( rev_Ar2020079950le_alt @ Ys_8 ) @ ( cons_A1142416030le_alt @ Y_12 @ nil_Ar52383470le_alt ) ) ) ) ).
thf(fact_630_listrel__reflcl__if__listrel1,axiom,
! [Xs_40: list_A1402527603le_alt,Ys_7: list_A1402527603le_alt,R_18: produc1572197287le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_40 @ Ys_7 ) @ ( listre830192455le_alt @ R_18 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_40 @ Ys_7 ) @ ( listre686844950le_alt @ ( transi1182735211le_alt @ R_18 ) ) ) ) ).
thf(fact_631_rtrancl_Ortrancl__refl,axiom,
! [A_21: list_A1402527603le_alt,R_17: produc2069254453le_alt > $o] : ( member735418658le_alt @ ( produc1014865963le_alt @ A_21 @ A_21 ) @ ( transi264395782le_alt @ R_17 ) ) ).
thf(fact_632_rtrancl_Ortrancl__refl,axiom,
! [A_21: arrow_1389031998le_alt,R_17: produc1572197287le_alt > $o] : ( member285112084le_alt @ ( produc897867031le_alt @ A_21 @ A_21 ) @ ( transi1182735211le_alt @ R_17 ) ) ).
thf(fact_633_r__into__rtrancl,axiom,
! [P_22: produc2069254453le_alt,R_16: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ P_22 @ R_16 )
=> ( member735418658le_alt @ P_22 @ ( transi264395782le_alt @ R_16 ) ) ) ).
thf(fact_634_r__into__rtrancl,axiom,
! [P_22: produc1572197287le_alt,R_16: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ P_22 @ R_16 )
=> ( member285112084le_alt @ P_22 @ ( transi1182735211le_alt @ R_16 ) ) ) ).
thf(fact_635_converse__rtrancl__into__rtrancl,axiom,
! [C_9: list_A1402527603le_alt,A_20: list_A1402527603le_alt,B_16: list_A1402527603le_alt,R_15: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_20 @ B_16 ) @ R_15 )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ B_16 @ C_9 ) @ ( transi264395782le_alt @ R_15 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ A_20 @ C_9 ) @ ( transi264395782le_alt @ R_15 ) ) ) ) ).
thf(fact_636_converse__rtrancl__into__rtrancl,axiom,
! [C_9: arrow_1389031998le_alt,A_20: arrow_1389031998le_alt,B_16: arrow_1389031998le_alt,R_15: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_20 @ B_16 ) @ R_15 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ B_16 @ C_9 ) @ ( transi1182735211le_alt @ R_15 ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_20 @ C_9 ) @ ( transi1182735211le_alt @ R_15 ) ) ) ) ).
thf(fact_637_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_8: list_A1402527603le_alt,A_19: list_A1402527603le_alt,B_15: list_A1402527603le_alt,R_14: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_19 @ B_15 ) @ ( transi264395782le_alt @ R_14 ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ B_15 @ C_8 ) @ R_14 )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ A_19 @ C_8 ) @ ( transi264395782le_alt @ R_14 ) ) ) ) ).
thf(fact_638_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_8: arrow_1389031998le_alt,A_19: arrow_1389031998le_alt,B_15: arrow_1389031998le_alt,R_14: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_19 @ B_15 ) @ ( transi1182735211le_alt @ R_14 ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ B_15 @ C_8 ) @ R_14 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_19 @ C_8 ) @ ( transi1182735211le_alt @ R_14 ) ) ) ) ).
thf(fact_639_rtrancl__trans,axiom,
! [C_7: list_A1402527603le_alt,A_18: list_A1402527603le_alt,B_14: list_A1402527603le_alt,R_13: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_18 @ B_14 ) @ ( transi264395782le_alt @ R_13 ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ B_14 @ C_7 ) @ ( transi264395782le_alt @ R_13 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ A_18 @ C_7 ) @ ( transi264395782le_alt @ R_13 ) ) ) ) ).
thf(fact_640_rtrancl__trans,axiom,
! [C_7: arrow_1389031998le_alt,A_18: arrow_1389031998le_alt,B_14: arrow_1389031998le_alt,R_13: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_18 @ B_14 ) @ ( transi1182735211le_alt @ R_13 ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ B_14 @ C_7 ) @ ( transi1182735211le_alt @ R_13 ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_18 @ C_7 ) @ ( transi1182735211le_alt @ R_13 ) ) ) ) ).
thf(fact_641_takeWhile__neq__rev,axiom,
! [X_38: arrow_1389031998le_alt,Xs_39: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ Xs_39 )
=> ( ( member998036369le_alt @ X_38 @ ( set_Ar1491127311le_alt @ Xs_39 ) )
=> ( ( takeWh462480871le_alt
@ ^ [Y_10: arrow_1389031998le_alt] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_Ar2020079950le_alt @ Xs_39 ) )
= ( rev_Ar2020079950le_alt
@ ( tl_Arr1379124165le_alt
@ ( dropWh82971279le_alt
@ ^ [Y_10: arrow_1389031998le_alt] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_642_takeWhile__neq__rev,axiom,
! [X_38: nat,Xs_39: list_nat] :
( ( distinct_nat @ Xs_39 )
=> ( ( member_nat @ X_38 @ ( set_nat @ Xs_39 ) )
=> ( ( takeWhile_nat
@ ^ [Y_10: nat] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_nat @ Xs_39 ) )
= ( rev_nat
@ ( tl_nat
@ ( dropWhile_nat
@ ^ [Y_10: nat] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_643_takeWhile__neq__rev,axiom,
! [X_38: produc2069254453le_alt,Xs_39: list_P1338624854le_alt] :
( ( distin1268295634le_alt @ Xs_39 )
=> ( ( member735418658le_alt @ X_38 @ ( set_Pr1119022372le_alt @ Xs_39 ) )
=> ( ( takeWh131124556le_alt
@ ^ [Y_10: produc2069254453le_alt] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_Pr178923045le_alt @ Xs_39 ) )
= ( rev_Pr178923045le_alt
@ ( tl_Pro7578606le_alt
@ ( dropWh1319308964le_alt
@ ^ [Y_10: produc2069254453le_alt] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_644_takeWhile__neq__rev,axiom,
! [X_38: arrow_1196572341e_indi,Xs_39: list_A1206016470e_indi] :
( ( distin1683769554e_indi @ Xs_39 )
=> ( ( member1818997282e_indi @ X_38 @ ( set_Ar545511716e_indi @ Xs_39 ) )
=> ( ( takeWh598881612e_indi
@ ^ [Y_10: arrow_1196572341e_indi] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_Ar268893093e_indi @ Xs_39 ) )
= ( rev_Ar268893093e_indi
@ ( tl_Arr1940180718e_indi
@ ( dropWh927087268e_indi
@ ^ [Y_10: arrow_1196572341e_indi] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_645_takeWhile__neq__rev,axiom,
! [X_38: $o,Xs_39: list_o] :
( ( distinct_o @ Xs_39 )
=> ( ( member_o @ X_38 @ ( set_o @ Xs_39 ) )
=> ( ( takeWhile_o
@ ^ [Y_10: $o] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_o @ Xs_39 ) )
= ( rev_o
@ ( tl_o
@ ( dropWhile_o
@ ^ [Y_10: $o] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_646_takeWhile__neq__rev,axiom,
! [X_38: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_39: list_A869418500_alt_o] :
( ( distin568845696_alt_o @ Xs_39 )
=> ( ( member1425217232_alt_o @ X_38 @ ( set_Ar17109714_alt_o @ Xs_39 ) )
=> ( ( takeWh1686115066_alt_o
@ ^ [Y_10: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_Ar813866963_alt_o @ Xs_39 ) )
= ( rev_Ar813866963_alt_o
@ ( tl_Arr678695324_alt_o
@ ( dropWh1391670354_alt_o
@ ^ [Y_10: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_647_takeWhile__neq__rev,axiom,
! [X_38: produc1572197287le_alt > $o,Xs_39: list_P811970973_alt_o] :
( ( distin299901067_alt_o @ Xs_39 )
=> ( ( member1241905979_alt_o @ X_38 @ ( set_Pr1457060537_alt_o @ Xs_39 ) )
=> ( ( takeWh432906385_alt_o
@ ^ [Y_10: produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_Pr1871457144_alt_o @ Xs_39 ) )
= ( rev_Pr1871457144_alt_o
@ ( tl_Pro452506991_alt_o
@ ( dropWh1914665273_alt_o
@ ^ [Y_10: produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_648_takeWhile__neq__rev,axiom,
! [X_38: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_39: list_A115096904_alt_o] :
( ( distin19168822_alt_o @ Xs_39 )
=> ( ( member822980838_alt_o @ X_38 @ ( set_Ar868233060_alt_o @ Xs_39 ) )
=> ( ( takeWh2122498364_alt_o
@ ^ [Y_10: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_Ar710647715_alt_o @ Xs_39 ) )
= ( rev_Ar710647715_alt_o
@ ( tl_Arr2000946458_alt_o
@ ( dropWh370535908_alt_o
@ ^ [Y_10: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_649_takeWhile__neq__rev,axiom,
! [X_38: produc1572197287le_alt,Xs_39: list_P1402680776le_alt] :
( ( distin1847856580le_alt @ Xs_39 )
=> ( ( member285112084le_alt @ X_38 @ ( set_Pr1596096022le_alt @ Xs_39 ) )
=> ( ( takeWh373185086le_alt
@ ^ [Y_10: produc1572197287le_alt] : ( (~) @ ( Y_10 = X_38 ) )
@ ( rev_Pr1287360663le_alt @ Xs_39 ) )
= ( rev_Pr1287360663le_alt
@ ( tl_Pro1003672544le_alt
@ ( dropWh751361942le_alt
@ ^ [Y_10: produc1572197287le_alt] : ( (~) @ ( Y_10 = X_38 ) )
@ Xs_39 ) ) ) ) ) ) ).
thf(fact_650_dropWhile__neq__rev,axiom,
! [X_37: arrow_1389031998le_alt,Xs_38: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ Xs_38 )
=> ( ( member998036369le_alt @ X_37 @ ( set_Ar1491127311le_alt @ Xs_38 ) )
=> ( ( dropWh82971279le_alt
@ ^ [Y_10: arrow_1389031998le_alt] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_Ar2020079950le_alt @ Xs_38 ) )
= ( cons_A1142416030le_alt @ X_37
@ ( rev_Ar2020079950le_alt
@ ( takeWh462480871le_alt
@ ^ [Y_10: arrow_1389031998le_alt] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_651_dropWhile__neq__rev,axiom,
! [X_37: nat,Xs_38: list_nat] :
( ( distinct_nat @ Xs_38 )
=> ( ( member_nat @ X_37 @ ( set_nat @ Xs_38 ) )
=> ( ( dropWhile_nat
@ ^ [Y_10: nat] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_nat @ Xs_38 ) )
= ( cons_nat @ X_37
@ ( rev_nat
@ ( takeWhile_nat
@ ^ [Y_10: nat] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_652_dropWhile__neq__rev,axiom,
! [X_37: produc2069254453le_alt,Xs_38: list_P1338624854le_alt] :
( ( distin1268295634le_alt @ Xs_38 )
=> ( ( member735418658le_alt @ X_37 @ ( set_Pr1119022372le_alt @ Xs_38 ) )
=> ( ( dropWh1319308964le_alt
@ ^ [Y_10: produc2069254453le_alt] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_Pr178923045le_alt @ Xs_38 ) )
= ( cons_P607717589le_alt @ X_37
@ ( rev_Pr178923045le_alt
@ ( takeWh131124556le_alt
@ ^ [Y_10: produc2069254453le_alt] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_653_dropWhile__neq__rev,axiom,
! [X_37: arrow_1196572341e_indi,Xs_38: list_A1206016470e_indi] :
( ( distin1683769554e_indi @ Xs_38 )
=> ( ( member1818997282e_indi @ X_37 @ ( set_Ar545511716e_indi @ Xs_38 ) )
=> ( ( dropWh927087268e_indi
@ ^ [Y_10: arrow_1196572341e_indi] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_Ar268893093e_indi @ Xs_38 ) )
= ( cons_A430007893e_indi @ X_37
@ ( rev_Ar268893093e_indi
@ ( takeWh598881612e_indi
@ ^ [Y_10: arrow_1196572341e_indi] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_654_dropWhile__neq__rev,axiom,
! [X_37: $o,Xs_38: list_o] :
( ( distinct_o @ Xs_38 )
=> ( ( member_o @ X_37 @ ( set_o @ Xs_38 ) )
=> ( ( dropWhile_o
@ ^ [Y_10: $o] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_o @ Xs_38 ) )
= ( cons_o @ X_37
@ ( rev_o
@ ( takeWhile_o
@ ^ [Y_10: $o] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_655_dropWhile__neq__rev,axiom,
! [X_37: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_38: list_A869418500_alt_o] :
( ( distin568845696_alt_o @ Xs_38 )
=> ( ( member1425217232_alt_o @ X_37 @ ( set_Ar17109714_alt_o @ Xs_38 ) )
=> ( ( dropWh1391670354_alt_o
@ ^ [Y_10: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_Ar813866963_alt_o @ Xs_38 ) )
= ( cons_A1087586947_alt_o @ X_37
@ ( rev_Ar813866963_alt_o
@ ( takeWh1686115066_alt_o
@ ^ [Y_10: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_656_dropWhile__neq__rev,axiom,
! [X_37: produc1572197287le_alt > $o,Xs_38: list_P811970973_alt_o] :
( ( distin299901067_alt_o @ Xs_38 )
=> ( ( member1241905979_alt_o @ X_37 @ ( set_Pr1457060537_alt_o @ Xs_38 ) )
=> ( ( dropWh1914665273_alt_o
@ ^ [Y_10: produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_Pr1871457144_alt_o @ Xs_38 ) )
= ( cons_P2104327368_alt_o @ X_37
@ ( rev_Pr1871457144_alt_o
@ ( takeWh432906385_alt_o
@ ^ [Y_10: produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_657_dropWhile__neq__rev,axiom,
! [X_37: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_38: list_A115096904_alt_o] :
( ( distin19168822_alt_o @ Xs_38 )
=> ( ( member822980838_alt_o @ X_37 @ ( set_Ar868233060_alt_o @ Xs_38 ) )
=> ( ( dropWh370535908_alt_o
@ ^ [Y_10: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_Ar710647715_alt_o @ Xs_38 ) )
= ( cons_A160405747_alt_o @ X_37
@ ( rev_Ar710647715_alt_o
@ ( takeWh2122498364_alt_o
@ ^ [Y_10: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_658_dropWhile__neq__rev,axiom,
! [X_37: produc1572197287le_alt,Xs_38: list_P1402680776le_alt] :
( ( distin1847856580le_alt @ Xs_38 )
=> ( ( member285112084le_alt @ X_37 @ ( set_Pr1596096022le_alt @ Xs_38 ) )
=> ( ( dropWh751361942le_alt
@ ^ [Y_10: produc1572197287le_alt] : ( (~) @ ( Y_10 = X_37 ) )
@ ( rev_Pr1287360663le_alt @ Xs_38 ) )
= ( cons_P1984625479le_alt @ X_37
@ ( rev_Pr1287360663le_alt
@ ( takeWh373185086le_alt
@ ^ [Y_10: produc1572197287le_alt] : ( (~) @ ( Y_10 = X_37 ) )
@ Xs_38 ) ) ) ) ) ) ).
thf(fact_659_set__ConsD,axiom,
! [Y_11: nat,X_36: nat,Xs_37: list_nat] :
( ( member_nat @ Y_11 @ ( set_nat @ ( cons_nat @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11 = X_36 )
| ( member_nat @ Y_11 @ ( set_nat @ Xs_37 ) ) ) ) ).
thf(fact_660_set__ConsD,axiom,
! [Y_11: arrow_1389031998le_alt,X_36: arrow_1389031998le_alt,Xs_37: list_A1402527603le_alt] :
( ( member998036369le_alt @ Y_11 @ ( set_Ar1491127311le_alt @ ( cons_A1142416030le_alt @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11 = X_36 )
| ( member998036369le_alt @ Y_11 @ ( set_Ar1491127311le_alt @ Xs_37 ) ) ) ) ).
thf(fact_661_set__ConsD,axiom,
! [Y_11: produc2069254453le_alt,X_36: produc2069254453le_alt,Xs_37: list_P1338624854le_alt] :
( ( member735418658le_alt @ Y_11 @ ( set_Pr1119022372le_alt @ ( cons_P607717589le_alt @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11 = X_36 )
| ( member735418658le_alt @ Y_11 @ ( set_Pr1119022372le_alt @ Xs_37 ) ) ) ) ).
thf(fact_662_set__ConsD,axiom,
! [Y_11: arrow_1196572341e_indi,X_36: arrow_1196572341e_indi,Xs_37: list_A1206016470e_indi] :
( ( member1818997282e_indi @ Y_11 @ ( set_Ar545511716e_indi @ ( cons_A430007893e_indi @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11 = X_36 )
| ( member1818997282e_indi @ Y_11 @ ( set_Ar545511716e_indi @ Xs_37 ) ) ) ) ).
thf(fact_663_set__ConsD,axiom,
! [Y_11: $o,X_36: $o,Xs_37: list_o] :
( ( member_o @ Y_11 @ ( set_o @ ( cons_o @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11
<=> X_36 )
| ( member_o @ Y_11 @ ( set_o @ Xs_37 ) ) ) ) ).
thf(fact_664_set__ConsD,axiom,
! [Y_11: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,X_36: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_37: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ Y_11 @ ( set_Ar17109714_alt_o @ ( cons_A1087586947_alt_o @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11 = X_36 )
| ( member1425217232_alt_o @ Y_11 @ ( set_Ar17109714_alt_o @ Xs_37 ) ) ) ) ).
thf(fact_665_set__ConsD,axiom,
! [Y_11: produc1572197287le_alt > $o,X_36: produc1572197287le_alt > $o,Xs_37: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ Y_11 @ ( set_Pr1457060537_alt_o @ ( cons_P2104327368_alt_o @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11 = X_36 )
| ( member1241905979_alt_o @ Y_11 @ ( set_Pr1457060537_alt_o @ Xs_37 ) ) ) ) ).
thf(fact_666_set__ConsD,axiom,
! [Y_11: arrow_1196572341e_indi > produc1572197287le_alt > $o,X_36: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_37: list_A115096904_alt_o] :
( ( member822980838_alt_o @ Y_11 @ ( set_Ar868233060_alt_o @ ( cons_A160405747_alt_o @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11 = X_36 )
| ( member822980838_alt_o @ Y_11 @ ( set_Ar868233060_alt_o @ Xs_37 ) ) ) ) ).
thf(fact_667_set__ConsD,axiom,
! [Y_11: produc1572197287le_alt,X_36: produc1572197287le_alt,Xs_37: list_P1402680776le_alt] :
( ( member285112084le_alt @ Y_11 @ ( set_Pr1596096022le_alt @ ( cons_P1984625479le_alt @ X_36 @ Xs_37 ) ) )
=> ( ( Y_11 = X_36 )
| ( member285112084le_alt @ Y_11 @ ( set_Pr1596096022le_alt @ Xs_37 ) ) ) ) ).
thf(fact_668_set__rev,axiom,
! [Xs_36: list_A1402527603le_alt] :
( ( set_Ar1491127311le_alt @ ( rev_Ar2020079950le_alt @ Xs_36 ) )
= ( set_Ar1491127311le_alt @ Xs_36 ) ) ).
thf(fact_669_in__set__dropD,axiom,
! [X_35: nat,N_6: nat,Xs_35: list_nat] :
( ( member_nat @ X_35 @ ( set_nat @ ( drop_nat @ N_6 @ Xs_35 ) ) )
=> ( member_nat @ X_35 @ ( set_nat @ Xs_35 ) ) ) ).
thf(fact_670_in__set__dropD,axiom,
! [X_35: arrow_1389031998le_alt,N_6: nat,Xs_35: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_35 @ ( set_Ar1491127311le_alt @ ( drop_A112899118le_alt @ N_6 @ Xs_35 ) ) )
=> ( member998036369le_alt @ X_35 @ ( set_Ar1491127311le_alt @ Xs_35 ) ) ) ).
thf(fact_671_in__set__dropD,axiom,
! [X_35: produc2069254453le_alt,N_6: nat,Xs_35: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_35 @ ( set_Pr1119022372le_alt @ ( drop_P2145219397le_alt @ N_6 @ Xs_35 ) ) )
=> ( member735418658le_alt @ X_35 @ ( set_Pr1119022372le_alt @ Xs_35 ) ) ) ).
thf(fact_672_in__set__dropD,axiom,
! [X_35: arrow_1196572341e_indi,N_6: nat,Xs_35: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_35 @ ( set_Ar545511716e_indi @ ( drop_A1363343557e_indi @ N_6 @ Xs_35 ) ) )
=> ( member1818997282e_indi @ X_35 @ ( set_Ar545511716e_indi @ Xs_35 ) ) ) ).
thf(fact_673_in__set__dropD,axiom,
! [X_35: $o,N_6: nat,Xs_35: list_o] :
( ( member_o @ X_35 @ ( set_o @ ( drop_o @ N_6 @ Xs_35 ) ) )
=> ( member_o @ X_35 @ ( set_o @ Xs_35 ) ) ) ).
thf(fact_674_in__set__dropD,axiom,
! [X_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,N_6: nat,Xs_35: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_35 @ ( set_Ar17109714_alt_o @ ( drop_A2135190771_alt_o @ N_6 @ Xs_35 ) ) )
=> ( member1425217232_alt_o @ X_35 @ ( set_Ar17109714_alt_o @ Xs_35 ) ) ) ).
thf(fact_675_in__set__dropD,axiom,
! [X_35: produc1572197287le_alt > $o,N_6: nat,Xs_35: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_35 @ ( set_Pr1457060537_alt_o @ ( drop_P1484576344_alt_o @ N_6 @ Xs_35 ) ) )
=> ( member1241905979_alt_o @ X_35 @ ( set_Pr1457060537_alt_o @ Xs_35 ) ) ) ).
thf(fact_676_in__set__dropD,axiom,
! [X_35: arrow_1196572341e_indi > produc1572197287le_alt > $o,N_6: nat,Xs_35: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_35 @ ( set_Ar868233060_alt_o @ ( drop_A1073592963_alt_o @ N_6 @ Xs_35 ) ) )
=> ( member822980838_alt_o @ X_35 @ ( set_Ar868233060_alt_o @ Xs_35 ) ) ) ).
thf(fact_677_in__set__dropD,axiom,
! [X_35: produc1572197287le_alt,N_6: nat,Xs_35: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_35 @ ( set_Pr1596096022le_alt @ ( drop_P1004899767le_alt @ N_6 @ Xs_35 ) ) )
=> ( member285112084le_alt @ X_35 @ ( set_Pr1596096022le_alt @ Xs_35 ) ) ) ).
thf(fact_678_takeWhile__eq__all__conv,axiom,
! [P_21: arrow_1389031998le_alt > $o,Xs_34: list_A1402527603le_alt] :
( ( ( takeWh462480871le_alt @ P_21 @ Xs_34 )
= Xs_34 )
<=> ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_34 ) )
=> ( P_21 @ X_1 ) ) ) ).
thf(fact_679_set__takeWhileD,axiom,
! [X_34: nat,P_20: nat > $o,Xs_33: list_nat] :
( ( member_nat @ X_34 @ ( set_nat @ ( takeWhile_nat @ P_20 @ Xs_33 ) ) )
=> ( ( member_nat @ X_34 @ ( set_nat @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_680_set__takeWhileD,axiom,
! [X_34: arrow_1389031998le_alt,P_20: arrow_1389031998le_alt > $o,Xs_33: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_34 @ ( set_Ar1491127311le_alt @ ( takeWh462480871le_alt @ P_20 @ Xs_33 ) ) )
=> ( ( member998036369le_alt @ X_34 @ ( set_Ar1491127311le_alt @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_681_set__takeWhileD,axiom,
! [X_34: produc2069254453le_alt,P_20: produc2069254453le_alt > $o,Xs_33: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_34 @ ( set_Pr1119022372le_alt @ ( takeWh131124556le_alt @ P_20 @ Xs_33 ) ) )
=> ( ( member735418658le_alt @ X_34 @ ( set_Pr1119022372le_alt @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_682_set__takeWhileD,axiom,
! [X_34: arrow_1196572341e_indi,P_20: arrow_1196572341e_indi > $o,Xs_33: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_34 @ ( set_Ar545511716e_indi @ ( takeWh598881612e_indi @ P_20 @ Xs_33 ) ) )
=> ( ( member1818997282e_indi @ X_34 @ ( set_Ar545511716e_indi @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_683_set__takeWhileD,axiom,
! [X_34: $o,P_20: $o > $o,Xs_33: list_o] :
( ( member_o @ X_34 @ ( set_o @ ( takeWhile_o @ P_20 @ Xs_33 ) ) )
=> ( ( member_o @ X_34 @ ( set_o @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_684_set__takeWhileD,axiom,
! [X_34: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,P_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Xs_33: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_34 @ ( set_Ar17109714_alt_o @ ( takeWh1686115066_alt_o @ P_20 @ Xs_33 ) ) )
=> ( ( member1425217232_alt_o @ X_34 @ ( set_Ar17109714_alt_o @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_685_set__takeWhileD,axiom,
! [X_34: produc1572197287le_alt > $o,P_20: ( produc1572197287le_alt > $o ) > $o,Xs_33: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_34 @ ( set_Pr1457060537_alt_o @ ( takeWh432906385_alt_o @ P_20 @ Xs_33 ) ) )
=> ( ( member1241905979_alt_o @ X_34 @ ( set_Pr1457060537_alt_o @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_686_set__takeWhileD,axiom,
! [X_34: arrow_1196572341e_indi > produc1572197287le_alt > $o,P_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Xs_33: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_34 @ ( set_Ar868233060_alt_o @ ( takeWh2122498364_alt_o @ P_20 @ Xs_33 ) ) )
=> ( ( member822980838_alt_o @ X_34 @ ( set_Ar868233060_alt_o @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_687_set__takeWhileD,axiom,
! [X_34: produc1572197287le_alt,P_20: produc1572197287le_alt > $o,Xs_33: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_34 @ ( set_Pr1596096022le_alt @ ( takeWh373185086le_alt @ P_20 @ Xs_33 ) ) )
=> ( ( member285112084le_alt @ X_34 @ ( set_Pr1596096022le_alt @ Xs_33 ) )
& ( P_20 @ X_34 ) ) ) ).
thf(fact_688_in__set__butlastD,axiom,
! [X_33: nat,Xs_32: list_nat] :
( ( member_nat @ X_33 @ ( set_nat @ ( butlast_nat @ Xs_32 ) ) )
=> ( member_nat @ X_33 @ ( set_nat @ Xs_32 ) ) ) ).
thf(fact_689_in__set__butlastD,axiom,
! [X_33: arrow_1389031998le_alt,Xs_32: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_33 @ ( set_Ar1491127311le_alt @ ( butlas1188620858le_alt @ Xs_32 ) ) )
=> ( member998036369le_alt @ X_33 @ ( set_Ar1491127311le_alt @ Xs_32 ) ) ) ).
thf(fact_690_in__set__butlastD,axiom,
! [X_33: produc2069254453le_alt,Xs_32: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_33 @ ( set_Pr1119022372le_alt @ ( butlas1171206713le_alt @ Xs_32 ) ) )
=> ( member735418658le_alt @ X_33 @ ( set_Pr1119022372le_alt @ Xs_32 ) ) ) ).
thf(fact_691_in__set__butlastD,axiom,
! [X_33: arrow_1196572341e_indi,Xs_32: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_33 @ ( set_Ar545511716e_indi @ ( butlas1321092537e_indi @ Xs_32 ) ) )
=> ( member1818997282e_indi @ X_33 @ ( set_Ar545511716e_indi @ Xs_32 ) ) ) ).
thf(fact_692_in__set__butlastD,axiom,
! [X_33: $o,Xs_32: list_o] :
( ( member_o @ X_33 @ ( set_o @ ( butlast_o @ Xs_32 ) ) )
=> ( member_o @ X_33 @ ( set_o @ Xs_32 ) ) ) ).
thf(fact_693_in__set__butlastD,axiom,
! [X_33: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_32: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_33 @ ( set_Ar17109714_alt_o @ ( butlas1946565607_alt_o @ Xs_32 ) ) )
=> ( member1425217232_alt_o @ X_33 @ ( set_Ar17109714_alt_o @ Xs_32 ) ) ) ).
thf(fact_694_in__set__butlastD,axiom,
! [X_33: produc1572197287le_alt > $o,Xs_32: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_33 @ ( set_Pr1457060537_alt_o @ ( butlas1233216100_alt_o @ Xs_32 ) ) )
=> ( member1241905979_alt_o @ X_33 @ ( set_Pr1457060537_alt_o @ Xs_32 ) ) ) ).
thf(fact_695_in__set__butlastD,axiom,
! [X_33: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_32: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_33 @ ( set_Ar868233060_alt_o @ ( butlas1110035599_alt_o @ Xs_32 ) ) )
=> ( member822980838_alt_o @ X_33 @ ( set_Ar868233060_alt_o @ Xs_32 ) ) ) ).
thf(fact_696_in__set__butlastD,axiom,
! [X_33: produc1572197287le_alt,Xs_32: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_33 @ ( set_Pr1596096022le_alt @ ( butlas732535467le_alt @ Xs_32 ) ) )
=> ( member285112084le_alt @ X_33 @ ( set_Pr1596096022le_alt @ Xs_32 ) ) ) ).
thf(fact_697_set__rotate1,axiom,
! [Xs_31: list_A1402527603le_alt] :
( ( set_Ar1491127311le_alt @ ( rotate1249022267le_alt @ Xs_31 ) )
= ( set_Ar1491127311le_alt @ Xs_31 ) ) ).
thf(fact_698_in__set__insert,axiom,
! [X_32: nat,Xs_30: list_nat] :
( ( member_nat @ X_32 @ ( set_nat @ Xs_30 ) )
=> ( ( insert_nat @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_699_in__set__insert,axiom,
! [X_32: arrow_1389031998le_alt,Xs_30: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_32 @ ( set_Ar1491127311le_alt @ Xs_30 ) )
=> ( ( insert886756100le_alt @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_700_in__set__insert,axiom,
! [X_32: produc2069254453le_alt,Xs_30: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_32 @ ( set_Pr1119022372le_alt @ Xs_30 ) )
=> ( ( insert2040953583le_alt @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_701_in__set__insert,axiom,
! [X_32: arrow_1196572341e_indi,Xs_30: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_32 @ ( set_Ar545511716e_indi @ Xs_30 ) )
=> ( ( insert1241550703e_indi @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_702_in__set__insert,axiom,
! [X_32: $o,Xs_30: list_o] :
( ( member_o @ X_32 @ ( set_o @ Xs_30 ) )
=> ( ( insert_o @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_703_in__set__insert,axiom,
! [X_32: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_30: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_32 @ ( set_Ar17109714_alt_o @ Xs_30 ) )
=> ( ( insert889535645_alt_o @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_704_in__set__insert,axiom,
! [X_32: produc1572197287le_alt > $o,Xs_30: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_32 @ ( set_Pr1457060537_alt_o @ Xs_30 ) )
=> ( ( insert1316276270_alt_o @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_705_in__set__insert,axiom,
! [X_32: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_30: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_32 @ ( set_Ar868233060_alt_o @ Xs_30 ) )
=> ( ( insert425285465_alt_o @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_706_in__set__insert,axiom,
! [X_32: produc1572197287le_alt,Xs_30: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_32 @ ( set_Pr1596096022le_alt @ Xs_30 ) )
=> ( ( insert1248101473le_alt @ X_32 @ Xs_30 )
= Xs_30 ) ) ).
thf(fact_707_distinct_Osimps_I2_J,axiom,
! [X_31: nat,Xs_29: list_nat] :
( ( distinct_nat @ ( cons_nat @ X_31 @ Xs_29 ) )
<=> ( ~ ( member_nat @ X_31 @ ( set_nat @ Xs_29 ) )
& ( distinct_nat @ Xs_29 ) ) ) ).
thf(fact_708_distinct_Osimps_I2_J,axiom,
! [X_31: arrow_1389031998le_alt,Xs_29: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ X_31 @ Xs_29 ) )
<=> ( ~ ( member998036369le_alt @ X_31 @ ( set_Ar1491127311le_alt @ Xs_29 ) )
& ( distin1149997281le_alt @ Xs_29 ) ) ) ).
thf(fact_709_distinct_Osimps_I2_J,axiom,
! [X_31: produc2069254453le_alt,Xs_29: list_P1338624854le_alt] :
( ( distin1268295634le_alt @ ( cons_P607717589le_alt @ X_31 @ Xs_29 ) )
<=> ( ~ ( member735418658le_alt @ X_31 @ ( set_Pr1119022372le_alt @ Xs_29 ) )
& ( distin1268295634le_alt @ Xs_29 ) ) ) ).
thf(fact_710_distinct_Osimps_I2_J,axiom,
! [X_31: arrow_1196572341e_indi,Xs_29: list_A1206016470e_indi] :
( ( distin1683769554e_indi @ ( cons_A430007893e_indi @ X_31 @ Xs_29 ) )
<=> ( ~ ( member1818997282e_indi @ X_31 @ ( set_Ar545511716e_indi @ Xs_29 ) )
& ( distin1683769554e_indi @ Xs_29 ) ) ) ).
thf(fact_711_distinct_Osimps_I2_J,axiom,
! [X_31: $o,Xs_29: list_o] :
( ( distinct_o @ ( cons_o @ X_31 @ Xs_29 ) )
<=> ( ~ ( member_o @ X_31 @ ( set_o @ Xs_29 ) )
& ( distinct_o @ Xs_29 ) ) ) ).
thf(fact_712_distinct_Osimps_I2_J,axiom,
! [X_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_29: list_A869418500_alt_o] :
( ( distin568845696_alt_o @ ( cons_A1087586947_alt_o @ X_31 @ Xs_29 ) )
<=> ( ~ ( member1425217232_alt_o @ X_31 @ ( set_Ar17109714_alt_o @ Xs_29 ) )
& ( distin568845696_alt_o @ Xs_29 ) ) ) ).
thf(fact_713_distinct_Osimps_I2_J,axiom,
! [X_31: produc1572197287le_alt > $o,Xs_29: list_P811970973_alt_o] :
( ( distin299901067_alt_o @ ( cons_P2104327368_alt_o @ X_31 @ Xs_29 ) )
<=> ( ~ ( member1241905979_alt_o @ X_31 @ ( set_Pr1457060537_alt_o @ Xs_29 ) )
& ( distin299901067_alt_o @ Xs_29 ) ) ) ).
thf(fact_714_distinct_Osimps_I2_J,axiom,
! [X_31: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_29: list_A115096904_alt_o] :
( ( distin19168822_alt_o @ ( cons_A160405747_alt_o @ X_31 @ Xs_29 ) )
<=> ( ~ ( member822980838_alt_o @ X_31 @ ( set_Ar868233060_alt_o @ Xs_29 ) )
& ( distin19168822_alt_o @ Xs_29 ) ) ) ).
thf(fact_715_distinct_Osimps_I2_J,axiom,
! [X_31: produc1572197287le_alt,Xs_29: list_P1402680776le_alt] :
( ( distin1847856580le_alt @ ( cons_P1984625479le_alt @ X_31 @ Xs_29 ) )
<=> ( ~ ( member285112084le_alt @ X_31 @ ( set_Pr1596096022le_alt @ Xs_29 ) )
& ( distin1847856580le_alt @ Xs_29 ) ) ) ).
thf(fact_716_takeWhile__append1,axiom,
! [Ys_6: list_nat,P_19: nat > $o,X_30: nat,Xs_28: list_nat] :
( ( member_nat @ X_30 @ ( set_nat @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWhile_nat @ P_19 @ ( append_nat @ Xs_28 @ Ys_6 ) )
= ( takeWhile_nat @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_717_takeWhile__append1,axiom,
! [Ys_6: list_A1402527603le_alt,P_19: arrow_1389031998le_alt > $o,X_30: arrow_1389031998le_alt,Xs_28: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_30 @ ( set_Ar1491127311le_alt @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWh462480871le_alt @ P_19 @ ( append1092755459le_alt @ Xs_28 @ Ys_6 ) )
= ( takeWh462480871le_alt @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_718_takeWhile__append1,axiom,
! [Ys_6: list_P1338624854le_alt,P_19: produc2069254453le_alt > $o,X_30: produc2069254453le_alt,Xs_28: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_30 @ ( set_Pr1119022372le_alt @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWh131124556le_alt @ P_19 @ ( append1130570800le_alt @ Xs_28 @ Ys_6 ) )
= ( takeWh131124556le_alt @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_719_takeWhile__append1,axiom,
! [Ys_6: list_A1206016470e_indi,P_19: arrow_1196572341e_indi > $o,X_30: arrow_1196572341e_indi,Xs_28: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_30 @ ( set_Ar545511716e_indi @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWh598881612e_indi @ P_19 @ ( append478904880e_indi @ Xs_28 @ Ys_6 ) )
= ( takeWh598881612e_indi @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_720_takeWhile__append1,axiom,
! [Ys_6: list_o,P_19: $o > $o,X_30: $o,Xs_28: list_o] :
( ( member_o @ X_30 @ ( set_o @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWhile_o @ P_19 @ ( append_o @ Xs_28 @ Ys_6 ) )
= ( takeWhile_o @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_721_takeWhile__append1,axiom,
! [Ys_6: list_A869418500_alt_o,P_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_28: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_30 @ ( set_Ar17109714_alt_o @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWh1686115066_alt_o @ P_19 @ ( append1134377438_alt_o @ Xs_28 @ Ys_6 ) )
= ( takeWh1686115066_alt_o @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_722_takeWhile__append1,axiom,
! [Ys_6: list_P811970973_alt_o,P_19: ( produc1572197287le_alt > $o ) > $o,X_30: produc1572197287le_alt > $o,Xs_28: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_30 @ ( set_Pr1457060537_alt_o @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWh432906385_alt_o @ P_19 @ ( append1477507245_alt_o @ Xs_28 @ Ys_6 ) )
= ( takeWh432906385_alt_o @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_723_takeWhile__append1,axiom,
! [Ys_6: list_A115096904_alt_o,P_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_30: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_28: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_30 @ ( set_Ar868233060_alt_o @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWh2122498364_alt_o @ P_19 @ ( append592815960_alt_o @ Xs_28 @ Ys_6 ) )
= ( takeWh2122498364_alt_o @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_724_takeWhile__append1,axiom,
! [Ys_6: list_P1402680776le_alt,P_19: produc1572197287le_alt > $o,X_30: produc1572197287le_alt,Xs_28: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_30 @ ( set_Pr1596096022le_alt @ Xs_28 ) )
=> ( ~ ( P_19 @ X_30 )
=> ( ( takeWh373185086le_alt @ P_19 @ ( append1300326178le_alt @ Xs_28 @ Ys_6 ) )
= ( takeWh373185086le_alt @ P_19 @ Xs_28 ) ) ) ) ).
thf(fact_725_last__in__set,axiom,
! [As: list_A1402527603le_alt] :
( ( As != nil_Ar52383470le_alt )
=> ( member998036369le_alt @ ( last_A2130988295le_alt @ As ) @ ( set_Ar1491127311le_alt @ As ) ) ) ).
thf(fact_726_last__in__set,axiom,
! [As: list_nat] :
( ( As != nil_nat )
=> ( member_nat @ ( last_nat @ As ) @ ( set_nat @ As ) ) ) ).
thf(fact_727_last__in__set,axiom,
! [As: list_P1338624854le_alt] :
( ( As != nil_Pr1072539781le_alt )
=> ( member735418658le_alt @ ( last_P438492716le_alt @ As ) @ ( set_Pr1119022372le_alt @ As ) ) ) ).
thf(fact_728_last__in__set,axiom,
! [As: list_A1206016470e_indi] :
( ( As != nil_Ar147131909e_indi )
=> ( member1818997282e_indi @ ( last_A70817324e_indi @ As ) @ ( set_Ar545511716e_indi @ As ) ) ) ).
thf(fact_729_last__in__set,axiom,
! [As: list_o] :
( ( As != nil_o )
=> ( member_o @ ( last_o @ As ) @ ( set_o @ As ) ) ) ).
thf(fact_730_last__in__set,axiom,
! [As: list_A869418500_alt_o] :
( ( As != nil_Ar1062052403_alt_o )
=> ( member1425217232_alt_o @ ( last_A2082186202_alt_o @ As ) @ ( set_Ar17109714_alt_o @ As ) ) ) ).
thf(fact_731_last__in__set,axiom,
! [As: list_P811970973_alt_o] :
( ( As != nil_Pr893112600_alt_o )
=> ( member1241905979_alt_o @ ( last_P1550587825_alt_o @ As ) @ ( set_Pr1457060537_alt_o @ As ) ) ) ).
thf(fact_732_last__in__set,axiom,
! [As: list_A115096904_alt_o] :
( ( As != nil_Ar26350915_alt_o )
=> ( member822980838_alt_o @ ( last_A1346422876_alt_o @ As ) @ ( set_Ar868233060_alt_o @ As ) ) ) ).
thf(fact_733_last__in__set,axiom,
! [As: list_P1402680776le_alt] :
( ( As != nil_Pr932422391le_alt )
=> ( member285112084le_alt @ ( last_P1727445790le_alt @ As ) @ ( set_Pr1596096022le_alt @ As ) ) ) ).
thf(fact_734_dropWhile__eq__Nil__conv,axiom,
! [P_18: arrow_1389031998le_alt > $o,Xs_27: list_A1402527603le_alt] :
( ( ( dropWh82971279le_alt @ P_18 @ Xs_27 )
= nil_Ar52383470le_alt )
<=> ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_27 ) )
=> ( P_18 @ X_1 ) ) ) ).
thf(fact_735_in__set__butlast__appendI,axiom,
! [Ys_5: list_nat,X_29: nat,Xs_26: list_nat] :
( ( ( member_nat @ X_29 @ ( set_nat @ ( butlast_nat @ Xs_26 ) ) )
| ( member_nat @ X_29 @ ( set_nat @ ( butlast_nat @ Ys_5 ) ) ) )
=> ( member_nat @ X_29 @ ( set_nat @ ( butlast_nat @ ( append_nat @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_736_in__set__butlast__appendI,axiom,
! [Ys_5: list_A1402527603le_alt,X_29: arrow_1389031998le_alt,Xs_26: list_A1402527603le_alt] :
( ( ( member998036369le_alt @ X_29 @ ( set_Ar1491127311le_alt @ ( butlas1188620858le_alt @ Xs_26 ) ) )
| ( member998036369le_alt @ X_29 @ ( set_Ar1491127311le_alt @ ( butlas1188620858le_alt @ Ys_5 ) ) ) )
=> ( member998036369le_alt @ X_29 @ ( set_Ar1491127311le_alt @ ( butlas1188620858le_alt @ ( append1092755459le_alt @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_737_in__set__butlast__appendI,axiom,
! [Ys_5: list_P1338624854le_alt,X_29: produc2069254453le_alt,Xs_26: list_P1338624854le_alt] :
( ( ( member735418658le_alt @ X_29 @ ( set_Pr1119022372le_alt @ ( butlas1171206713le_alt @ Xs_26 ) ) )
| ( member735418658le_alt @ X_29 @ ( set_Pr1119022372le_alt @ ( butlas1171206713le_alt @ Ys_5 ) ) ) )
=> ( member735418658le_alt @ X_29 @ ( set_Pr1119022372le_alt @ ( butlas1171206713le_alt @ ( append1130570800le_alt @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_738_in__set__butlast__appendI,axiom,
! [Ys_5: list_A1206016470e_indi,X_29: arrow_1196572341e_indi,Xs_26: list_A1206016470e_indi] :
( ( ( member1818997282e_indi @ X_29 @ ( set_Ar545511716e_indi @ ( butlas1321092537e_indi @ Xs_26 ) ) )
| ( member1818997282e_indi @ X_29 @ ( set_Ar545511716e_indi @ ( butlas1321092537e_indi @ Ys_5 ) ) ) )
=> ( member1818997282e_indi @ X_29 @ ( set_Ar545511716e_indi @ ( butlas1321092537e_indi @ ( append478904880e_indi @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_739_in__set__butlast__appendI,axiom,
! [Ys_5: list_o,X_29: $o,Xs_26: list_o] :
( ( ( member_o @ X_29 @ ( set_o @ ( butlast_o @ Xs_26 ) ) )
| ( member_o @ X_29 @ ( set_o @ ( butlast_o @ Ys_5 ) ) ) )
=> ( member_o @ X_29 @ ( set_o @ ( butlast_o @ ( append_o @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_740_in__set__butlast__appendI,axiom,
! [Ys_5: list_A869418500_alt_o,X_29: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_26: list_A869418500_alt_o] :
( ( ( member1425217232_alt_o @ X_29 @ ( set_Ar17109714_alt_o @ ( butlas1946565607_alt_o @ Xs_26 ) ) )
| ( member1425217232_alt_o @ X_29 @ ( set_Ar17109714_alt_o @ ( butlas1946565607_alt_o @ Ys_5 ) ) ) )
=> ( member1425217232_alt_o @ X_29 @ ( set_Ar17109714_alt_o @ ( butlas1946565607_alt_o @ ( append1134377438_alt_o @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_741_in__set__butlast__appendI,axiom,
! [Ys_5: list_P811970973_alt_o,X_29: produc1572197287le_alt > $o,Xs_26: list_P811970973_alt_o] :
( ( ( member1241905979_alt_o @ X_29 @ ( set_Pr1457060537_alt_o @ ( butlas1233216100_alt_o @ Xs_26 ) ) )
| ( member1241905979_alt_o @ X_29 @ ( set_Pr1457060537_alt_o @ ( butlas1233216100_alt_o @ Ys_5 ) ) ) )
=> ( member1241905979_alt_o @ X_29 @ ( set_Pr1457060537_alt_o @ ( butlas1233216100_alt_o @ ( append1477507245_alt_o @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_742_in__set__butlast__appendI,axiom,
! [Ys_5: list_A115096904_alt_o,X_29: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_26: list_A115096904_alt_o] :
( ( ( member822980838_alt_o @ X_29 @ ( set_Ar868233060_alt_o @ ( butlas1110035599_alt_o @ Xs_26 ) ) )
| ( member822980838_alt_o @ X_29 @ ( set_Ar868233060_alt_o @ ( butlas1110035599_alt_o @ Ys_5 ) ) ) )
=> ( member822980838_alt_o @ X_29 @ ( set_Ar868233060_alt_o @ ( butlas1110035599_alt_o @ ( append592815960_alt_o @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_743_in__set__butlast__appendI,axiom,
! [Ys_5: list_P1402680776le_alt,X_29: produc1572197287le_alt,Xs_26: list_P1402680776le_alt] :
( ( ( member285112084le_alt @ X_29 @ ( set_Pr1596096022le_alt @ ( butlas732535467le_alt @ Xs_26 ) ) )
| ( member285112084le_alt @ X_29 @ ( set_Pr1596096022le_alt @ ( butlas732535467le_alt @ Ys_5 ) ) ) )
=> ( member285112084le_alt @ X_29 @ ( set_Pr1596096022le_alt @ ( butlas732535467le_alt @ ( append1300326178le_alt @ Xs_26 @ Ys_5 ) ) ) ) ) ).
thf(fact_744_hd__in__set,axiom,
! [Xs_25: list_A1402527603le_alt] :
( ( Xs_25 != nil_Ar52383470le_alt )
=> ( member998036369le_alt @ ( hd_Arr731872705le_alt @ Xs_25 ) @ ( set_Ar1491127311le_alt @ Xs_25 ) ) ) ).
thf(fact_745_hd__in__set,axiom,
! [Xs_25: list_nat] :
( ( Xs_25 != nil_nat )
=> ( member_nat @ ( hd_nat @ Xs_25 ) @ ( set_nat @ Xs_25 ) ) ) ).
thf(fact_746_hd__in__set,axiom,
! [Xs_25: list_P1338624854le_alt] :
( ( Xs_25 != nil_Pr1072539781le_alt )
=> ( member735418658le_alt @ ( hd_Pro1563575026le_alt @ Xs_25 ) @ ( set_Pr1119022372le_alt @ Xs_25 ) ) ) ).
thf(fact_747_hd__in__set,axiom,
! [Xs_25: list_A1206016470e_indi] :
( ( Xs_25 != nil_Ar147131909e_indi )
=> ( member1818997282e_indi @ ( hd_Arr790860786e_indi @ Xs_25 ) @ ( set_Ar545511716e_indi @ Xs_25 ) ) ) ).
thf(fact_748_hd__in__set,axiom,
! [Xs_25: list_o] :
( ( Xs_25 != nil_o )
=> ( member_o @ ( hd_o @ Xs_25 ) @ ( set_o @ Xs_25 ) ) ) ).
thf(fact_749_hd__in__set,axiom,
! [Xs_25: list_A869418500_alt_o] :
( ( Xs_25 != nil_Ar1062052403_alt_o )
=> ( member1425217232_alt_o @ ( hd_Arr447217824_alt_o @ Xs_25 ) @ ( set_Ar17109714_alt_o @ Xs_25 ) ) ) ).
thf(fact_750_hd__in__set,axiom,
! [Xs_25: list_P811970973_alt_o] :
( ( Xs_25 != nil_Pr893112600_alt_o )
=> ( member1241905979_alt_o @ ( hd_Pro1487076715_alt_o @ Xs_25 ) @ ( set_Pr1457060537_alt_o @ Xs_25 ) ) ) ).
thf(fact_751_hd__in__set,axiom,
! [Xs_25: list_A115096904_alt_o] :
( ( Xs_25 != nil_Ar26350915_alt_o )
=> ( member822980838_alt_o @ ( hd_Arr871484182_alt_o @ Xs_25 ) @ ( set_Ar868233060_alt_o @ Xs_25 ) ) ) ).
thf(fact_752_hd__in__set,axiom,
! [Xs_25: list_P1402680776le_alt] :
( ( Xs_25 != nil_Pr932422391le_alt )
=> ( member285112084le_alt @ ( hd_Pro368662756le_alt @ Xs_25 ) @ ( set_Pr1596096022le_alt @ Xs_25 ) ) ) ).
thf(fact_753_dropWhile__append1,axiom,
! [Ys_4: list_nat,P_17: nat > $o,X_28: nat,Xs_24: list_nat] :
( ( member_nat @ X_28 @ ( set_nat @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWhile_nat @ P_17 @ ( append_nat @ Xs_24 @ Ys_4 ) )
= ( append_nat @ ( dropWhile_nat @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_754_dropWhile__append1,axiom,
! [Ys_4: list_A1402527603le_alt,P_17: arrow_1389031998le_alt > $o,X_28: arrow_1389031998le_alt,Xs_24: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_28 @ ( set_Ar1491127311le_alt @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWh82971279le_alt @ P_17 @ ( append1092755459le_alt @ Xs_24 @ Ys_4 ) )
= ( append1092755459le_alt @ ( dropWh82971279le_alt @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_755_dropWhile__append1,axiom,
! [Ys_4: list_P1338624854le_alt,P_17: produc2069254453le_alt > $o,X_28: produc2069254453le_alt,Xs_24: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_28 @ ( set_Pr1119022372le_alt @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWh1319308964le_alt @ P_17 @ ( append1130570800le_alt @ Xs_24 @ Ys_4 ) )
= ( append1130570800le_alt @ ( dropWh1319308964le_alt @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_756_dropWhile__append1,axiom,
! [Ys_4: list_A1206016470e_indi,P_17: arrow_1196572341e_indi > $o,X_28: arrow_1196572341e_indi,Xs_24: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_28 @ ( set_Ar545511716e_indi @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWh927087268e_indi @ P_17 @ ( append478904880e_indi @ Xs_24 @ Ys_4 ) )
= ( append478904880e_indi @ ( dropWh927087268e_indi @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_757_dropWhile__append1,axiom,
! [Ys_4: list_o,P_17: $o > $o,X_28: $o,Xs_24: list_o] :
( ( member_o @ X_28 @ ( set_o @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWhile_o @ P_17 @ ( append_o @ Xs_24 @ Ys_4 ) )
= ( append_o @ ( dropWhile_o @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_758_dropWhile__append1,axiom,
! [Ys_4: list_A869418500_alt_o,P_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_28: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_24: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_28 @ ( set_Ar17109714_alt_o @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWh1391670354_alt_o @ P_17 @ ( append1134377438_alt_o @ Xs_24 @ Ys_4 ) )
= ( append1134377438_alt_o @ ( dropWh1391670354_alt_o @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_759_dropWhile__append1,axiom,
! [Ys_4: list_P811970973_alt_o,P_17: ( produc1572197287le_alt > $o ) > $o,X_28: produc1572197287le_alt > $o,Xs_24: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_28 @ ( set_Pr1457060537_alt_o @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWh1914665273_alt_o @ P_17 @ ( append1477507245_alt_o @ Xs_24 @ Ys_4 ) )
= ( append1477507245_alt_o @ ( dropWh1914665273_alt_o @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_760_dropWhile__append1,axiom,
! [Ys_4: list_A115096904_alt_o,P_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_28: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_24: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_28 @ ( set_Ar868233060_alt_o @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWh370535908_alt_o @ P_17 @ ( append592815960_alt_o @ Xs_24 @ Ys_4 ) )
= ( append592815960_alt_o @ ( dropWh370535908_alt_o @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_761_dropWhile__append1,axiom,
! [Ys_4: list_P1402680776le_alt,P_17: produc1572197287le_alt > $o,X_28: produc1572197287le_alt,Xs_24: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_28 @ ( set_Pr1596096022le_alt @ Xs_24 ) )
=> ( ~ ( P_17 @ X_28 )
=> ( ( dropWh751361942le_alt @ P_17 @ ( append1300326178le_alt @ Xs_24 @ Ys_4 ) )
= ( append1300326178le_alt @ ( dropWh751361942le_alt @ P_17 @ Xs_24 ) @ Ys_4 ) ) ) ) ).
thf(fact_762_List_Oinsert__def,axiom,
! [X_27: nat,Xs_23: list_nat] :
( ( ( member_nat @ X_27 @ ( set_nat @ Xs_23 ) )
=> ( ( insert_nat @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member_nat @ X_27 @ ( set_nat @ Xs_23 ) )
=> ( ( insert_nat @ X_27 @ Xs_23 )
= ( cons_nat @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_763_List_Oinsert__def,axiom,
! [X_27: arrow_1389031998le_alt,Xs_23: list_A1402527603le_alt] :
( ( ( member998036369le_alt @ X_27 @ ( set_Ar1491127311le_alt @ Xs_23 ) )
=> ( ( insert886756100le_alt @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member998036369le_alt @ X_27 @ ( set_Ar1491127311le_alt @ Xs_23 ) )
=> ( ( insert886756100le_alt @ X_27 @ Xs_23 )
= ( cons_A1142416030le_alt @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_764_List_Oinsert__def,axiom,
! [X_27: produc2069254453le_alt,Xs_23: list_P1338624854le_alt] :
( ( ( member735418658le_alt @ X_27 @ ( set_Pr1119022372le_alt @ Xs_23 ) )
=> ( ( insert2040953583le_alt @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member735418658le_alt @ X_27 @ ( set_Pr1119022372le_alt @ Xs_23 ) )
=> ( ( insert2040953583le_alt @ X_27 @ Xs_23 )
= ( cons_P607717589le_alt @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_765_List_Oinsert__def,axiom,
! [X_27: arrow_1196572341e_indi,Xs_23: list_A1206016470e_indi] :
( ( ( member1818997282e_indi @ X_27 @ ( set_Ar545511716e_indi @ Xs_23 ) )
=> ( ( insert1241550703e_indi @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member1818997282e_indi @ X_27 @ ( set_Ar545511716e_indi @ Xs_23 ) )
=> ( ( insert1241550703e_indi @ X_27 @ Xs_23 )
= ( cons_A430007893e_indi @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_766_List_Oinsert__def,axiom,
! [X_27: $o,Xs_23: list_o] :
( ( ( member_o @ X_27 @ ( set_o @ Xs_23 ) )
=> ( ( insert_o @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member_o @ X_27 @ ( set_o @ Xs_23 ) )
=> ( ( insert_o @ X_27 @ Xs_23 )
= ( cons_o @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_767_List_Oinsert__def,axiom,
! [X_27: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_23: list_A869418500_alt_o] :
( ( ( member1425217232_alt_o @ X_27 @ ( set_Ar17109714_alt_o @ Xs_23 ) )
=> ( ( insert889535645_alt_o @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member1425217232_alt_o @ X_27 @ ( set_Ar17109714_alt_o @ Xs_23 ) )
=> ( ( insert889535645_alt_o @ X_27 @ Xs_23 )
= ( cons_A1087586947_alt_o @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_768_List_Oinsert__def,axiom,
! [X_27: produc1572197287le_alt > $o,Xs_23: list_P811970973_alt_o] :
( ( ( member1241905979_alt_o @ X_27 @ ( set_Pr1457060537_alt_o @ Xs_23 ) )
=> ( ( insert1316276270_alt_o @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member1241905979_alt_o @ X_27 @ ( set_Pr1457060537_alt_o @ Xs_23 ) )
=> ( ( insert1316276270_alt_o @ X_27 @ Xs_23 )
= ( cons_P2104327368_alt_o @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_769_List_Oinsert__def,axiom,
! [X_27: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_23: list_A115096904_alt_o] :
( ( ( member822980838_alt_o @ X_27 @ ( set_Ar868233060_alt_o @ Xs_23 ) )
=> ( ( insert425285465_alt_o @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member822980838_alt_o @ X_27 @ ( set_Ar868233060_alt_o @ Xs_23 ) )
=> ( ( insert425285465_alt_o @ X_27 @ Xs_23 )
= ( cons_A160405747_alt_o @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_770_List_Oinsert__def,axiom,
! [X_27: produc1572197287le_alt,Xs_23: list_P1402680776le_alt] :
( ( ( member285112084le_alt @ X_27 @ ( set_Pr1596096022le_alt @ Xs_23 ) )
=> ( ( insert1248101473le_alt @ X_27 @ Xs_23 )
= Xs_23 ) )
& ( ~ ( member285112084le_alt @ X_27 @ ( set_Pr1596096022le_alt @ Xs_23 ) )
=> ( ( insert1248101473le_alt @ X_27 @ Xs_23 )
= ( cons_P1984625479le_alt @ X_27 @ Xs_23 ) ) ) ) ).
thf(fact_771_not__in__set__insert,axiom,
! [X_26: nat,Xs_22: list_nat] :
( ~ ( member_nat @ X_26 @ ( set_nat @ Xs_22 ) )
=> ( ( insert_nat @ X_26 @ Xs_22 )
= ( cons_nat @ X_26 @ Xs_22 ) ) ) ).
thf(fact_772_not__in__set__insert,axiom,
! [X_26: arrow_1389031998le_alt,Xs_22: list_A1402527603le_alt] :
( ~ ( member998036369le_alt @ X_26 @ ( set_Ar1491127311le_alt @ Xs_22 ) )
=> ( ( insert886756100le_alt @ X_26 @ Xs_22 )
= ( cons_A1142416030le_alt @ X_26 @ Xs_22 ) ) ) ).
thf(fact_773_not__in__set__insert,axiom,
! [X_26: produc2069254453le_alt,Xs_22: list_P1338624854le_alt] :
( ~ ( member735418658le_alt @ X_26 @ ( set_Pr1119022372le_alt @ Xs_22 ) )
=> ( ( insert2040953583le_alt @ X_26 @ Xs_22 )
= ( cons_P607717589le_alt @ X_26 @ Xs_22 ) ) ) ).
thf(fact_774_not__in__set__insert,axiom,
! [X_26: arrow_1196572341e_indi,Xs_22: list_A1206016470e_indi] :
( ~ ( member1818997282e_indi @ X_26 @ ( set_Ar545511716e_indi @ Xs_22 ) )
=> ( ( insert1241550703e_indi @ X_26 @ Xs_22 )
= ( cons_A430007893e_indi @ X_26 @ Xs_22 ) ) ) ).
thf(fact_775_not__in__set__insert,axiom,
! [X_26: $o,Xs_22: list_o] :
( ~ ( member_o @ X_26 @ ( set_o @ Xs_22 ) )
=> ( ( insert_o @ X_26 @ Xs_22 )
= ( cons_o @ X_26 @ Xs_22 ) ) ) ).
thf(fact_776_not__in__set__insert,axiom,
! [X_26: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_22: list_A869418500_alt_o] :
( ~ ( member1425217232_alt_o @ X_26 @ ( set_Ar17109714_alt_o @ Xs_22 ) )
=> ( ( insert889535645_alt_o @ X_26 @ Xs_22 )
= ( cons_A1087586947_alt_o @ X_26 @ Xs_22 ) ) ) ).
thf(fact_777_not__in__set__insert,axiom,
! [X_26: produc1572197287le_alt > $o,Xs_22: list_P811970973_alt_o] :
( ~ ( member1241905979_alt_o @ X_26 @ ( set_Pr1457060537_alt_o @ Xs_22 ) )
=> ( ( insert1316276270_alt_o @ X_26 @ Xs_22 )
= ( cons_P2104327368_alt_o @ X_26 @ Xs_22 ) ) ) ).
thf(fact_778_not__in__set__insert,axiom,
! [X_26: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_22: list_A115096904_alt_o] :
( ~ ( member822980838_alt_o @ X_26 @ ( set_Ar868233060_alt_o @ Xs_22 ) )
=> ( ( insert425285465_alt_o @ X_26 @ Xs_22 )
= ( cons_A160405747_alt_o @ X_26 @ Xs_22 ) ) ) ).
thf(fact_779_not__in__set__insert,axiom,
! [X_26: produc1572197287le_alt,Xs_22: list_P1402680776le_alt] :
( ~ ( member285112084le_alt @ X_26 @ ( set_Pr1596096022le_alt @ Xs_22 ) )
=> ( ( insert1248101473le_alt @ X_26 @ Xs_22 )
= ( cons_P1984625479le_alt @ X_26 @ Xs_22 ) ) ) ).
thf(fact_780_partition__P,axiom,
! [P_16: arrow_1389031998le_alt > $o,Xs_21: list_A1402527603le_alt,Yes: list_A1402527603le_alt,No: list_A1402527603le_alt] :
( ( ( partit253767143le_alt @ P_16 @ Xs_21 )
= ( produc1014865963le_alt @ Yes @ No ) )
=> ( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Yes ) )
=> ( P_16 @ X_1 ) )
& ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ No ) )
=> ~ ( P_16 @ X_1 ) ) ) ) ).
thf(fact_781_lexord__partial__trans,axiom,
! [Zs_1: list_A1402527603le_alt,Ys_3: list_A1402527603le_alt,R_12: produc1572197287le_alt > $o,Xs_20: list_A1402527603le_alt] :
( ! [X_1: arrow_1389031998le_alt,Y_10: arrow_1389031998le_alt,Z_4: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_20 ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ Y_10 @ Z_4 ) @ R_12 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_20 @ Ys_3 ) @ ( lexord1871768411le_alt @ R_12 ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Ys_3 @ Zs_1 ) @ ( lexord1871768411le_alt @ R_12 ) )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ Xs_20 @ Zs_1 ) @ ( lexord1871768411le_alt @ R_12 ) ) ) ) ) ).
thf(fact_782_lexord__partial__trans,axiom,
! [Zs_1: list_l1230899348le_alt,Ys_3: list_l1230899348le_alt,R_12: produc2069254453le_alt > $o,Xs_20: list_l1230899348le_alt] :
( ! [X_1: list_A1402527603le_alt,Y_10: list_A1402527603le_alt,Z_4: list_A1402527603le_alt] :
( ( member285423712le_alt @ X_1 @ ( set_li919271010le_alt @ Xs_20 ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Y_10 @ Z_4 ) @ R_12 )
=> ( member735418658le_alt @ ( produc1014865963le_alt @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member104660884le_alt @ ( produc110512663le_alt @ Xs_20 @ Ys_3 ) @ ( lexord1904689174le_alt @ R_12 ) )
=> ( ( member104660884le_alt @ ( produc110512663le_alt @ Ys_3 @ Zs_1 ) @ ( lexord1904689174le_alt @ R_12 ) )
=> ( member104660884le_alt @ ( produc110512663le_alt @ Xs_20 @ Zs_1 ) @ ( lexord1904689174le_alt @ R_12 ) ) ) ) ) ).
thf(fact_783_lexord__partial__trans,axiom,
! [Zs_1: list_nat,Ys_3: list_nat,R_12: product_prod_nat_nat > $o,Xs_20: list_nat] :
( ! [X_1: nat,Y_10: nat,Z_4: nat] :
( ( member_nat @ X_1 @ ( set_nat @ Xs_20 ) )
=> ( ( member232255508at_nat @ ( product_Pair_nat_nat @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member232255508at_nat @ ( product_Pair_nat_nat @ Y_10 @ Z_4 ) @ R_12 )
=> ( member232255508at_nat @ ( product_Pair_nat_nat @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member910422074st_nat @ ( produc1869962435st_nat @ Xs_20 @ Ys_3 ) @ ( lexord_nat @ R_12 ) )
=> ( ( member910422074st_nat @ ( produc1869962435st_nat @ Ys_3 @ Zs_1 ) @ ( lexord_nat @ R_12 ) )
=> ( member910422074st_nat @ ( produc1869962435st_nat @ Xs_20 @ Zs_1 ) @ ( lexord_nat @ R_12 ) ) ) ) ) ).
thf(fact_784_lexord__partial__trans,axiom,
! [Zs_1: list_P1338624854le_alt,Ys_3: list_P1338624854le_alt,R_12: produc2139050425le_alt > $o,Xs_20: list_P1338624854le_alt] :
( ! [X_1: produc2069254453le_alt,Y_10: produc2069254453le_alt,Z_4: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ ( set_Pr1119022372le_alt @ Xs_20 ) )
=> ( ( member1253537702le_alt @ ( produc310818479le_alt @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member1253537702le_alt @ ( produc310818479le_alt @ Y_10 @ Z_4 ) @ R_12 )
=> ( member1253537702le_alt @ ( produc310818479le_alt @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member198626580le_alt @ ( produc535661975le_alt @ Xs_20 @ Ys_3 ) @ ( lexord1680143064le_alt @ R_12 ) )
=> ( ( member198626580le_alt @ ( produc535661975le_alt @ Ys_3 @ Zs_1 ) @ ( lexord1680143064le_alt @ R_12 ) )
=> ( member198626580le_alt @ ( produc535661975le_alt @ Xs_20 @ Zs_1 ) @ ( lexord1680143064le_alt @ R_12 ) ) ) ) ) ).
thf(fact_785_lexord__partial__trans,axiom,
! [Zs_1: list_A1206016470e_indi,Ys_3: list_A1206016470e_indi,R_12: produc1723200057e_indi > $o,Xs_20: list_A1206016470e_indi] :
( ! [X_1: arrow_1196572341e_indi,Y_10: arrow_1196572341e_indi,Z_4: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ ( set_Ar545511716e_indi @ Xs_20 ) )
=> ( ( member1871294246e_indi @ ( produc381140399e_indi @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member1871294246e_indi @ ( produc381140399e_indi @ Y_10 @ Z_4 ) @ R_12 )
=> ( member1871294246e_indi @ ( produc381140399e_indi @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member1903641876e_indi @ ( produc1625955351e_indi @ Xs_20 @ Ys_3 ) @ ( lexord1428655320e_indi @ R_12 ) )
=> ( ( member1903641876e_indi @ ( produc1625955351e_indi @ Ys_3 @ Zs_1 ) @ ( lexord1428655320e_indi @ R_12 ) )
=> ( member1903641876e_indi @ ( produc1625955351e_indi @ Xs_20 @ Zs_1 ) @ ( lexord1428655320e_indi @ R_12 ) ) ) ) ) ).
thf(fact_786_lexord__partial__trans,axiom,
! [Zs_1: list_o,Ys_3: list_o,R_12: product_prod_o_o > $o,Xs_20: list_o] :
( ! [X_1: $o,Y_10: $o,Z_4: $o] :
( ( member_o @ X_1 @ ( set_o @ Xs_20 ) )
=> ( ( member1392690260od_o_o @ ( product_Pair_o_o @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member1392690260od_o_o @ ( product_Pair_o_o @ Y_10 @ Z_4 ) @ R_12 )
=> ( member1392690260od_o_o @ ( product_Pair_o_o @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member806300420list_o @ ( produc1835210381list_o @ Xs_20 @ Ys_3 ) @ ( lexord_o @ R_12 ) )
=> ( ( member806300420list_o @ ( produc1835210381list_o @ Ys_3 @ Zs_1 ) @ ( lexord_o @ R_12 ) )
=> ( member806300420list_o @ ( produc1835210381list_o @ Xs_20 @ Zs_1 ) @ ( lexord_o @ R_12 ) ) ) ) ) ).
thf(fact_787_lexord__partial__trans,axiom,
! [Zs_1: list_A869418500_alt_o,Ys_3: list_A869418500_alt_o,R_12: produc1182572821_alt_o > $o,Xs_20: list_A869418500_alt_o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Y_10: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Z_4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ ( set_Ar17109714_alt_o @ Xs_20 ) )
=> ( ( member599543554_alt_o @ ( produc1729571083_alt_o @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member599543554_alt_o @ ( produc1729571083_alt_o @ Y_10 @ Z_4 ) @ R_12 )
=> ( member599543554_alt_o @ ( produc1729571083_alt_o @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member995889556_alt_o @ ( produc1459025175_alt_o @ Xs_20 @ Ys_3 ) @ ( lexord1912481926_alt_o @ R_12 ) )
=> ( ( member995889556_alt_o @ ( produc1459025175_alt_o @ Ys_3 @ Zs_1 ) @ ( lexord1912481926_alt_o @ R_12 ) )
=> ( member995889556_alt_o @ ( produc1459025175_alt_o @ Xs_20 @ Zs_1 ) @ ( lexord1912481926_alt_o @ R_12 ) ) ) ) ) ).
thf(fact_788_lexord__partial__trans,axiom,
! [Zs_1: list_P811970973_alt_o,Ys_3: list_P811970973_alt_o,R_12: produc563823143_alt_o > $o,Xs_20: list_P811970973_alt_o] :
( ! [X_1: produc1572197287le_alt > $o,Y_10: produc1572197287le_alt > $o,Z_4: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ ( set_Pr1457060537_alt_o @ Xs_20 ) )
=> ( ( member1958570644_alt_o @ ( produc1739106583_alt_o @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member1958570644_alt_o @ ( produc1739106583_alt_o @ Y_10 @ Z_4 ) @ R_12 )
=> ( member1958570644_alt_o @ ( produc1739106583_alt_o @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member1189996790_alt_o @ ( produc1859089279_alt_o @ Xs_20 @ Ys_3 ) @ ( lexord1707544581_alt_o @ R_12 ) )
=> ( ( member1189996790_alt_o @ ( produc1859089279_alt_o @ Ys_3 @ Zs_1 ) @ ( lexord1707544581_alt_o @ R_12 ) )
=> ( member1189996790_alt_o @ ( produc1859089279_alt_o @ Xs_20 @ Zs_1 ) @ ( lexord1707544581_alt_o @ R_12 ) ) ) ) ) ).
thf(fact_789_lexord__partial__trans,axiom,
! [Zs_1: list_A115096904_alt_o,Ys_3: list_A115096904_alt_o,R_12: produc346017511_alt_o > $o,Xs_20: list_A115096904_alt_o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o,Y_10: arrow_1196572341e_indi > produc1572197287le_alt > $o,Z_4: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ ( set_Ar868233060_alt_o @ Xs_20 ) )
=> ( ( member135324756_alt_o @ ( produc843458519_alt_o @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member135324756_alt_o @ ( produc843458519_alt_o @ Y_10 @ Z_4 ) @ R_12 )
=> ( member135324756_alt_o @ ( produc843458519_alt_o @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member405332940_alt_o @ ( produc1670706773_alt_o @ Xs_20 @ Ys_3 ) @ ( lexord1942121136_alt_o @ R_12 ) )
=> ( ( member405332940_alt_o @ ( produc1670706773_alt_o @ Ys_3 @ Zs_1 ) @ ( lexord1942121136_alt_o @ R_12 ) )
=> ( member405332940_alt_o @ ( produc1670706773_alt_o @ Xs_20 @ Zs_1 ) @ ( lexord1942121136_alt_o @ R_12 ) ) ) ) ) ).
thf(fact_790_lexord__partial__trans,axiom,
! [Zs_1: list_P1402680776le_alt,Ys_3: list_P1402680776le_alt,R_12: produc307320605le_alt > $o,Xs_20: list_P1402680776le_alt] :
( ! [X_1: produc1572197287le_alt,Y_10: produc1572197287le_alt,Z_4: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ ( set_Pr1596096022le_alt @ Xs_20 ) )
=> ( ( member894661642le_alt @ ( produc2131135379le_alt @ X_1 @ Y_10 ) @ R_12 )
=> ( ( member894661642le_alt @ ( produc2131135379le_alt @ Y_10 @ Z_4 ) @ R_12 )
=> ( member894661642le_alt @ ( produc2131135379le_alt @ X_1 @ Z_4 ) @ R_12 ) ) ) )
=> ( ( member778872212le_alt @ ( produc2092721559le_alt @ Xs_20 @ Ys_3 ) @ ( lexord572715466le_alt @ R_12 ) )
=> ( ( member778872212le_alt @ ( produc2092721559le_alt @ Ys_3 @ Zs_1 ) @ ( lexord572715466le_alt @ R_12 ) )
=> ( member778872212le_alt @ ( produc2092721559le_alt @ Xs_20 @ Zs_1 ) @ ( lexord572715466le_alt @ R_12 ) ) ) ) ) ).
thf(fact_791_dropWhile__append2,axiom,
! [Ys_2: list_nat,P_15: nat > $o,Xs_19: list_nat] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ ( set_nat @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWhile_nat @ P_15 @ ( append_nat @ Xs_19 @ Ys_2 ) )
= ( dropWhile_nat @ P_15 @ Ys_2 ) ) ) ).
thf(fact_792_dropWhile__append2,axiom,
! [Ys_2: list_A1402527603le_alt,P_15: arrow_1389031998le_alt > $o,Xs_19: list_A1402527603le_alt] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWh82971279le_alt @ P_15 @ ( append1092755459le_alt @ Xs_19 @ Ys_2 ) )
= ( dropWh82971279le_alt @ P_15 @ Ys_2 ) ) ) ).
thf(fact_793_dropWhile__append2,axiom,
! [Ys_2: list_P1338624854le_alt,P_15: produc2069254453le_alt > $o,Xs_19: list_P1338624854le_alt] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ ( set_Pr1119022372le_alt @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWh1319308964le_alt @ P_15 @ ( append1130570800le_alt @ Xs_19 @ Ys_2 ) )
= ( dropWh1319308964le_alt @ P_15 @ Ys_2 ) ) ) ).
thf(fact_794_dropWhile__append2,axiom,
! [Ys_2: list_A1206016470e_indi,P_15: arrow_1196572341e_indi > $o,Xs_19: list_A1206016470e_indi] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ ( set_Ar545511716e_indi @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWh927087268e_indi @ P_15 @ ( append478904880e_indi @ Xs_19 @ Ys_2 ) )
= ( dropWh927087268e_indi @ P_15 @ Ys_2 ) ) ) ).
thf(fact_795_dropWhile__append2,axiom,
! [Ys_2: list_o,P_15: $o > $o,Xs_19: list_o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ ( set_o @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWhile_o @ P_15 @ ( append_o @ Xs_19 @ Ys_2 ) )
= ( dropWhile_o @ P_15 @ Ys_2 ) ) ) ).
thf(fact_796_dropWhile__append2,axiom,
! [Ys_2: list_A869418500_alt_o,P_15: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Xs_19: list_A869418500_alt_o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ ( set_Ar17109714_alt_o @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWh1391670354_alt_o @ P_15 @ ( append1134377438_alt_o @ Xs_19 @ Ys_2 ) )
= ( dropWh1391670354_alt_o @ P_15 @ Ys_2 ) ) ) ).
thf(fact_797_dropWhile__append2,axiom,
! [Ys_2: list_P811970973_alt_o,P_15: ( produc1572197287le_alt > $o ) > $o,Xs_19: list_P811970973_alt_o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ ( set_Pr1457060537_alt_o @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWh1914665273_alt_o @ P_15 @ ( append1477507245_alt_o @ Xs_19 @ Ys_2 ) )
= ( dropWh1914665273_alt_o @ P_15 @ Ys_2 ) ) ) ).
thf(fact_798_dropWhile__append2,axiom,
! [Ys_2: list_A115096904_alt_o,P_15: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Xs_19: list_A115096904_alt_o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ ( set_Ar868233060_alt_o @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWh370535908_alt_o @ P_15 @ ( append592815960_alt_o @ Xs_19 @ Ys_2 ) )
= ( dropWh370535908_alt_o @ P_15 @ Ys_2 ) ) ) ).
thf(fact_799_dropWhile__append2,axiom,
! [Ys_2: list_P1402680776le_alt,P_15: produc1572197287le_alt > $o,Xs_19: list_P1402680776le_alt] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ ( set_Pr1596096022le_alt @ Xs_19 ) )
=> ( P_15 @ X_1 ) )
=> ( ( dropWh751361942le_alt @ P_15 @ ( append1300326178le_alt @ Xs_19 @ Ys_2 ) )
= ( dropWh751361942le_alt @ P_15 @ Ys_2 ) ) ) ).
thf(fact_800_takeWhile__append2,axiom,
! [Ys_1: list_nat,P_14: nat > $o,Xs_18: list_nat] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ ( set_nat @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWhile_nat @ P_14 @ ( append_nat @ Xs_18 @ Ys_1 ) )
= ( append_nat @ Xs_18 @ ( takeWhile_nat @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_801_takeWhile__append2,axiom,
! [Ys_1: list_A1402527603le_alt,P_14: arrow_1389031998le_alt > $o,Xs_18: list_A1402527603le_alt] :
( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWh462480871le_alt @ P_14 @ ( append1092755459le_alt @ Xs_18 @ Ys_1 ) )
= ( append1092755459le_alt @ Xs_18 @ ( takeWh462480871le_alt @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_802_takeWhile__append2,axiom,
! [Ys_1: list_P1338624854le_alt,P_14: produc2069254453le_alt > $o,Xs_18: list_P1338624854le_alt] :
( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ ( set_Pr1119022372le_alt @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWh131124556le_alt @ P_14 @ ( append1130570800le_alt @ Xs_18 @ Ys_1 ) )
= ( append1130570800le_alt @ Xs_18 @ ( takeWh131124556le_alt @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_803_takeWhile__append2,axiom,
! [Ys_1: list_A1206016470e_indi,P_14: arrow_1196572341e_indi > $o,Xs_18: list_A1206016470e_indi] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ ( set_Ar545511716e_indi @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWh598881612e_indi @ P_14 @ ( append478904880e_indi @ Xs_18 @ Ys_1 ) )
= ( append478904880e_indi @ Xs_18 @ ( takeWh598881612e_indi @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_804_takeWhile__append2,axiom,
! [Ys_1: list_o,P_14: $o > $o,Xs_18: list_o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ ( set_o @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWhile_o @ P_14 @ ( append_o @ Xs_18 @ Ys_1 ) )
= ( append_o @ Xs_18 @ ( takeWhile_o @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_805_takeWhile__append2,axiom,
! [Ys_1: list_A869418500_alt_o,P_14: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Xs_18: list_A869418500_alt_o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ ( set_Ar17109714_alt_o @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWh1686115066_alt_o @ P_14 @ ( append1134377438_alt_o @ Xs_18 @ Ys_1 ) )
= ( append1134377438_alt_o @ Xs_18 @ ( takeWh1686115066_alt_o @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_806_takeWhile__append2,axiom,
! [Ys_1: list_P811970973_alt_o,P_14: ( produc1572197287le_alt > $o ) > $o,Xs_18: list_P811970973_alt_o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ ( set_Pr1457060537_alt_o @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWh432906385_alt_o @ P_14 @ ( append1477507245_alt_o @ Xs_18 @ Ys_1 ) )
= ( append1477507245_alt_o @ Xs_18 @ ( takeWh432906385_alt_o @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_807_takeWhile__append2,axiom,
! [Ys_1: list_A115096904_alt_o,P_14: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Xs_18: list_A115096904_alt_o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ ( set_Ar868233060_alt_o @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWh2122498364_alt_o @ P_14 @ ( append592815960_alt_o @ Xs_18 @ Ys_1 ) )
= ( append592815960_alt_o @ Xs_18 @ ( takeWh2122498364_alt_o @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_808_takeWhile__append2,axiom,
! [Ys_1: list_P1402680776le_alt,P_14: produc1572197287le_alt > $o,Xs_18: list_P1402680776le_alt] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ ( set_Pr1596096022le_alt @ Xs_18 ) )
=> ( P_14 @ X_1 ) )
=> ( ( takeWh373185086le_alt @ P_14 @ ( append1300326178le_alt @ Xs_18 @ Ys_1 ) )
= ( append1300326178le_alt @ Xs_18 @ ( takeWh373185086le_alt @ P_14 @ Ys_1 ) ) ) ) ).
thf(fact_809_split__list__propE,axiom,
! [P_13: arrow_1389031998le_alt > $o,Xs_17: list_A1402527603le_alt] :
( ? [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_17 ) )
& ( P_13 @ X_1 ) )
=> ~ ! [Ys: list_A1402527603le_alt,X_1: arrow_1389031998le_alt] :
( ? [Zs: list_A1402527603le_alt] :
( Xs_17
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_1 @ Zs ) ) )
=> ~ ( P_13 @ X_1 ) ) ) ).
thf(fact_810_in__set__conv__decomp__first,axiom,
! [X_25: nat,Xs_16: list_nat] :
( ( member_nat @ X_25 @ ( set_nat @ Xs_16 ) )
<=> ? [Ys: list_nat,Zs: list_nat] :
( ( Xs_16
= ( append_nat @ Ys @ ( cons_nat @ X_25 @ Zs ) ) )
& ~ ( member_nat @ X_25 @ ( set_nat @ Ys ) ) ) ) ).
thf(fact_811_in__set__conv__decomp__first,axiom,
! [X_25: arrow_1389031998le_alt,Xs_16: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_25 @ ( set_Ar1491127311le_alt @ Xs_16 ) )
<=> ? [Ys: list_A1402527603le_alt,Zs: list_A1402527603le_alt] :
( ( Xs_16
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_25 @ Zs ) ) )
& ~ ( member998036369le_alt @ X_25 @ ( set_Ar1491127311le_alt @ Ys ) ) ) ) ).
thf(fact_812_in__set__conv__decomp__first,axiom,
! [X_25: produc2069254453le_alt,Xs_16: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_25 @ ( set_Pr1119022372le_alt @ Xs_16 ) )
<=> ? [Ys: list_P1338624854le_alt,Zs: list_P1338624854le_alt] :
( ( Xs_16
= ( append1130570800le_alt @ Ys @ ( cons_P607717589le_alt @ X_25 @ Zs ) ) )
& ~ ( member735418658le_alt @ X_25 @ ( set_Pr1119022372le_alt @ Ys ) ) ) ) ).
thf(fact_813_in__set__conv__decomp__first,axiom,
! [X_25: arrow_1196572341e_indi,Xs_16: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_25 @ ( set_Ar545511716e_indi @ Xs_16 ) )
<=> ? [Ys: list_A1206016470e_indi,Zs: list_A1206016470e_indi] :
( ( Xs_16
= ( append478904880e_indi @ Ys @ ( cons_A430007893e_indi @ X_25 @ Zs ) ) )
& ~ ( member1818997282e_indi @ X_25 @ ( set_Ar545511716e_indi @ Ys ) ) ) ) ).
thf(fact_814_in__set__conv__decomp__first,axiom,
! [X_25: $o,Xs_16: list_o] :
( ( member_o @ X_25 @ ( set_o @ Xs_16 ) )
<=> ? [Ys: list_o,Zs: list_o] :
( ( Xs_16
= ( append_o @ Ys @ ( cons_o @ X_25 @ Zs ) ) )
& ~ ( member_o @ X_25 @ ( set_o @ Ys ) ) ) ) ).
thf(fact_815_in__set__conv__decomp__first,axiom,
! [X_25: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_16: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_25 @ ( set_Ar17109714_alt_o @ Xs_16 ) )
<=> ? [Ys: list_A869418500_alt_o,Zs: list_A869418500_alt_o] :
( ( Xs_16
= ( append1134377438_alt_o @ Ys @ ( cons_A1087586947_alt_o @ X_25 @ Zs ) ) )
& ~ ( member1425217232_alt_o @ X_25 @ ( set_Ar17109714_alt_o @ Ys ) ) ) ) ).
thf(fact_816_in__set__conv__decomp__first,axiom,
! [X_25: produc1572197287le_alt > $o,Xs_16: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_25 @ ( set_Pr1457060537_alt_o @ Xs_16 ) )
<=> ? [Ys: list_P811970973_alt_o,Zs: list_P811970973_alt_o] :
( ( Xs_16
= ( append1477507245_alt_o @ Ys @ ( cons_P2104327368_alt_o @ X_25 @ Zs ) ) )
& ~ ( member1241905979_alt_o @ X_25 @ ( set_Pr1457060537_alt_o @ Ys ) ) ) ) ).
thf(fact_817_in__set__conv__decomp__first,axiom,
! [X_25: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_16: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_25 @ ( set_Ar868233060_alt_o @ Xs_16 ) )
<=> ? [Ys: list_A115096904_alt_o,Zs: list_A115096904_alt_o] :
( ( Xs_16
= ( append592815960_alt_o @ Ys @ ( cons_A160405747_alt_o @ X_25 @ Zs ) ) )
& ~ ( member822980838_alt_o @ X_25 @ ( set_Ar868233060_alt_o @ Ys ) ) ) ) ).
thf(fact_818_in__set__conv__decomp__first,axiom,
! [X_25: produc1572197287le_alt,Xs_16: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_25 @ ( set_Pr1596096022le_alt @ Xs_16 ) )
<=> ? [Ys: list_P1402680776le_alt,Zs: list_P1402680776le_alt] :
( ( Xs_16
= ( append1300326178le_alt @ Ys @ ( cons_P1984625479le_alt @ X_25 @ Zs ) ) )
& ~ ( member285112084le_alt @ X_25 @ ( set_Pr1596096022le_alt @ Ys ) ) ) ) ).
thf(fact_819_in__set__conv__decomp__last,axiom,
! [X_24: nat,Xs_15: list_nat] :
( ( member_nat @ X_24 @ ( set_nat @ Xs_15 ) )
<=> ? [Ys: list_nat,Zs: list_nat] :
( ( Xs_15
= ( append_nat @ Ys @ ( cons_nat @ X_24 @ Zs ) ) )
& ~ ( member_nat @ X_24 @ ( set_nat @ Zs ) ) ) ) ).
thf(fact_820_in__set__conv__decomp__last,axiom,
! [X_24: arrow_1389031998le_alt,Xs_15: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_24 @ ( set_Ar1491127311le_alt @ Xs_15 ) )
<=> ? [Ys: list_A1402527603le_alt,Zs: list_A1402527603le_alt] :
( ( Xs_15
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_24 @ Zs ) ) )
& ~ ( member998036369le_alt @ X_24 @ ( set_Ar1491127311le_alt @ Zs ) ) ) ) ).
thf(fact_821_in__set__conv__decomp__last,axiom,
! [X_24: produc2069254453le_alt,Xs_15: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_24 @ ( set_Pr1119022372le_alt @ Xs_15 ) )
<=> ? [Ys: list_P1338624854le_alt,Zs: list_P1338624854le_alt] :
( ( Xs_15
= ( append1130570800le_alt @ Ys @ ( cons_P607717589le_alt @ X_24 @ Zs ) ) )
& ~ ( member735418658le_alt @ X_24 @ ( set_Pr1119022372le_alt @ Zs ) ) ) ) ).
thf(fact_822_in__set__conv__decomp__last,axiom,
! [X_24: arrow_1196572341e_indi,Xs_15: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_24 @ ( set_Ar545511716e_indi @ Xs_15 ) )
<=> ? [Ys: list_A1206016470e_indi,Zs: list_A1206016470e_indi] :
( ( Xs_15
= ( append478904880e_indi @ Ys @ ( cons_A430007893e_indi @ X_24 @ Zs ) ) )
& ~ ( member1818997282e_indi @ X_24 @ ( set_Ar545511716e_indi @ Zs ) ) ) ) ).
thf(fact_823_in__set__conv__decomp__last,axiom,
! [X_24: $o,Xs_15: list_o] :
( ( member_o @ X_24 @ ( set_o @ Xs_15 ) )
<=> ? [Ys: list_o,Zs: list_o] :
( ( Xs_15
= ( append_o @ Ys @ ( cons_o @ X_24 @ Zs ) ) )
& ~ ( member_o @ X_24 @ ( set_o @ Zs ) ) ) ) ).
thf(fact_824_in__set__conv__decomp__last,axiom,
! [X_24: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_15: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_24 @ ( set_Ar17109714_alt_o @ Xs_15 ) )
<=> ? [Ys: list_A869418500_alt_o,Zs: list_A869418500_alt_o] :
( ( Xs_15
= ( append1134377438_alt_o @ Ys @ ( cons_A1087586947_alt_o @ X_24 @ Zs ) ) )
& ~ ( member1425217232_alt_o @ X_24 @ ( set_Ar17109714_alt_o @ Zs ) ) ) ) ).
thf(fact_825_in__set__conv__decomp__last,axiom,
! [X_24: produc1572197287le_alt > $o,Xs_15: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_24 @ ( set_Pr1457060537_alt_o @ Xs_15 ) )
<=> ? [Ys: list_P811970973_alt_o,Zs: list_P811970973_alt_o] :
( ( Xs_15
= ( append1477507245_alt_o @ Ys @ ( cons_P2104327368_alt_o @ X_24 @ Zs ) ) )
& ~ ( member1241905979_alt_o @ X_24 @ ( set_Pr1457060537_alt_o @ Zs ) ) ) ) ).
thf(fact_826_in__set__conv__decomp__last,axiom,
! [X_24: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_15: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_24 @ ( set_Ar868233060_alt_o @ Xs_15 ) )
<=> ? [Ys: list_A115096904_alt_o,Zs: list_A115096904_alt_o] :
( ( Xs_15
= ( append592815960_alt_o @ Ys @ ( cons_A160405747_alt_o @ X_24 @ Zs ) ) )
& ~ ( member822980838_alt_o @ X_24 @ ( set_Ar868233060_alt_o @ Zs ) ) ) ) ).
thf(fact_827_in__set__conv__decomp__last,axiom,
! [X_24: produc1572197287le_alt,Xs_15: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_24 @ ( set_Pr1596096022le_alt @ Xs_15 ) )
<=> ? [Ys: list_P1402680776le_alt,Zs: list_P1402680776le_alt] :
( ( Xs_15
= ( append1300326178le_alt @ Ys @ ( cons_P1984625479le_alt @ X_24 @ Zs ) ) )
& ~ ( member285112084le_alt @ X_24 @ ( set_Pr1596096022le_alt @ Zs ) ) ) ) ).
thf(fact_828_in__set__conv__decomp,axiom,
! [X_23: nat,Xs_14: list_nat] :
( ( member_nat @ X_23 @ ( set_nat @ Xs_14 ) )
<=> ? [Ys: list_nat,Zs: list_nat] :
( Xs_14
= ( append_nat @ Ys @ ( cons_nat @ X_23 @ Zs ) ) ) ) ).
thf(fact_829_in__set__conv__decomp,axiom,
! [X_23: arrow_1389031998le_alt,Xs_14: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_23 @ ( set_Ar1491127311le_alt @ Xs_14 ) )
<=> ? [Ys: list_A1402527603le_alt,Zs: list_A1402527603le_alt] :
( Xs_14
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_23 @ Zs ) ) ) ) ).
thf(fact_830_in__set__conv__decomp,axiom,
! [X_23: produc2069254453le_alt,Xs_14: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_23 @ ( set_Pr1119022372le_alt @ Xs_14 ) )
<=> ? [Ys: list_P1338624854le_alt,Zs: list_P1338624854le_alt] :
( Xs_14
= ( append1130570800le_alt @ Ys @ ( cons_P607717589le_alt @ X_23 @ Zs ) ) ) ) ).
thf(fact_831_in__set__conv__decomp,axiom,
! [X_23: arrow_1196572341e_indi,Xs_14: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_23 @ ( set_Ar545511716e_indi @ Xs_14 ) )
<=> ? [Ys: list_A1206016470e_indi,Zs: list_A1206016470e_indi] :
( Xs_14
= ( append478904880e_indi @ Ys @ ( cons_A430007893e_indi @ X_23 @ Zs ) ) ) ) ).
thf(fact_832_in__set__conv__decomp,axiom,
! [X_23: $o,Xs_14: list_o] :
( ( member_o @ X_23 @ ( set_o @ Xs_14 ) )
<=> ? [Ys: list_o,Zs: list_o] :
( Xs_14
= ( append_o @ Ys @ ( cons_o @ X_23 @ Zs ) ) ) ) ).
thf(fact_833_in__set__conv__decomp,axiom,
! [X_23: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_14: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_23 @ ( set_Ar17109714_alt_o @ Xs_14 ) )
<=> ? [Ys: list_A869418500_alt_o,Zs: list_A869418500_alt_o] :
( Xs_14
= ( append1134377438_alt_o @ Ys @ ( cons_A1087586947_alt_o @ X_23 @ Zs ) ) ) ) ).
thf(fact_834_in__set__conv__decomp,axiom,
! [X_23: produc1572197287le_alt > $o,Xs_14: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_23 @ ( set_Pr1457060537_alt_o @ Xs_14 ) )
<=> ? [Ys: list_P811970973_alt_o,Zs: list_P811970973_alt_o] :
( Xs_14
= ( append1477507245_alt_o @ Ys @ ( cons_P2104327368_alt_o @ X_23 @ Zs ) ) ) ) ).
thf(fact_835_in__set__conv__decomp,axiom,
! [X_23: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_14: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_23 @ ( set_Ar868233060_alt_o @ Xs_14 ) )
<=> ? [Ys: list_A115096904_alt_o,Zs: list_A115096904_alt_o] :
( Xs_14
= ( append592815960_alt_o @ Ys @ ( cons_A160405747_alt_o @ X_23 @ Zs ) ) ) ) ).
thf(fact_836_in__set__conv__decomp,axiom,
! [X_23: produc1572197287le_alt,Xs_14: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_23 @ ( set_Pr1596096022le_alt @ Xs_14 ) )
<=> ? [Ys: list_P1402680776le_alt,Zs: list_P1402680776le_alt] :
( Xs_14
= ( append1300326178le_alt @ Ys @ ( cons_P1984625479le_alt @ X_23 @ Zs ) ) ) ) ).
thf(fact_837_dropWhile__cong,axiom,
! [Q_1: nat > $o,P_12: nat > $o,L_2: list_nat,K_3: list_nat] :
( ( L_2 = K_3 )
=> ( ! [X_1: nat] :
( ( member_nat @ X_1 @ ( set_nat @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWhile_nat @ P_12 @ L_2 )
= ( dropWhile_nat @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_838_dropWhile__cong,axiom,
! [Q_1: arrow_1389031998le_alt > $o,P_12: arrow_1389031998le_alt > $o,L_2: list_A1402527603le_alt,K_3: list_A1402527603le_alt] :
( ( L_2 = K_3 )
=> ( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWh82971279le_alt @ P_12 @ L_2 )
= ( dropWh82971279le_alt @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_839_dropWhile__cong,axiom,
! [Q_1: produc2069254453le_alt > $o,P_12: produc2069254453le_alt > $o,L_2: list_P1338624854le_alt,K_3: list_P1338624854le_alt] :
( ( L_2 = K_3 )
=> ( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ ( set_Pr1119022372le_alt @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWh1319308964le_alt @ P_12 @ L_2 )
= ( dropWh1319308964le_alt @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_840_dropWhile__cong,axiom,
! [Q_1: arrow_1196572341e_indi > $o,P_12: arrow_1196572341e_indi > $o,L_2: list_A1206016470e_indi,K_3: list_A1206016470e_indi] :
( ( L_2 = K_3 )
=> ( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ ( set_Ar545511716e_indi @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWh927087268e_indi @ P_12 @ L_2 )
= ( dropWh927087268e_indi @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_841_dropWhile__cong,axiom,
! [Q_1: $o > $o,P_12: $o > $o,L_2: list_o,K_3: list_o] :
( ( L_2 = K_3 )
=> ( ! [X_1: $o] :
( ( member_o @ X_1 @ ( set_o @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWhile_o @ P_12 @ L_2 )
= ( dropWhile_o @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_842_dropWhile__cong,axiom,
! [Q_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,P_12: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,L_2: list_A869418500_alt_o,K_3: list_A869418500_alt_o] :
( ( L_2 = K_3 )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ ( set_Ar17109714_alt_o @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWh1391670354_alt_o @ P_12 @ L_2 )
= ( dropWh1391670354_alt_o @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_843_dropWhile__cong,axiom,
! [Q_1: ( produc1572197287le_alt > $o ) > $o,P_12: ( produc1572197287le_alt > $o ) > $o,L_2: list_P811970973_alt_o,K_3: list_P811970973_alt_o] :
( ( L_2 = K_3 )
=> ( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ ( set_Pr1457060537_alt_o @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWh1914665273_alt_o @ P_12 @ L_2 )
= ( dropWh1914665273_alt_o @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_844_dropWhile__cong,axiom,
! [Q_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,P_12: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,L_2: list_A115096904_alt_o,K_3: list_A115096904_alt_o] :
( ( L_2 = K_3 )
=> ( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ ( set_Ar868233060_alt_o @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWh370535908_alt_o @ P_12 @ L_2 )
= ( dropWh370535908_alt_o @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_845_dropWhile__cong,axiom,
! [Q_1: produc1572197287le_alt > $o,P_12: produc1572197287le_alt > $o,L_2: list_P1402680776le_alt,K_3: list_P1402680776le_alt] :
( ( L_2 = K_3 )
=> ( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ ( set_Pr1596096022le_alt @ L_2 ) )
=> ( ( P_12 @ X_1 )
<=> ( Q_1 @ X_1 ) ) )
=> ( ( dropWh751361942le_alt @ P_12 @ L_2 )
= ( dropWh751361942le_alt @ Q_1 @ K_3 ) ) ) ) ).
thf(fact_846_takeWhile__cong,axiom,
! [Q: nat > $o,P_11: nat > $o,L_1: list_nat,K_2: list_nat] :
( ( L_1 = K_2 )
=> ( ! [X_1: nat] :
( ( member_nat @ X_1 @ ( set_nat @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWhile_nat @ P_11 @ L_1 )
= ( takeWhile_nat @ Q @ K_2 ) ) ) ) ).
thf(fact_847_takeWhile__cong,axiom,
! [Q: arrow_1389031998le_alt > $o,P_11: arrow_1389031998le_alt > $o,L_1: list_A1402527603le_alt,K_2: list_A1402527603le_alt] :
( ( L_1 = K_2 )
=> ( ! [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWh462480871le_alt @ P_11 @ L_1 )
= ( takeWh462480871le_alt @ Q @ K_2 ) ) ) ) ).
thf(fact_848_takeWhile__cong,axiom,
! [Q: produc2069254453le_alt > $o,P_11: produc2069254453le_alt > $o,L_1: list_P1338624854le_alt,K_2: list_P1338624854le_alt] :
( ( L_1 = K_2 )
=> ( ! [X_1: produc2069254453le_alt] :
( ( member735418658le_alt @ X_1 @ ( set_Pr1119022372le_alt @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWh131124556le_alt @ P_11 @ L_1 )
= ( takeWh131124556le_alt @ Q @ K_2 ) ) ) ) ).
thf(fact_849_takeWhile__cong,axiom,
! [Q: arrow_1196572341e_indi > $o,P_11: arrow_1196572341e_indi > $o,L_1: list_A1206016470e_indi,K_2: list_A1206016470e_indi] :
( ( L_1 = K_2 )
=> ( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ ( set_Ar545511716e_indi @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWh598881612e_indi @ P_11 @ L_1 )
= ( takeWh598881612e_indi @ Q @ K_2 ) ) ) ) ).
thf(fact_850_takeWhile__cong,axiom,
! [Q: $o > $o,P_11: $o > $o,L_1: list_o,K_2: list_o] :
( ( L_1 = K_2 )
=> ( ! [X_1: $o] :
( ( member_o @ X_1 @ ( set_o @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWhile_o @ P_11 @ L_1 )
= ( takeWhile_o @ Q @ K_2 ) ) ) ) ).
thf(fact_851_takeWhile__cong,axiom,
! [Q: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,P_11: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,L_1: list_A869418500_alt_o,K_2: list_A869418500_alt_o] :
( ( L_1 = K_2 )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ X_1 @ ( set_Ar17109714_alt_o @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWh1686115066_alt_o @ P_11 @ L_1 )
= ( takeWh1686115066_alt_o @ Q @ K_2 ) ) ) ) ).
thf(fact_852_takeWhile__cong,axiom,
! [Q: ( produc1572197287le_alt > $o ) > $o,P_11: ( produc1572197287le_alt > $o ) > $o,L_1: list_P811970973_alt_o,K_2: list_P811970973_alt_o] :
( ( L_1 = K_2 )
=> ( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ ( set_Pr1457060537_alt_o @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWh432906385_alt_o @ P_11 @ L_1 )
= ( takeWh432906385_alt_o @ Q @ K_2 ) ) ) ) ).
thf(fact_853_takeWhile__cong,axiom,
! [Q: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,P_11: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,L_1: list_A115096904_alt_o,K_2: list_A115096904_alt_o] :
( ( L_1 = K_2 )
=> ( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ ( set_Ar868233060_alt_o @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWh2122498364_alt_o @ P_11 @ L_1 )
= ( takeWh2122498364_alt_o @ Q @ K_2 ) ) ) ) ).
thf(fact_854_takeWhile__cong,axiom,
! [Q: produc1572197287le_alt > $o,P_11: produc1572197287le_alt > $o,L_1: list_P1402680776le_alt,K_2: list_P1402680776le_alt] :
( ( L_1 = K_2 )
=> ( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ ( set_Pr1596096022le_alt @ L_1 ) )
=> ( ( P_11 @ X_1 )
<=> ( Q @ X_1 ) ) )
=> ( ( takeWh373185086le_alt @ P_11 @ L_1 )
= ( takeWh373185086le_alt @ Q @ K_2 ) ) ) ) ).
thf(fact_855_rtrancl__induct,axiom,
! [P_10: list_A1402527603le_alt > $o,A_17: list_A1402527603le_alt,B_13: list_A1402527603le_alt,R_11: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_17 @ B_13 ) @ ( transi264395782le_alt @ R_11 ) )
=> ( ( P_10 @ A_17 )
=> ( ! [Y_10: list_A1402527603le_alt,Z_4: list_A1402527603le_alt] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_17 @ Y_10 ) @ ( transi264395782le_alt @ R_11 ) )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Y_10 @ Z_4 ) @ R_11 )
=> ( ( P_10 @ Y_10 )
=> ( P_10 @ Z_4 ) ) ) )
=> ( P_10 @ B_13 ) ) ) ) ).
thf(fact_856_rtrancl__induct,axiom,
! [P_10: arrow_1389031998le_alt > $o,A_17: arrow_1389031998le_alt,B_13: arrow_1389031998le_alt,R_11: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_17 @ B_13 ) @ ( transi1182735211le_alt @ R_11 ) )
=> ( ( P_10 @ A_17 )
=> ( ! [Y_10: arrow_1389031998le_alt,Z_4: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_17 @ Y_10 ) @ ( transi1182735211le_alt @ R_11 ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ Y_10 @ Z_4 ) @ R_11 )
=> ( ( P_10 @ Y_10 )
=> ( P_10 @ Z_4 ) ) ) )
=> ( P_10 @ B_13 ) ) ) ) ).
thf(fact_857_converse__rtrancl__induct,axiom,
! [P_9: list_A1402527603le_alt > $o,A_16: list_A1402527603le_alt,B_12: list_A1402527603le_alt,R_10: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_16 @ B_12 ) @ ( transi264395782le_alt @ R_10 ) )
=> ( ( P_9 @ B_12 )
=> ( ! [Y_10: list_A1402527603le_alt,Z_4: list_A1402527603le_alt] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ Y_10 @ Z_4 ) @ R_10 )
=> ( ( member735418658le_alt @ ( produc1014865963le_alt @ Z_4 @ B_12 ) @ ( transi264395782le_alt @ R_10 ) )
=> ( ( P_9 @ Z_4 )
=> ( P_9 @ Y_10 ) ) ) )
=> ( P_9 @ A_16 ) ) ) ) ).
thf(fact_858_converse__rtrancl__induct,axiom,
! [P_9: arrow_1389031998le_alt > $o,A_16: arrow_1389031998le_alt,B_12: arrow_1389031998le_alt,R_10: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_16 @ B_12 ) @ ( transi1182735211le_alt @ R_10 ) )
=> ( ( P_9 @ B_12 )
=> ( ! [Y_10: arrow_1389031998le_alt,Z_4: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ Y_10 @ Z_4 ) @ R_10 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ Z_4 @ B_12 ) @ ( transi1182735211le_alt @ R_10 ) )
=> ( ( P_9 @ Z_4 )
=> ( P_9 @ Y_10 ) ) ) )
=> ( P_9 @ A_16 ) ) ) ) ).
thf(fact_859_converse__rtranclE,axiom,
! [X_22: list_A1402527603le_alt,Z_3: list_A1402527603le_alt,R_9: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_22 @ Z_3 ) @ ( transi264395782le_alt @ R_9 ) )
=> ( ( X_22 != Z_3 )
=> ~ ! [Y_10: list_A1402527603le_alt] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ X_22 @ Y_10 ) @ R_9 )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ Y_10 @ Z_3 ) @ ( transi264395782le_alt @ R_9 ) ) ) ) ) ).
thf(fact_860_converse__rtranclE,axiom,
! [X_22: arrow_1389031998le_alt,Z_3: arrow_1389031998le_alt,R_9: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_22 @ Z_3 ) @ ( transi1182735211le_alt @ R_9 ) )
=> ( ( X_22 != Z_3 )
=> ~ ! [Y_10: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_22 @ Y_10 ) @ R_9 )
=> ~ ( member285112084le_alt @ ( produc897867031le_alt @ Y_10 @ Z_3 ) @ ( transi1182735211le_alt @ R_9 ) ) ) ) ) ).
thf(fact_861_rtranclE,axiom,
! [A_15: list_A1402527603le_alt,B_11: list_A1402527603le_alt,R_8: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_15 @ B_11 ) @ ( transi264395782le_alt @ R_8 ) )
=> ( ( A_15 != B_11 )
=> ~ ! [Y_10: list_A1402527603le_alt] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A_15 @ Y_10 ) @ ( transi264395782le_alt @ R_8 ) )
=> ~ ( member735418658le_alt @ ( produc1014865963le_alt @ Y_10 @ B_11 ) @ R_8 ) ) ) ) ).
thf(fact_862_rtranclE,axiom,
! [A_15: arrow_1389031998le_alt,B_11: arrow_1389031998le_alt,R_8: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_15 @ B_11 ) @ ( transi1182735211le_alt @ R_8 ) )
=> ( ( A_15 != B_11 )
=> ~ ! [Y_10: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_15 @ Y_10 ) @ ( transi1182735211le_alt @ R_8 ) )
=> ~ ( member285112084le_alt @ ( produc897867031le_alt @ Y_10 @ B_11 ) @ R_8 ) ) ) ) ).
thf(fact_863_split__list__first__propE,axiom,
! [P_8: arrow_1389031998le_alt > $o,Xs_13: list_A1402527603le_alt] :
( ? [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_13 ) )
& ( P_8 @ X_1 ) )
=> ~ ! [Ys: list_A1402527603le_alt,X_1: arrow_1389031998le_alt] :
( ? [Zs: list_A1402527603le_alt] :
( Xs_13
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_1 @ Zs ) ) )
=> ( ( P_8 @ X_1 )
=> ~ ! [Xa: arrow_1389031998le_alt] :
( ( member998036369le_alt @ Xa @ ( set_Ar1491127311le_alt @ Ys ) )
=> ~ ( P_8 @ Xa ) ) ) ) ) ).
thf(fact_864_split__list__last__propE,axiom,
! [P_7: arrow_1389031998le_alt > $o,Xs_12: list_A1402527603le_alt] :
( ? [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_12 ) )
& ( P_7 @ X_1 ) )
=> ~ ! [Ys: list_A1402527603le_alt,X_1: arrow_1389031998le_alt,Zs: list_A1402527603le_alt] :
( ( Xs_12
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_1 @ Zs ) ) )
=> ( ( P_7 @ X_1 )
=> ~ ! [Xa: arrow_1389031998le_alt] :
( ( member998036369le_alt @ Xa @ ( set_Ar1491127311le_alt @ Zs ) )
=> ~ ( P_7 @ Xa ) ) ) ) ) ).
thf(fact_865_split__list__first,axiom,
! [X_21: nat,Xs_11: list_nat] :
( ( member_nat @ X_21 @ ( set_nat @ Xs_11 ) )
=> ? [Ys: list_nat,Zs: list_nat] :
( ( Xs_11
= ( append_nat @ Ys @ ( cons_nat @ X_21 @ Zs ) ) )
& ~ ( member_nat @ X_21 @ ( set_nat @ Ys ) ) ) ) ).
thf(fact_866_split__list__first,axiom,
! [X_21: arrow_1389031998le_alt,Xs_11: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_21 @ ( set_Ar1491127311le_alt @ Xs_11 ) )
=> ? [Ys: list_A1402527603le_alt,Zs: list_A1402527603le_alt] :
( ( Xs_11
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_21 @ Zs ) ) )
& ~ ( member998036369le_alt @ X_21 @ ( set_Ar1491127311le_alt @ Ys ) ) ) ) ).
thf(fact_867_split__list__first,axiom,
! [X_21: produc2069254453le_alt,Xs_11: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_21 @ ( set_Pr1119022372le_alt @ Xs_11 ) )
=> ? [Ys: list_P1338624854le_alt,Zs: list_P1338624854le_alt] :
( ( Xs_11
= ( append1130570800le_alt @ Ys @ ( cons_P607717589le_alt @ X_21 @ Zs ) ) )
& ~ ( member735418658le_alt @ X_21 @ ( set_Pr1119022372le_alt @ Ys ) ) ) ) ).
thf(fact_868_split__list__first,axiom,
! [X_21: arrow_1196572341e_indi,Xs_11: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_21 @ ( set_Ar545511716e_indi @ Xs_11 ) )
=> ? [Ys: list_A1206016470e_indi,Zs: list_A1206016470e_indi] :
( ( Xs_11
= ( append478904880e_indi @ Ys @ ( cons_A430007893e_indi @ X_21 @ Zs ) ) )
& ~ ( member1818997282e_indi @ X_21 @ ( set_Ar545511716e_indi @ Ys ) ) ) ) ).
thf(fact_869_split__list__first,axiom,
! [X_21: $o,Xs_11: list_o] :
( ( member_o @ X_21 @ ( set_o @ Xs_11 ) )
=> ? [Ys: list_o,Zs: list_o] :
( ( Xs_11
= ( append_o @ Ys @ ( cons_o @ X_21 @ Zs ) ) )
& ~ ( member_o @ X_21 @ ( set_o @ Ys ) ) ) ) ).
thf(fact_870_split__list__first,axiom,
! [X_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_11: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_21 @ ( set_Ar17109714_alt_o @ Xs_11 ) )
=> ? [Ys: list_A869418500_alt_o,Zs: list_A869418500_alt_o] :
( ( Xs_11
= ( append1134377438_alt_o @ Ys @ ( cons_A1087586947_alt_o @ X_21 @ Zs ) ) )
& ~ ( member1425217232_alt_o @ X_21 @ ( set_Ar17109714_alt_o @ Ys ) ) ) ) ).
thf(fact_871_split__list__first,axiom,
! [X_21: produc1572197287le_alt > $o,Xs_11: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_21 @ ( set_Pr1457060537_alt_o @ Xs_11 ) )
=> ? [Ys: list_P811970973_alt_o,Zs: list_P811970973_alt_o] :
( ( Xs_11
= ( append1477507245_alt_o @ Ys @ ( cons_P2104327368_alt_o @ X_21 @ Zs ) ) )
& ~ ( member1241905979_alt_o @ X_21 @ ( set_Pr1457060537_alt_o @ Ys ) ) ) ) ).
thf(fact_872_split__list__first,axiom,
! [X_21: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_11: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_21 @ ( set_Ar868233060_alt_o @ Xs_11 ) )
=> ? [Ys: list_A115096904_alt_o,Zs: list_A115096904_alt_o] :
( ( Xs_11
= ( append592815960_alt_o @ Ys @ ( cons_A160405747_alt_o @ X_21 @ Zs ) ) )
& ~ ( member822980838_alt_o @ X_21 @ ( set_Ar868233060_alt_o @ Ys ) ) ) ) ).
thf(fact_873_split__list__first,axiom,
! [X_21: produc1572197287le_alt,Xs_11: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_21 @ ( set_Pr1596096022le_alt @ Xs_11 ) )
=> ? [Ys: list_P1402680776le_alt,Zs: list_P1402680776le_alt] :
( ( Xs_11
= ( append1300326178le_alt @ Ys @ ( cons_P1984625479le_alt @ X_21 @ Zs ) ) )
& ~ ( member285112084le_alt @ X_21 @ ( set_Pr1596096022le_alt @ Ys ) ) ) ) ).
thf(fact_874_split__list__last,axiom,
! [X_20: nat,Xs_10: list_nat] :
( ( member_nat @ X_20 @ ( set_nat @ Xs_10 ) )
=> ? [Ys: list_nat,Zs: list_nat] :
( ( Xs_10
= ( append_nat @ Ys @ ( cons_nat @ X_20 @ Zs ) ) )
& ~ ( member_nat @ X_20 @ ( set_nat @ Zs ) ) ) ) ).
thf(fact_875_split__list__last,axiom,
! [X_20: arrow_1389031998le_alt,Xs_10: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_20 @ ( set_Ar1491127311le_alt @ Xs_10 ) )
=> ? [Ys: list_A1402527603le_alt,Zs: list_A1402527603le_alt] :
( ( Xs_10
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_20 @ Zs ) ) )
& ~ ( member998036369le_alt @ X_20 @ ( set_Ar1491127311le_alt @ Zs ) ) ) ) ).
thf(fact_876_split__list__last,axiom,
! [X_20: produc2069254453le_alt,Xs_10: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_20 @ ( set_Pr1119022372le_alt @ Xs_10 ) )
=> ? [Ys: list_P1338624854le_alt,Zs: list_P1338624854le_alt] :
( ( Xs_10
= ( append1130570800le_alt @ Ys @ ( cons_P607717589le_alt @ X_20 @ Zs ) ) )
& ~ ( member735418658le_alt @ X_20 @ ( set_Pr1119022372le_alt @ Zs ) ) ) ) ).
thf(fact_877_split__list__last,axiom,
! [X_20: arrow_1196572341e_indi,Xs_10: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_20 @ ( set_Ar545511716e_indi @ Xs_10 ) )
=> ? [Ys: list_A1206016470e_indi,Zs: list_A1206016470e_indi] :
( ( Xs_10
= ( append478904880e_indi @ Ys @ ( cons_A430007893e_indi @ X_20 @ Zs ) ) )
& ~ ( member1818997282e_indi @ X_20 @ ( set_Ar545511716e_indi @ Zs ) ) ) ) ).
thf(fact_878_split__list__last,axiom,
! [X_20: $o,Xs_10: list_o] :
( ( member_o @ X_20 @ ( set_o @ Xs_10 ) )
=> ? [Ys: list_o,Zs: list_o] :
( ( Xs_10
= ( append_o @ Ys @ ( cons_o @ X_20 @ Zs ) ) )
& ~ ( member_o @ X_20 @ ( set_o @ Zs ) ) ) ) ).
thf(fact_879_split__list__last,axiom,
! [X_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_10: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_20 @ ( set_Ar17109714_alt_o @ Xs_10 ) )
=> ? [Ys: list_A869418500_alt_o,Zs: list_A869418500_alt_o] :
( ( Xs_10
= ( append1134377438_alt_o @ Ys @ ( cons_A1087586947_alt_o @ X_20 @ Zs ) ) )
& ~ ( member1425217232_alt_o @ X_20 @ ( set_Ar17109714_alt_o @ Zs ) ) ) ) ).
thf(fact_880_split__list__last,axiom,
! [X_20: produc1572197287le_alt > $o,Xs_10: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_20 @ ( set_Pr1457060537_alt_o @ Xs_10 ) )
=> ? [Ys: list_P811970973_alt_o,Zs: list_P811970973_alt_o] :
( ( Xs_10
= ( append1477507245_alt_o @ Ys @ ( cons_P2104327368_alt_o @ X_20 @ Zs ) ) )
& ~ ( member1241905979_alt_o @ X_20 @ ( set_Pr1457060537_alt_o @ Zs ) ) ) ) ).
thf(fact_881_split__list__last,axiom,
! [X_20: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_10: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_20 @ ( set_Ar868233060_alt_o @ Xs_10 ) )
=> ? [Ys: list_A115096904_alt_o,Zs: list_A115096904_alt_o] :
( ( Xs_10
= ( append592815960_alt_o @ Ys @ ( cons_A160405747_alt_o @ X_20 @ Zs ) ) )
& ~ ( member822980838_alt_o @ X_20 @ ( set_Ar868233060_alt_o @ Zs ) ) ) ) ).
thf(fact_882_split__list__last,axiom,
! [X_20: produc1572197287le_alt,Xs_10: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_20 @ ( set_Pr1596096022le_alt @ Xs_10 ) )
=> ? [Ys: list_P1402680776le_alt,Zs: list_P1402680776le_alt] :
( ( Xs_10
= ( append1300326178le_alt @ Ys @ ( cons_P1984625479le_alt @ X_20 @ Zs ) ) )
& ~ ( member285112084le_alt @ X_20 @ ( set_Pr1596096022le_alt @ Zs ) ) ) ) ).
thf(fact_883_split__list,axiom,
! [X_19: nat,Xs_9: list_nat] :
( ( member_nat @ X_19 @ ( set_nat @ Xs_9 ) )
=> ? [Ys: list_nat,Zs: list_nat] :
( Xs_9
= ( append_nat @ Ys @ ( cons_nat @ X_19 @ Zs ) ) ) ) ).
thf(fact_884_split__list,axiom,
! [X_19: arrow_1389031998le_alt,Xs_9: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_19 @ ( set_Ar1491127311le_alt @ Xs_9 ) )
=> ? [Ys: list_A1402527603le_alt,Zs: list_A1402527603le_alt] :
( Xs_9
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_19 @ Zs ) ) ) ) ).
thf(fact_885_split__list,axiom,
! [X_19: produc2069254453le_alt,Xs_9: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_19 @ ( set_Pr1119022372le_alt @ Xs_9 ) )
=> ? [Ys: list_P1338624854le_alt,Zs: list_P1338624854le_alt] :
( Xs_9
= ( append1130570800le_alt @ Ys @ ( cons_P607717589le_alt @ X_19 @ Zs ) ) ) ) ).
thf(fact_886_split__list,axiom,
! [X_19: arrow_1196572341e_indi,Xs_9: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_19 @ ( set_Ar545511716e_indi @ Xs_9 ) )
=> ? [Ys: list_A1206016470e_indi,Zs: list_A1206016470e_indi] :
( Xs_9
= ( append478904880e_indi @ Ys @ ( cons_A430007893e_indi @ X_19 @ Zs ) ) ) ) ).
thf(fact_887_split__list,axiom,
! [X_19: $o,Xs_9: list_o] :
( ( member_o @ X_19 @ ( set_o @ Xs_9 ) )
=> ? [Ys: list_o,Zs: list_o] :
( Xs_9
= ( append_o @ Ys @ ( cons_o @ X_19 @ Zs ) ) ) ) ).
thf(fact_888_split__list,axiom,
! [X_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,Xs_9: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_19 @ ( set_Ar17109714_alt_o @ Xs_9 ) )
=> ? [Ys: list_A869418500_alt_o,Zs: list_A869418500_alt_o] :
( Xs_9
= ( append1134377438_alt_o @ Ys @ ( cons_A1087586947_alt_o @ X_19 @ Zs ) ) ) ) ).
thf(fact_889_split__list,axiom,
! [X_19: produc1572197287le_alt > $o,Xs_9: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_19 @ ( set_Pr1457060537_alt_o @ Xs_9 ) )
=> ? [Ys: list_P811970973_alt_o,Zs: list_P811970973_alt_o] :
( Xs_9
= ( append1477507245_alt_o @ Ys @ ( cons_P2104327368_alt_o @ X_19 @ Zs ) ) ) ) ).
thf(fact_890_split__list,axiom,
! [X_19: arrow_1196572341e_indi > produc1572197287le_alt > $o,Xs_9: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_19 @ ( set_Ar868233060_alt_o @ Xs_9 ) )
=> ? [Ys: list_A115096904_alt_o,Zs: list_A115096904_alt_o] :
( Xs_9
= ( append592815960_alt_o @ Ys @ ( cons_A160405747_alt_o @ X_19 @ Zs ) ) ) ) ).
thf(fact_891_split__list,axiom,
! [X_19: produc1572197287le_alt,Xs_9: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_19 @ ( set_Pr1596096022le_alt @ Xs_9 ) )
=> ? [Ys: list_P1402680776le_alt,Zs: list_P1402680776le_alt] :
( Xs_9
= ( append1300326178le_alt @ Ys @ ( cons_P1984625479le_alt @ X_19 @ Zs ) ) ) ) ).
thf(fact_892_split__list__last__prop__iff,axiom,
! [P_6: arrow_1389031998le_alt > $o,Xs_8: list_A1402527603le_alt] :
( ? [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_8 ) )
& ( P_6 @ X_1 ) )
<=> ? [Ys: list_A1402527603le_alt,X_1: arrow_1389031998le_alt,Zs: list_A1402527603le_alt] :
( ( Xs_8
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_1 @ Zs ) ) )
& ( P_6 @ X_1 )
& ! [Xa: arrow_1389031998le_alt] :
( ( member998036369le_alt @ Xa @ ( set_Ar1491127311le_alt @ Zs ) )
=> ~ ( P_6 @ Xa ) ) ) ) ).
thf(fact_893_split__list__first__prop__iff,axiom,
! [P_5: arrow_1389031998le_alt > $o,Xs_7: list_A1402527603le_alt] :
( ? [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_7 ) )
& ( P_5 @ X_1 ) )
<=> ? [Ys: list_A1402527603le_alt,X_1: arrow_1389031998le_alt] :
( ? [Zs: list_A1402527603le_alt] :
( Xs_7
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_1 @ Zs ) ) )
& ( P_5 @ X_1 )
& ! [Xa: arrow_1389031998le_alt] :
( ( member998036369le_alt @ Xa @ ( set_Ar1491127311le_alt @ Ys ) )
=> ~ ( P_5 @ Xa ) ) ) ) ).
thf(fact_894_list__update_Osimps_I2_J,axiom,
! [X_18: arrow_1389031998le_alt,Xs_6: list_A1402527603le_alt,I_3: nat,V: arrow_1389031998le_alt] :
( ( list_u976150870le_alt @ ( cons_A1142416030le_alt @ X_18 @ Xs_6 ) @ I_3 @ V )
= ( nat_ca1434653759le_alt @ ( cons_A1142416030le_alt @ V @ Xs_6 )
@ ^ [J_1: nat] : ( cons_A1142416030le_alt @ X_18 @ ( list_u976150870le_alt @ Xs_6 @ J_1 @ V ) )
@ I_3 ) ) ).
thf(fact_895_drop__Cons,axiom,
! [N_5: nat,X_17: arrow_1389031998le_alt,Xs_5: list_A1402527603le_alt] :
( ( drop_A112899118le_alt @ N_5 @ ( cons_A1142416030le_alt @ X_17 @ Xs_5 ) )
= ( nat_ca1434653759le_alt @ ( cons_A1142416030le_alt @ X_17 @ Xs_5 )
@ ^ [M_1: nat] : ( drop_A112899118le_alt @ M_1 @ Xs_5 )
@ N_5 ) ) ).
thf(fact_896_converse__rtranclE2,axiom,
! [Xa_1: list_A1402527603le_alt,Xb: list_A1402527603le_alt,Za: list_A1402527603le_alt,Zb: list_A1402527603le_alt,R_7: produc2139050425le_alt > $o] :
( ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ Xa_1 @ Xb ) @ ( produc1014865963le_alt @ Za @ Zb ) ) @ ( transi1916231368le_alt @ R_7 ) )
=> ( ( ( produc1014865963le_alt @ Xa_1 @ Xb )
!= ( produc1014865963le_alt @ Za @ Zb ) )
=> ~ ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt] :
( ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ Xa_1 @ Xb ) @ ( produc1014865963le_alt @ A_14 @ B_10 ) ) @ R_7 )
=> ~ ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ A_14 @ B_10 ) @ ( produc1014865963le_alt @ Za @ Zb ) ) @ ( transi1916231368le_alt @ R_7 ) ) ) ) ) ).
thf(fact_897_converse__rtranclE2,axiom,
! [Xa_1: arrow_1389031998le_alt,Xb: arrow_1389031998le_alt,Za: arrow_1389031998le_alt,Zb: arrow_1389031998le_alt,R_7: produc307320605le_alt > $o] :
( ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ Xa_1 @ Xb ) @ ( produc897867031le_alt @ Za @ Zb ) ) @ ( transi1571931578le_alt @ R_7 ) )
=> ( ( ( produc897867031le_alt @ Xa_1 @ Xb )
!= ( produc897867031le_alt @ Za @ Zb ) )
=> ~ ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt] :
( ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ Xa_1 @ Xb ) @ ( produc897867031le_alt @ A_14 @ B_10 ) ) @ R_7 )
=> ~ ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( produc897867031le_alt @ Za @ Zb ) ) @ ( transi1571931578le_alt @ R_7 ) ) ) ) ) ).
thf(fact_898_converse__rtrancl__induct2,axiom,
! [P_4: list_A1402527603le_alt > list_A1402527603le_alt > $o,Ax_1: list_A1402527603le_alt,Ay_1: list_A1402527603le_alt,Bx_1: list_A1402527603le_alt,By_1: list_A1402527603le_alt,R_6: produc2139050425le_alt > $o] :
( ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ Ax_1 @ Ay_1 ) @ ( produc1014865963le_alt @ Bx_1 @ By_1 ) ) @ ( transi1916231368le_alt @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt,Aa: list_A1402527603le_alt,Ba: list_A1402527603le_alt] :
( ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ A_14 @ B_10 ) @ ( produc1014865963le_alt @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ Aa @ Ba ) @ ( produc1014865963le_alt @ Bx_1 @ By_1 ) ) @ ( transi1916231368le_alt @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_14 @ B_10 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_899_converse__rtrancl__induct2,axiom,
! [P_4: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Ax_1: arrow_1389031998le_alt,Ay_1: arrow_1389031998le_alt,Bx_1: arrow_1389031998le_alt,By_1: arrow_1389031998le_alt,R_6: produc307320605le_alt > $o] :
( ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ Ax_1 @ Ay_1 ) @ ( produc897867031le_alt @ Bx_1 @ By_1 ) ) @ ( transi1571931578le_alt @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt,Aa: arrow_1389031998le_alt,Ba: arrow_1389031998le_alt] :
( ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( produc897867031le_alt @ Aa @ Ba ) ) @ R_6 )
=> ( ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ Aa @ Ba ) @ ( produc897867031le_alt @ Bx_1 @ By_1 ) ) @ ( transi1571931578le_alt @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_14 @ B_10 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_900_rtrancl__induct2,axiom,
! [P_3: list_A1402527603le_alt > list_A1402527603le_alt > $o,Ax: list_A1402527603le_alt,Ay: list_A1402527603le_alt,Bx: list_A1402527603le_alt,By: list_A1402527603le_alt,R_5: produc2139050425le_alt > $o] :
( ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ Ax @ Ay ) @ ( produc1014865963le_alt @ Bx @ By ) ) @ ( transi1916231368le_alt @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt,Aa: list_A1402527603le_alt,Ba: list_A1402527603le_alt] :
( ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ Ax @ Ay ) @ ( produc1014865963le_alt @ A_14 @ B_10 ) ) @ ( transi1916231368le_alt @ R_5 ) )
=> ( ( member1253537702le_alt @ ( produc310818479le_alt @ ( produc1014865963le_alt @ A_14 @ B_10 ) @ ( produc1014865963le_alt @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_14 @ B_10 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_901_rtrancl__induct2,axiom,
! [P_3: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Ax: arrow_1389031998le_alt,Ay: arrow_1389031998le_alt,Bx: arrow_1389031998le_alt,By: arrow_1389031998le_alt,R_5: produc307320605le_alt > $o] :
( ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ Ax @ Ay ) @ ( produc897867031le_alt @ Bx @ By ) ) @ ( transi1571931578le_alt @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt,Aa: arrow_1389031998le_alt,Ba: arrow_1389031998le_alt] :
( ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ Ax @ Ay ) @ ( produc897867031le_alt @ A_14 @ B_10 ) ) @ ( transi1571931578le_alt @ R_5 ) )
=> ( ( member894661642le_alt @ ( produc2131135379le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( produc897867031le_alt @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_14 @ B_10 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_902_take__Cons,axiom,
! [N_4: nat,X_16: arrow_1389031998le_alt,Xs_4: list_A1402527603le_alt] :
( ( take_A1527720662le_alt @ N_4 @ ( cons_A1142416030le_alt @ X_16 @ Xs_4 ) )
= ( nat_ca1434653759le_alt @ nil_Ar52383470le_alt
@ ^ [M_1: nat] : ( cons_A1142416030le_alt @ X_16 @ ( take_A1527720662le_alt @ M_1 @ Xs_4 ) )
@ N_4 ) ) ).
thf(fact_903_rtrancl_Osimps,axiom,
! [A1: list_A1402527603le_alt,A2: list_A1402527603le_alt,R_4: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ ( produc1014865963le_alt @ A1 @ A2 ) @ ( transi264395782le_alt @ R_4 ) )
<=> ( ? [A_14: list_A1402527603le_alt] :
( ( A1 = A_14 )
& ( A2 = A_14 ) )
| ? [A_14: list_A1402527603le_alt,B_10: list_A1402527603le_alt,C_6: list_A1402527603le_alt] :
( ( A1 = A_14 )
& ( A2 = C_6 )
& ( member735418658le_alt @ ( produc1014865963le_alt @ A_14 @ B_10 ) @ ( transi264395782le_alt @ R_4 ) )
& ( member735418658le_alt @ ( produc1014865963le_alt @ B_10 @ C_6 ) @ R_4 ) ) ) ) ).
thf(fact_904_rtrancl_Osimps,axiom,
! [A1: arrow_1389031998le_alt,A2: arrow_1389031998le_alt,R_4: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A1 @ A2 ) @ ( transi1182735211le_alt @ R_4 ) )
<=> ( ? [A_14: arrow_1389031998le_alt] :
( ( A1 = A_14 )
& ( A2 = A_14 ) )
| ? [A_14: arrow_1389031998le_alt,B_10: arrow_1389031998le_alt,C_6: arrow_1389031998le_alt] :
( ( A1 = A_14 )
& ( A2 = C_6 )
& ( member285112084le_alt @ ( produc897867031le_alt @ A_14 @ B_10 ) @ ( transi1182735211le_alt @ R_4 ) )
& ( member285112084le_alt @ ( produc897867031le_alt @ B_10 @ C_6 ) @ R_4 ) ) ) ) ).
thf(fact_905_listrel__subset__rtrancl__listrel1,axiom,
! [R_3: produc1572197287le_alt > $o] : ( ord_le2064394532_alt_o @ ( listre686844950le_alt @ R_3 ) @ ( transi264395782le_alt @ ( listre830192455le_alt @ R_3 ) ) ) ).
thf(fact_906_split__list__first__prop,axiom,
! [P_2: arrow_1389031998le_alt > $o,Xs_3: list_A1402527603le_alt] :
( ? [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_3 ) )
& ( P_2 @ X_1 ) )
=> ? [Ys: list_A1402527603le_alt,X_1: arrow_1389031998le_alt] :
( ? [Zs: list_A1402527603le_alt] :
( Xs_3
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_1 @ Zs ) ) )
& ( P_2 @ X_1 )
& ! [Xa: arrow_1389031998le_alt] :
( ( member998036369le_alt @ Xa @ ( set_Ar1491127311le_alt @ Ys ) )
=> ~ ( P_2 @ Xa ) ) ) ) ).
thf(fact_907_split__list__last__prop,axiom,
! [P_1: arrow_1389031998le_alt > $o,Xs_2: list_A1402527603le_alt] :
( ? [X_1: arrow_1389031998le_alt] :
( ( member998036369le_alt @ X_1 @ ( set_Ar1491127311le_alt @ Xs_2 ) )
& ( P_1 @ X_1 ) )
=> ? [Ys: list_A1402527603le_alt,X_1: arrow_1389031998le_alt,Zs: list_A1402527603le_alt] :
( ( Xs_2
= ( append1092755459le_alt @ Ys @ ( cons_A1142416030le_alt @ X_1 @ Zs ) ) )
& ( P_1 @ X_1 )
& ! [Xa: arrow_1389031998le_alt] :
( ( member998036369le_alt @ Xa @ ( set_Ar1491127311le_alt @ Zs ) )
=> ~ ( P_1 @ Xa ) ) ) ) ).
thf(fact_908_order__refl,axiom,
! [X_15: nat] : ( ord_less_eq_nat @ X_15 @ X_15 ) ).
thf(fact_909_subsetD,axiom,
! [C_5: nat,A_13: nat > $o,B_9: nat > $o] :
( ( ord_less_eq_nat_o @ A_13 @ B_9 )
=> ( ( member_nat @ C_5 @ A_13 )
=> ( member_nat @ C_5 @ B_9 ) ) ) ).
thf(fact_910_subsetD,axiom,
! [C_5: arrow_1389031998le_alt,A_13: arrow_1389031998le_alt > $o,B_9: arrow_1389031998le_alt > $o] :
( ( ord_le1423491573_alt_o @ A_13 @ B_9 )
=> ( ( member998036369le_alt @ C_5 @ A_13 )
=> ( member998036369le_alt @ C_5 @ B_9 ) ) ) ).
thf(fact_911_subsetD,axiom,
! [C_5: produc2069254453le_alt,A_13: produc2069254453le_alt > $o,B_9: produc2069254453le_alt > $o] :
( ( ord_le2064394532_alt_o @ A_13 @ B_9 )
=> ( ( member735418658le_alt @ C_5 @ A_13 )
=> ( member735418658le_alt @ C_5 @ B_9 ) ) ) ).
thf(fact_912_subsetD,axiom,
! [C_5: arrow_1196572341e_indi,A_13: arrow_1196572341e_indi > $o,B_9: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_13 @ B_9 )
=> ( ( member1818997282e_indi @ C_5 @ A_13 )
=> ( member1818997282e_indi @ C_5 @ B_9 ) ) ) ).
thf(fact_913_subsetD,axiom,
! [C_5: $o,A_13: $o > $o,B_9: $o > $o] :
( ( ord_less_eq_o_o @ A_13 @ B_9 )
=> ( ( member_o @ C_5 @ A_13 )
=> ( member_o @ C_5 @ B_9 ) ) ) ).
thf(fact_914_subsetD,axiom,
! [C_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_13: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_9: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_13 @ B_9 )
=> ( ( member1425217232_alt_o @ C_5 @ A_13 )
=> ( member1425217232_alt_o @ C_5 @ B_9 ) ) ) ).
thf(fact_915_subsetD,axiom,
! [C_5: produc1572197287le_alt > $o,A_13: ( produc1572197287le_alt > $o ) > $o,B_9: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_13 @ B_9 )
=> ( ( member1241905979_alt_o @ C_5 @ A_13 )
=> ( member1241905979_alt_o @ C_5 @ B_9 ) ) ) ).
thf(fact_916_subsetD,axiom,
! [C_5: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_13: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_9: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_13 @ B_9 )
=> ( ( member822980838_alt_o @ C_5 @ A_13 )
=> ( member822980838_alt_o @ C_5 @ B_9 ) ) ) ).
thf(fact_917_subsetD,axiom,
! [C_5: produc1572197287le_alt,A_13: produc1572197287le_alt > $o,B_9: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_13 @ B_9 )
=> ( ( member285112084le_alt @ C_5 @ A_13 )
=> ( member285112084le_alt @ C_5 @ B_9 ) ) ) ).
thf(fact_918_listrel__mono,axiom,
! [R_2: produc1572197287le_alt > $o,S_3: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ R_2 @ S_3 )
=> ( ord_le2064394532_alt_o @ ( listre686844950le_alt @ R_2 ) @ ( listre686844950le_alt @ S_3 ) ) ) ).
thf(fact_919_listrel1__mono,axiom,
! [R_1: produc1572197287le_alt > $o,S_2: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ R_1 @ S_2 )
=> ( ord_le2064394532_alt_o @ ( listre830192455le_alt @ R_1 ) @ ( listre830192455le_alt @ S_2 ) ) ) ).
thf(fact_920_Pi__anti__mono,axiom,
! [B_8: produc1572197287le_alt > $o > $o,A_12: produc1572197287le_alt > $o,A_11: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_12 @ A_11 )
=> ( ord_le1027220427lt_o_o @ ( pi_Pro418549519_alt_o @ A_11 @ B_8 ) @ ( pi_Pro418549519_alt_o @ A_12 @ B_8 ) ) ) ).
thf(fact_921_Pi__anti__mono,axiom,
! [B_8: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,A_12: arrow_1196572341e_indi > $o,A_11: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_12 @ A_11 )
=> ( ord_le602483040lt_o_o @ ( pi_Arr1309696186_alt_o @ A_11 @ B_8 ) @ ( pi_Arr1309696186_alt_o @ A_12 @ B_8 ) ) ) ).
thf(fact_922_Pi__anti__mono,axiom,
! [B_8: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o,A_12: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_11: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_12 @ A_11 )
=> ( ord_le1805007862lt_o_o @ ( pi_Arr1196397536_alt_o @ A_11 @ B_8 ) @ ( pi_Arr1196397536_alt_o @ A_12 @ B_8 ) ) ) ).
thf(fact_923_pred__subset__eq,axiom,
! [R: nat > $o,S_1: nat > $o] :
( ( ord_less_eq_nat_o
@ ^ [X_1: nat] : ( member_nat @ X_1 @ R )
@ ^ [X_1: nat] : ( member_nat @ X_1 @ S_1 ) )
<=> ( ord_less_eq_nat_o @ R @ S_1 ) ) ).
thf(fact_924_pred__subset__eq,axiom,
! [R: arrow_1389031998le_alt > $o,S_1: arrow_1389031998le_alt > $o] :
( ( ord_le1423491573_alt_o
@ ^ [X_1: arrow_1389031998le_alt] : ( member998036369le_alt @ X_1 @ R )
@ ^ [X_1: arrow_1389031998le_alt] : ( member998036369le_alt @ X_1 @ S_1 ) )
<=> ( ord_le1423491573_alt_o @ R @ S_1 ) ) ).
thf(fact_925_pred__subset__eq,axiom,
! [R: produc2069254453le_alt > $o,S_1: produc2069254453le_alt > $o] :
( ( ord_le2064394532_alt_o
@ ^ [X_1: produc2069254453le_alt] : ( member735418658le_alt @ X_1 @ R )
@ ^ [X_1: produc2069254453le_alt] : ( member735418658le_alt @ X_1 @ S_1 ) )
<=> ( ord_le2064394532_alt_o @ R @ S_1 ) ) ).
thf(fact_926_pred__subset__eq,axiom,
! [R: arrow_1196572341e_indi > $o,S_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o
@ ^ [X_1: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_1 @ R )
@ ^ [X_1: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_1 @ S_1 ) )
<=> ( ord_le865407012indi_o @ R @ S_1 ) ) ).
thf(fact_927_pred__subset__eq,axiom,
! [R: $o > $o,S_1: $o > $o] :
( ( ord_less_eq_o_o
@ ^ [X_1: $o] : ( member_o @ X_1 @ R )
@ ^ [X_1: $o] : ( member_o @ X_1 @ S_1 ) )
<=> ( ord_less_eq_o_o @ R @ S_1 ) ) ).
thf(fact_928_pred__subset__eq,axiom,
! [R: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,S_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o
@ ^ [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( member1425217232_alt_o @ X_1 @ R )
@ ^ [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( member1425217232_alt_o @ X_1 @ S_1 ) )
<=> ( ord_le1805007862lt_o_o @ R @ S_1 ) ) ).
thf(fact_929_pred__subset__eq,axiom,
! [R: ( produc1572197287le_alt > $o ) > $o,S_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o
@ ^ [X_1: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ X_1 @ R )
@ ^ [X_1: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ X_1 @ S_1 ) )
<=> ( ord_le1027220427lt_o_o @ R @ S_1 ) ) ).
thf(fact_930_pred__subset__eq,axiom,
! [R: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,S_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o
@ ^ [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( member822980838_alt_o @ X_1 @ R )
@ ^ [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( member822980838_alt_o @ X_1 @ S_1 ) )
<=> ( ord_le602483040lt_o_o @ R @ S_1 ) ) ).
thf(fact_931_pred__subset__eq,axiom,
! [R: produc1572197287le_alt > $o,S_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o
@ ^ [X_1: produc1572197287le_alt] : ( member285112084le_alt @ X_1 @ R )
@ ^ [X_1: produc1572197287le_alt] : ( member285112084le_alt @ X_1 @ S_1 ) )
<=> ( ord_le962286258_alt_o @ R @ S_1 ) ) ).
thf(fact_932_linorder__le__cases,axiom,
! [X_14: nat,Y_9: nat] :
( ~ ( ord_less_eq_nat @ X_14 @ Y_9 )
=> ( ord_less_eq_nat @ Y_9 @ X_14 ) ) ).
thf(fact_933_xt1_I6_J,axiom,
! [Z_2: nat,Y_8: nat,X_13: nat] :
( ( ord_less_eq_nat @ Y_8 @ X_13 )
=> ( ( ord_less_eq_nat @ Z_2 @ Y_8 )
=> ( ord_less_eq_nat @ Z_2 @ X_13 ) ) ) ).
thf(fact_934_xt1_I5_J,axiom,
! [Y_7: nat,X_12: nat] :
( ( ord_less_eq_nat @ Y_7 @ X_12 )
=> ( ( ord_less_eq_nat @ X_12 @ Y_7 )
=> ( X_12 = Y_7 ) ) ) ).
thf(fact_935_order__trans,axiom,
! [Z_1: nat,X_11: nat,Y_6: nat] :
( ( ord_less_eq_nat @ X_11 @ Y_6 )
=> ( ( ord_less_eq_nat @ Y_6 @ Z_1 )
=> ( ord_less_eq_nat @ X_11 @ Z_1 ) ) ) ).
thf(fact_936_order__antisym,axiom,
! [X_10: nat,Y_5: nat] :
( ( ord_less_eq_nat @ X_10 @ Y_5 )
=> ( ( ord_less_eq_nat @ Y_5 @ X_10 )
=> ( X_10 = Y_5 ) ) ) ).
thf(fact_937_xt1_I4_J,axiom,
! [C_4: nat,B_7: nat,A_10: nat] :
( ( ord_less_eq_nat @ B_7 @ A_10 )
=> ( ( B_7 = C_4 )
=> ( ord_less_eq_nat @ C_4 @ A_10 ) ) ) ).
thf(fact_938_ord__le__eq__trans,axiom,
! [C_3: nat,A_9: nat,B_6: nat] :
( ( ord_less_eq_nat @ A_9 @ B_6 )
=> ( ( B_6 = C_3 )
=> ( ord_less_eq_nat @ A_9 @ C_3 ) ) ) ).
thf(fact_939_set__mp,axiom,
! [X_9: nat,A_8: nat > $o,B_5: nat > $o] :
( ( ord_less_eq_nat_o @ A_8 @ B_5 )
=> ( ( member_nat @ X_9 @ A_8 )
=> ( member_nat @ X_9 @ B_5 ) ) ) ).
thf(fact_940_set__mp,axiom,
! [X_9: arrow_1389031998le_alt,A_8: arrow_1389031998le_alt > $o,B_5: arrow_1389031998le_alt > $o] :
( ( ord_le1423491573_alt_o @ A_8 @ B_5 )
=> ( ( member998036369le_alt @ X_9 @ A_8 )
=> ( member998036369le_alt @ X_9 @ B_5 ) ) ) ).
thf(fact_941_set__mp,axiom,
! [X_9: produc2069254453le_alt,A_8: produc2069254453le_alt > $o,B_5: produc2069254453le_alt > $o] :
( ( ord_le2064394532_alt_o @ A_8 @ B_5 )
=> ( ( member735418658le_alt @ X_9 @ A_8 )
=> ( member735418658le_alt @ X_9 @ B_5 ) ) ) ).
thf(fact_942_set__mp,axiom,
! [X_9: arrow_1196572341e_indi,A_8: arrow_1196572341e_indi > $o,B_5: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_8 @ B_5 )
=> ( ( member1818997282e_indi @ X_9 @ A_8 )
=> ( member1818997282e_indi @ X_9 @ B_5 ) ) ) ).
thf(fact_943_set__mp,axiom,
! [X_9: $o,A_8: $o > $o,B_5: $o > $o] :
( ( ord_less_eq_o_o @ A_8 @ B_5 )
=> ( ( member_o @ X_9 @ A_8 )
=> ( member_o @ X_9 @ B_5 ) ) ) ).
thf(fact_944_set__mp,axiom,
! [X_9: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_8: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_5: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_8 @ B_5 )
=> ( ( member1425217232_alt_o @ X_9 @ A_8 )
=> ( member1425217232_alt_o @ X_9 @ B_5 ) ) ) ).
thf(fact_945_set__mp,axiom,
! [X_9: produc1572197287le_alt > $o,A_8: ( produc1572197287le_alt > $o ) > $o,B_5: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_8 @ B_5 )
=> ( ( member1241905979_alt_o @ X_9 @ A_8 )
=> ( member1241905979_alt_o @ X_9 @ B_5 ) ) ) ).
thf(fact_946_set__mp,axiom,
! [X_9: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_8: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_8 @ B_5 )
=> ( ( member822980838_alt_o @ X_9 @ A_8 )
=> ( member822980838_alt_o @ X_9 @ B_5 ) ) ) ).
thf(fact_947_set__mp,axiom,
! [X_9: produc1572197287le_alt,A_8: produc1572197287le_alt > $o,B_5: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_8 @ B_5 )
=> ( ( member285112084le_alt @ X_9 @ A_8 )
=> ( member285112084le_alt @ X_9 @ B_5 ) ) ) ).
thf(fact_948_set__rev__mp,axiom,
! [B_4: nat > $o,X_8: nat,A_7: nat > $o] :
( ( member_nat @ X_8 @ A_7 )
=> ( ( ord_less_eq_nat_o @ A_7 @ B_4 )
=> ( member_nat @ X_8 @ B_4 ) ) ) ).
thf(fact_949_set__rev__mp,axiom,
! [B_4: arrow_1389031998le_alt > $o,X_8: arrow_1389031998le_alt,A_7: arrow_1389031998le_alt > $o] :
( ( member998036369le_alt @ X_8 @ A_7 )
=> ( ( ord_le1423491573_alt_o @ A_7 @ B_4 )
=> ( member998036369le_alt @ X_8 @ B_4 ) ) ) ).
thf(fact_950_set__rev__mp,axiom,
! [B_4: produc2069254453le_alt > $o,X_8: produc2069254453le_alt,A_7: produc2069254453le_alt > $o] :
( ( member735418658le_alt @ X_8 @ A_7 )
=> ( ( ord_le2064394532_alt_o @ A_7 @ B_4 )
=> ( member735418658le_alt @ X_8 @ B_4 ) ) ) ).
thf(fact_951_set__rev__mp,axiom,
! [B_4: arrow_1196572341e_indi > $o,X_8: arrow_1196572341e_indi,A_7: arrow_1196572341e_indi > $o] :
( ( member1818997282e_indi @ X_8 @ A_7 )
=> ( ( ord_le865407012indi_o @ A_7 @ B_4 )
=> ( member1818997282e_indi @ X_8 @ B_4 ) ) ) ).
thf(fact_952_set__rev__mp,axiom,
! [B_4: $o > $o,X_8: $o,A_7: $o > $o] :
( ( member_o @ X_8 @ A_7 )
=> ( ( ord_less_eq_o_o @ A_7 @ B_4 )
=> ( member_o @ X_8 @ B_4 ) ) ) ).
thf(fact_953_set__rev__mp,axiom,
! [B_4: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_8: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_7: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ X_8 @ A_7 )
=> ( ( ord_le1805007862lt_o_o @ A_7 @ B_4 )
=> ( member1425217232_alt_o @ X_8 @ B_4 ) ) ) ).
thf(fact_954_set__rev__mp,axiom,
! [B_4: ( produc1572197287le_alt > $o ) > $o,X_8: produc1572197287le_alt > $o,A_7: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ X_8 @ A_7 )
=> ( ( ord_le1027220427lt_o_o @ A_7 @ B_4 )
=> ( member1241905979_alt_o @ X_8 @ B_4 ) ) ) ).
thf(fact_955_set__rev__mp,axiom,
! [B_4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_8: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_7: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X_8 @ A_7 )
=> ( ( ord_le602483040lt_o_o @ A_7 @ B_4 )
=> ( member822980838_alt_o @ X_8 @ B_4 ) ) ) ).
thf(fact_956_set__rev__mp,axiom,
! [B_4: produc1572197287le_alt > $o,X_8: produc1572197287le_alt,A_7: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X_8 @ A_7 )
=> ( ( ord_le962286258_alt_o @ A_7 @ B_4 )
=> ( member285112084le_alt @ X_8 @ B_4 ) ) ) ).
thf(fact_957_xt1_I3_J,axiom,
! [C_2: nat,A_6: nat,B_3: nat] :
( ( A_6 = B_3 )
=> ( ( ord_less_eq_nat @ C_2 @ B_3 )
=> ( ord_less_eq_nat @ C_2 @ A_6 ) ) ) ).
thf(fact_958_ord__eq__le__trans,axiom,
! [C_1: nat,A_5: nat,B_2: nat] :
( ( A_5 = B_2 )
=> ( ( ord_less_eq_nat @ B_2 @ C_1 )
=> ( ord_less_eq_nat @ A_5 @ C_1 ) ) ) ).
thf(fact_959_order__antisym__conv,axiom,
! [Y_4: nat,X_7: nat] :
( ( ord_less_eq_nat @ Y_4 @ X_7 )
=> ( ( ord_less_eq_nat @ X_7 @ Y_4 )
<=> ( X_7 = Y_4 ) ) ) ).
thf(fact_960_in__mono,axiom,
! [X_6: nat,A_4: nat > $o,B_1: nat > $o] :
( ( ord_less_eq_nat_o @ A_4 @ B_1 )
=> ( ( member_nat @ X_6 @ A_4 )
=> ( member_nat @ X_6 @ B_1 ) ) ) ).
thf(fact_961_in__mono,axiom,
! [X_6: arrow_1389031998le_alt,A_4: arrow_1389031998le_alt > $o,B_1: arrow_1389031998le_alt > $o] :
( ( ord_le1423491573_alt_o @ A_4 @ B_1 )
=> ( ( member998036369le_alt @ X_6 @ A_4 )
=> ( member998036369le_alt @ X_6 @ B_1 ) ) ) ).
thf(fact_962_in__mono,axiom,
! [X_6: produc2069254453le_alt,A_4: produc2069254453le_alt > $o,B_1: produc2069254453le_alt > $o] :
( ( ord_le2064394532_alt_o @ A_4 @ B_1 )
=> ( ( member735418658le_alt @ X_6 @ A_4 )
=> ( member735418658le_alt @ X_6 @ B_1 ) ) ) ).
thf(fact_963_in__mono,axiom,
! [X_6: arrow_1196572341e_indi,A_4: arrow_1196572341e_indi > $o,B_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_4 @ B_1 )
=> ( ( member1818997282e_indi @ X_6 @ A_4 )
=> ( member1818997282e_indi @ X_6 @ B_1 ) ) ) ).
thf(fact_964_in__mono,axiom,
! [X_6: $o,A_4: $o > $o,B_1: $o > $o] :
( ( ord_less_eq_o_o @ A_4 @ B_1 )
=> ( ( member_o @ X_6 @ A_4 )
=> ( member_o @ X_6 @ B_1 ) ) ) ).
thf(fact_965_in__mono,axiom,
! [X_6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_4: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_4 @ B_1 )
=> ( ( member1425217232_alt_o @ X_6 @ A_4 )
=> ( member1425217232_alt_o @ X_6 @ B_1 ) ) ) ).
thf(fact_966_in__mono,axiom,
! [X_6: produc1572197287le_alt > $o,A_4: ( produc1572197287le_alt > $o ) > $o,B_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_4 @ B_1 )
=> ( ( member1241905979_alt_o @ X_6 @ A_4 )
=> ( member1241905979_alt_o @ X_6 @ B_1 ) ) ) ).
thf(fact_967_in__mono,axiom,
! [X_6: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_4 @ B_1 )
=> ( ( member822980838_alt_o @ X_6 @ A_4 )
=> ( member822980838_alt_o @ X_6 @ B_1 ) ) ) ).
thf(fact_968_in__mono,axiom,
! [X_6: produc1572197287le_alt,A_4: produc1572197287le_alt > $o,B_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_4 @ B_1 )
=> ( ( member285112084le_alt @ X_6 @ A_4 )
=> ( member285112084le_alt @ X_6 @ B_1 ) ) ) ).
thf(fact_969_order__eq__refl,axiom,
! [X_5: nat,Y_3: nat] :
( ( X_5 = Y_3 )
=> ( ord_less_eq_nat @ X_5 @ Y_3 ) ) ).
thf(fact_970_order__eq__iff,axiom,
! [X_4: nat,Y_2: nat] :
( ( X_4 = Y_2 )
<=> ( ( ord_less_eq_nat @ X_4 @ Y_2 )
& ( ord_less_eq_nat @ Y_2 @ X_4 ) ) ) ).
thf(fact_971_linorder__linear,axiom,
! [X_3: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_3 @ Y_1 )
| ( ord_less_eq_nat @ Y_1 @ X_3 ) ) ).
thf(fact_972_take__Nil,axiom,
! [N_3: nat] :
( ( take_A1527720662le_alt @ N_3 @ nil_Ar52383470le_alt )
= nil_Ar52383470le_alt ) ).
thf(fact_973_in__set__takeD,axiom,
! [X_2: nat,N_2: nat,Xs_1: list_nat] :
( ( member_nat @ X_2 @ ( set_nat @ ( take_nat @ N_2 @ Xs_1 ) ) )
=> ( member_nat @ X_2 @ ( set_nat @ Xs_1 ) ) ) ).
thf(fact_974_in__set__takeD,axiom,
! [X_2: arrow_1389031998le_alt,N_2: nat,Xs_1: list_A1402527603le_alt] :
( ( member998036369le_alt @ X_2 @ ( set_Ar1491127311le_alt @ ( take_A1527720662le_alt @ N_2 @ Xs_1 ) ) )
=> ( member998036369le_alt @ X_2 @ ( set_Ar1491127311le_alt @ Xs_1 ) ) ) ).
thf(fact_975_in__set__takeD,axiom,
! [X_2: produc2069254453le_alt,N_2: nat,Xs_1: list_P1338624854le_alt] :
( ( member735418658le_alt @ X_2 @ ( set_Pr1119022372le_alt @ ( take_P295428765le_alt @ N_2 @ Xs_1 ) ) )
=> ( member735418658le_alt @ X_2 @ ( set_Pr1119022372le_alt @ Xs_1 ) ) ) ).
thf(fact_976_in__set__takeD,axiom,
! [X_2: arrow_1196572341e_indi,N_2: nat,Xs_1: list_A1206016470e_indi] :
( ( member1818997282e_indi @ X_2 @ ( set_Ar545511716e_indi @ ( take_A146025501e_indi @ N_2 @ Xs_1 ) ) )
=> ( member1818997282e_indi @ X_2 @ ( set_Ar545511716e_indi @ Xs_1 ) ) ) ).
thf(fact_977_in__set__takeD,axiom,
! [X_2: $o,N_2: nat,Xs_1: list_o] :
( ( member_o @ X_2 @ ( set_o @ ( take_o @ N_2 @ Xs_1 ) ) )
=> ( member_o @ X_2 @ ( set_o @ Xs_1 ) ) ) ).
thf(fact_978_in__set__takeD,axiom,
! [X_2: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,N_2: nat,Xs_1: list_A869418500_alt_o] :
( ( member1425217232_alt_o @ X_2 @ ( set_Ar17109714_alt_o @ ( take_A1941683275_alt_o @ N_2 @ Xs_1 ) ) )
=> ( member1425217232_alt_o @ X_2 @ ( set_Ar17109714_alt_o @ Xs_1 ) ) ) ).
thf(fact_979_in__set__takeD,axiom,
! [X_2: produc1572197287le_alt > $o,N_2: nat,Xs_1: list_P811970973_alt_o] :
( ( member1241905979_alt_o @ X_2 @ ( set_Pr1457060537_alt_o @ ( take_P1700987136_alt_o @ N_2 @ Xs_1 ) ) )
=> ( member1241905979_alt_o @ X_2 @ ( set_Pr1457060537_alt_o @ Xs_1 ) ) ) ).
thf(fact_980_in__set__takeD,axiom,
! [X_2: arrow_1196572341e_indi > produc1572197287le_alt > $o,N_2: nat,Xs_1: list_A115096904_alt_o] :
( ( member822980838_alt_o @ X_2 @ ( set_Ar868233060_alt_o @ ( take_A1888368939_alt_o @ N_2 @ Xs_1 ) ) )
=> ( member822980838_alt_o @ X_2 @ ( set_Ar868233060_alt_o @ Xs_1 ) ) ) ).
thf(fact_981_in__set__takeD,axiom,
! [X_2: produc1572197287le_alt,N_2: nat,Xs_1: list_P1402680776le_alt] :
( ( member285112084le_alt @ X_2 @ ( set_Pr1596096022le_alt @ ( take_P124862735le_alt @ N_2 @ Xs_1 ) ) )
=> ( member285112084le_alt @ X_2 @ ( set_Pr1596096022le_alt @ Xs_1 ) ) ) ).
thf(fact_982_distinct__take,axiom,
! [I_2: nat,Xs: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ Xs )
=> ( distin1149997281le_alt @ ( take_A1527720662le_alt @ I_2 @ Xs ) ) ) ).
thf(fact_983_top__greatest,axiom,
! [A_3: $o] : ( ord_less_eq_o @ A_3 @ top_top_o ) ).
thf(fact_984_top__greatest,axiom,
! [A_3: produc1572197287le_alt > $o] : ( ord_le962286258_alt_o @ A_3 @ top_to558618722_alt_o ) ).
thf(fact_985_top__greatest,axiom,
! [A_3: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] : ( ord_le602483040lt_o_o @ A_3 @ top_to732317616lt_o_o ) ).
thf(fact_986_top__greatest,axiom,
! [A_3: ( produc1572197287le_alt > $o ) > $o] : ( ord_le1027220427lt_o_o @ A_3 @ top_to1806834203lt_o_o ) ).
thf(fact_987_top__greatest,axiom,
! [A_3: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] : ( ord_le1805007862lt_o_o @ A_3 @ top_to1492351398lt_o_o ) ).
thf(fact_988_top__greatest,axiom,
! [A_3: arrow_1389031998le_alt > $o] : ( ord_le1423491573_alt_o @ A_3 @ top_to1031852101_alt_o ) ).
thf(fact_989_top__greatest,axiom,
! [A_3: arrow_1196572341e_indi > $o] : ( ord_le865407012indi_o @ A_3 @ top_to54564308indi_o ) ).
thf(fact_990_top__unique,axiom,
! [A_2: $o] :
( ( ord_less_eq_o @ top_top_o @ A_2 )
<=> ( A_2
<=> top_top_o ) ) ).
thf(fact_991_top__unique,axiom,
! [A_2: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ top_to558618722_alt_o @ A_2 )
<=> ( A_2 = top_to558618722_alt_o ) ) ).
thf(fact_992_top__unique,axiom,
! [A_2: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ top_to732317616lt_o_o @ A_2 )
<=> ( A_2 = top_to732317616lt_o_o ) ) ).
thf(fact_993_top__unique,axiom,
! [A_2: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ top_to1806834203lt_o_o @ A_2 )
<=> ( A_2 = top_to1806834203lt_o_o ) ) ).
thf(fact_994_top__unique,axiom,
! [A_2: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ top_to1492351398lt_o_o @ A_2 )
<=> ( A_2 = top_to1492351398lt_o_o ) ) ).
thf(fact_995_top__unique,axiom,
! [A_2: arrow_1389031998le_alt > $o] :
( ( ord_le1423491573_alt_o @ top_to1031852101_alt_o @ A_2 )
<=> ( A_2 = top_to1031852101_alt_o ) ) ).
thf(fact_996_top__unique,axiom,
! [A_2: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ top_to54564308indi_o @ A_2 )
<=> ( A_2 = top_to54564308indi_o ) ) ).
thf(fact_997_top__le,axiom,
! [A_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ top_to558618722_alt_o @ A_1 )
=> ( A_1 = top_to558618722_alt_o ) ) ).
thf(fact_998_top__le,axiom,
! [A_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ top_to732317616lt_o_o @ A_1 )
=> ( A_1 = top_to732317616lt_o_o ) ) ).
thf(fact_999_top__le,axiom,
! [A_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ top_to1806834203lt_o_o @ A_1 )
=> ( A_1 = top_to1806834203lt_o_o ) ) ).
thf(fact_1000_top__le,axiom,
! [A_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ top_to1492351398lt_o_o @ A_1 )
=> ( A_1 = top_to1492351398lt_o_o ) ) ).
thf(fact_1001_top__le,axiom,
! [A_1: arrow_1389031998le_alt > $o] :
( ( ord_le1423491573_alt_o @ top_to1031852101_alt_o @ A_1 )
=> ( A_1 = top_to1031852101_alt_o ) ) ).
thf(fact_1002_top__le,axiom,
! [A_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ top_to54564308indi_o @ A_1 )
=> ( A_1 = top_to54564308indi_o ) ) ).
thf(fact_1003_termination__basic__simps_I5_J,axiom,
! [X: nat,Y: nat] :
( ( ord_less_nat @ X @ Y )
=> ( ord_less_eq_nat @ X @ Y ) ) ).
thf(fact_1004_lessI,axiom,
! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
thf(fact_1005_Suc__mono,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
thf(fact_1006_less__eq__Suc__le__raw,axiom,
! [X_1: nat] :
( ( ord_less_nat @ X_1 )
= ( ord_less_eq_nat @ ( suc @ X_1 ) ) ) ).
thf(fact_1007_n__not__Suc__n,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ) ).
thf(fact_1008_Suc__n__not__n,axiom,
! [N: nat] :
( ( suc @ N )
!= N ) ).
thf(fact_1009_nat_Oinject,axiom,
! [Nat: nat,Nat_3: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat_3 ) )
<=> ( Nat = Nat_3 ) ) ).
thf(fact_1010_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
thf(fact_1011_less__not__refl,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
thf(fact_1012_nat__neq__iff,axiom,
! [M: nat,N: nat] :
( ( M != N )
<=> ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) ).
thf(fact_1013_linorder__neqE__nat,axiom,
! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ) ).
thf(fact_1014_less__irrefl__nat,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
thf(fact_1015_less__not__refl2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) ).
thf(fact_1016_less__not__refl3,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) ).
thf(fact_1017_nat__less__cases,axiom,
! [P: nat > nat > $o,M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
=> ( P @ N @ M ) )
=> ( ( ( M = N )
=> ( P @ N @ M ) )
=> ( ( ( ord_less_nat @ N @ M )
=> ( P @ N @ M ) )
=> ( P @ N @ M ) ) ) ) ).
thf(fact_1018_le__refl,axiom,
! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
thf(fact_1019_nat__le__linear,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) ).
thf(fact_1020_eq__imp__le,axiom,
! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
thf(fact_1021_le__trans,axiom,
! [K: nat,I_1: nat,J: nat] :
( ( ord_less_eq_nat @ I_1 @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I_1 @ K ) ) ) ).
thf(fact_1022_le__antisym,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ) ).
thf(fact_1023_Suc__less__SucD,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
=> ( ord_less_nat @ M @ N ) ) ).
thf(fact_1024_Suc__lessD,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) ).
thf(fact_1025_less__SucE,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_nat @ M @ N )
=> ( M = N ) ) ) ).
thf(fact_1026_less__trans__Suc,axiom,
! [K: nat,I_1: nat,J: nat] :
( ( ord_less_nat @ I_1 @ J )
=> ( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( suc @ I_1 ) @ K ) ) ) ).
thf(fact_1027_Suc__lessI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ( suc @ M )
!= N )
=> ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
thf(fact_1028_less__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
thf(fact_1029_less__antisym,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
=> ( M = N ) ) ) ).
thf(fact_1030_not__less__less__Suc__eq,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
<=> ( N = M ) ) ) ).
thf(fact_1031_Suc__less__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
<=> ( ord_less_nat @ M @ N ) ) ).
thf(fact_1032_less__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
<=> ( ( ord_less_nat @ M @ N )
| ( M = N ) ) ) ).
thf(fact_1033_not__less__eq,axiom,
! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
<=> ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
thf(fact_1034_Suc__n__not__le__n,axiom,
! [N: nat] :
~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
thf(fact_1035_not__less__eq__eq,axiom,
! [M: nat,N: nat] :
( ~ ( ord_less_eq_nat @ M @ N )
<=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
thf(fact_1036_le__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
<=> ( ( ord_less_eq_nat @ M @ N )
| ( M
= ( suc @ N ) ) ) ) ).
thf(fact_1037_Suc__le__mono,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
<=> ( ord_less_eq_nat @ N @ M ) ) ).
thf(fact_1038_le__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
thf(fact_1039_le__SucE,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_eq_nat @ M @ N )
=> ( M
= ( suc @ N ) ) ) ) ).
thf(fact_1040_Suc__leD,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
thf(fact_1041_less__or__eq__imp__le,axiom,
! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) ).
thf(fact_1042_le__neq__implies__less,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) ).
thf(fact_1043_less__imp__le__nat,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
thf(fact_1044_le__eq__less__or__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
<=> ( ( ord_less_nat @ M @ N )
| ( M = N ) ) ) ).
thf(fact_1045_nat__less__le,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
<=> ( ( ord_less_eq_nat @ M @ N )
& ( M != N ) ) ) ).
thf(fact_1046_less__eq__Suc__le,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
<=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
thf(fact_1047_less__Suc__eq__le,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
<=> ( ord_less_eq_nat @ M @ N ) ) ).
thf(fact_1048_Suc__le__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
<=> ( ord_less_nat @ M @ N ) ) ).
thf(fact_1049_le__imp__less__Suc,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
thf(fact_1050_Suc__leI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
thf(fact_1051_le__less__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
<=> ( N = M ) ) ) ).
thf(fact_1052_Suc__le__lessD,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) ).
thf(fact_1053_inc__induct,axiom,
! [P: nat > $o,I_1: nat,J: nat] :
( ( ord_less_eq_nat @ I_1 @ J )
=> ( ( P @ J )
=> ( ! [I: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( P @ ( suc @ I ) )
=> ( P @ I ) ) )
=> ( P @ I_1 ) ) ) ) ).
thf(fact_1054_less__eq__nat_Osimps_I2_J,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
<=> ( nat_case_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
thf(fact_1055_less__mono__imp__le__mono,axiom,
! [I_1: nat,J: nat,F: nat > nat] :
( ! [I: nat,J_1: nat] :
( ( ord_less_nat @ I @ J_1 )
=> ( ord_less_nat @ ( F @ I ) @ ( F @ J_1 ) ) )
=> ( ( ord_less_eq_nat @ I_1 @ J )
=> ( ord_less_eq_nat @ ( F @ I_1 ) @ ( F @ J ) ) ) ) ).
thf(fact_1056_Suc__le__D,axiom,
! [N: nat,M_3: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ M_3 )
=> ? [M_1: nat] :
( M_3
= ( suc @ M_1 ) ) ) ).
thf(fact_1057_lessE,axiom,
! [I_1: nat,K: nat] :
( ( ord_less_nat @ I_1 @ K )
=> ( ( K
!= ( suc @ I_1 ) )
=> ~ ! [J_1: nat] :
( ( ord_less_nat @ I_1 @ J_1 )
=> ( K
!= ( suc @ J_1 ) ) ) ) ) ).
thf(fact_1058_Suc__lessE,axiom,
! [I_1: nat,K: nat] :
( ( ord_less_nat @ ( suc @ I_1 ) @ K )
=> ~ ! [J_1: nat] :
( ( ord_less_nat @ I_1 @ J_1 )
=> ( K
!= ( suc @ J_1 ) ) ) ) ).
thf(fact_1059_termination__basic__simps_I1_J,axiom,
! [Z: nat,X: nat,Y: nat] :
( ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
thf(fact_1060_termination__basic__simps_I2_J,axiom,
! [Y: nat,X: nat,Z: nat] :
( ( ord_less_nat @ X @ Z )
=> ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
thf(fact_1061_add__lessD1,axiom,
! [I_1: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J ) @ K )
=> ( ord_less_nat @ I_1 @ K ) ) ).
thf(fact_1062_less__add__eq__less,axiom,
! [M: nat,N: nat,K: nat,L: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) ).
thf(fact_1063_add__less__mono,axiom,
! [K: nat,L: nat,I_1: nat,J: nat] :
( ( ord_less_nat @ I_1 @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
thf(fact_1064_add__less__mono1,axiom,
! [K: nat,I_1: nat,J: nat] :
( ( ord_less_nat @ I_1 @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
thf(fact_1065_trans__less__add2,axiom,
! [M: nat,I_1: nat,J: nat] :
( ( ord_less_nat @ I_1 @ J )
=> ( ord_less_nat @ I_1 @ ( plus_plus_nat @ M @ J ) ) ) ).
thf(fact_1066_trans__less__add1,axiom,
! [M: nat,I_1: nat,J: nat] :
( ( ord_less_nat @ I_1 @ J )
=> ( ord_less_nat @ I_1 @ ( plus_plus_nat @ J @ M ) ) ) ).
thf(fact_1067_nat__add__left__cancel__less,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
<=> ( ord_less_nat @ M @ N ) ) ).
thf(fact_1068_not__add__less2,axiom,
! [J: nat,I_1: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I_1 ) @ I_1 ) ).
thf(fact_1069_not__add__less1,axiom,
! [I_1: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J ) @ I_1 ) ).
thf(fact_1070_termination__basic__simps_I3_J,axiom,
! [Z: nat,X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
thf(fact_1071_termination__basic__simps_I4_J,axiom,
! [Y: nat,X: nat,Z: nat] :
( ( ord_less_eq_nat @ X @ Z )
=> ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
thf(fact_1072_le__add2,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
thf(fact_1073_le__add1,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
thf(fact_1074_le__iff__add,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
<=> ? [K_1: nat] :
( N
= ( plus_plus_nat @ M @ K_1 ) ) ) ).
thf(fact_1075_nat__add__left__cancel__le,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
<=> ( ord_less_eq_nat @ M @ N ) ) ).
thf(fact_1076_trans__le__add1,axiom,
! [M: nat,I_1: nat,J: nat] :
( ( ord_less_eq_nat @ I_1 @ J )
=> ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ J @ M ) ) ) ).
thf(fact_1077_trans__le__add2,axiom,
! [M: nat,I_1: nat,J: nat] :
( ( ord_less_eq_nat @ I_1 @ J )
=> ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ M @ J ) ) ) ).
thf(fact_1078_add__le__mono1,axiom,
! [K: nat,I_1: nat,J: nat] :
( ( ord_less_eq_nat @ I_1 @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
thf(fact_1079_add__le__mono,axiom,
! [K: nat,L: nat,I_1: nat,J: nat] :
( ( ord_less_eq_nat @ I_1 @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
thf(fact_1080_add__leD2,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ K @ N ) ) ).
thf(fact_1081_add__leD1,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
thf(fact_1082_add__leE,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ~ ( ( ord_less_eq_nat @ M @ N )
=> ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
thf(fact_1083_add__Suc__right,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ M @ ( suc @ N ) )
= ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
thf(fact_1084_add__Suc,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M ) @ N )
= ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
thf(fact_1085_add__Suc__shift,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M ) @ N )
= ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
thf(fact_1086_min__Suc__Suc,axiom,
! [M: nat,N: nat] :
( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
thf(fact_1087_nat__add__right__cancel,axiom,
! [M: nat,K: nat,N: nat] :
( ( ( plus_plus_nat @ M @ K )
= ( plus_plus_nat @ N @ K ) )
<=> ( M = N ) ) ).
thf(fact_1088_nat__add__left__cancel,axiom,
! [K: nat,M: nat,N: nat] :
( ( ( plus_plus_nat @ K @ M )
= ( plus_plus_nat @ K @ N ) )
<=> ( M = N ) ) ).
thf(fact_1089_nat__add__assoc,axiom,
! [M: nat,N: nat,K: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ M @ N ) @ K )
= ( plus_plus_nat @ M @ ( plus_plus_nat @ N @ K ) ) ) ).
thf(fact_1090_nat__add__left__commute,axiom,
! [X: nat,Y: nat,Z: nat] :
( ( plus_plus_nat @ X @ ( plus_plus_nat @ Y @ Z ) )
= ( plus_plus_nat @ Y @ ( plus_plus_nat @ X @ Z ) ) ) ).
thf(fact_1091_nat__add__commute,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ M @ N )
= ( plus_plus_nat @ N @ M ) ) ).
thf(fact_1092_less__iff__Suc__add,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
<=> ? [K_1: nat] :
( N
= ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
thf(fact_1093_less__add__Suc2,axiom,
! [I_1: nat,M: nat] : ( ord_less_nat @ I_1 @ ( suc @ ( plus_plus_nat @ M @ I_1 ) ) ) ).
thf(fact_1094_less__add__Suc1,axiom,
! [I_1: nat,M: nat] : ( ord_less_nat @ I_1 @ ( suc @ ( plus_plus_nat @ I_1 @ M ) ) ) ).
thf(fact_1095_mono__nat__linear__lb,axiom,
! [M: nat,K: nat,F: nat > nat] :
( ! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
=> ( ord_less_nat @ ( F @ M_1 ) @ ( F @ N_1 ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
thf(fact_1096_less__imp__Suc__add,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ? [K_1: nat] :
( N
= ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
thf(fact_1097_weak__decr__stable,axiom,
! [F: nat > nat] :
( ! [I: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ I ) ) @ ( F @ I ) )
=> ? [I: nat] :
! [K_1: nat] :
( ( F @ ( plus_plus_nat @ I @ K_1 ) )
= ( F @ I ) ) ) ).
thf(fact_1098_less__zeroE,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
thf(fact_1099_le0,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
thf(fact_1100_zero__less__Suc,axiom,
! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
thf(fact_1101_nat__diff__split,axiom,
! [P: nat > $o,A: nat,B: nat] :
( ( P @ ( minus_minus_nat @ A @ B ) )
<=> ( ( ( ord_less_nat @ A @ B )
=> ( P @ zero_zero_nat ) )
& ! [D: nat] :
( ( A
= ( plus_plus_nat @ B @ D ) )
=> ( P @ D ) ) ) ) ).
thf(fact_1102_nat__diff__split__asm,axiom,
! [P: nat > $o,A: nat,B: nat] :
( ( P @ ( minus_minus_nat @ A @ B ) )
<=> ~ ( ( ( ord_less_nat @ A @ B )
& ~ ( P @ zero_zero_nat ) )
| ? [D: nat] :
( ( A
= ( plus_plus_nat @ B @ D ) )
& ~ ( P @ D ) ) ) ) ).
thf(fact_1103_add__eq__self__zero,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= M )
=> ( N = zero_zero_nat ) ) ).
thf(fact_1104_min__diff,axiom,
! [M: nat,I_1: nat,N: nat] :
( ( ord_min_nat @ ( minus_minus_nat @ M @ I_1 ) @ ( minus_minus_nat @ N @ I_1 ) )
= ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I_1 ) ) ).
thf(fact_1105_diff__cancel2,axiom,
! [M: nat,K: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ).
thf(fact_1106_diff__cancel,axiom,
! [K: nat,M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( minus_minus_nat @ M @ N ) ) ).
thf(fact_1107_diff__diff__left,axiom,
! [I_1: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J ) @ K )
= ( minus_minus_nat @ I_1 @ ( plus_plus_nat @ J @ K ) ) ) ).
thf(fact_1108_diff__add__inverse,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
= M ) ).
thf(fact_1109_diff__add__inverse2,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
= M ) ).
thf(fact_1110_add__is__0,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= zero_zero_nat )
<=> ( ( M = zero_zero_nat )
& ( N = zero_zero_nat ) ) ) ).
thf(fact_1111_diff__add__0,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
= zero_zero_nat ) ).
thf(fact_1112_Nat_Oadd__0__right,axiom,
! [M: nat] :
( ( plus_plus_nat @ M @ zero_zero_nat )
= M ) ).
thf(fact_1113_min__0R,axiom,
! [N: nat] :
( ( ord_min_nat @ N @ zero_zero_nat )
= zero_zero_nat ) ).
thf(fact_1114_plus__nat_Oadd__0,axiom,
! [N: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N )
= N ) ).
thf(fact_1115_min__0L,axiom,
! [N: nat] :
( ( ord_min_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ).
thf(fact_1116_Suc__pred,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
= N ) ) ).
thf(fact_1117_diff__Suc__less,axiom,
! [I_1: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I_1 ) ) @ N ) ) ).
thf(fact_1118_gr0I,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
thf(fact_1119_diff__less__mono2,axiom,
! [L: nat,M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ord_less_nat @ M @ L )
=> ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
thf(fact_1120_less__imp__diff__less,axiom,
! [N: nat,J: nat,K: nat] :
( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
thf(fact_1121_gr__implies__not0,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) ).
thf(fact_1122_diff__less,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_nat @ zero_zero_nat @ M )
=> ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
thf(fact_1123_less__nat__zero__code,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
thf(fact_1124_zero__less__diff,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
<=> ( ord_less_nat @ M @ N ) ) ).
thf(fact_1125_neq0__conv,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
<=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
thf(fact_1126_not__less0,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
thf(fact_1127_less__eq__nat_Osimps_I1_J,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
thf(fact_1128_le__0__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
<=> ( N = zero_zero_nat ) ) ).
thf(fact_1129_diff__le__self,axiom,
! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
thf(fact_1130_diff__is__0__eq,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
<=> ( ord_less_eq_nat @ M @ N ) ) ).
thf(fact_1131_diff__is__0__eq_H,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ) ).
thf(fact_1132_diff__le__mono2,axiom,
! [L: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
thf(fact_1133_diff__le__mono,axiom,
! [L: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
thf(fact_1134_diff__diff__cancel,axiom,
! [I_1: nat,N: nat] :
( ( ord_less_eq_nat @ I_1 @ N )
=> ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I_1 ) )
= I_1 ) ) ).
thf(fact_1135_eq__diff__iff,axiom,
! [N: nat,K: nat,M: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ( minus_minus_nat @ M @ K )
= ( minus_minus_nat @ N @ K ) )
<=> ( M = N ) ) ) ) ).
thf(fact_1136_Nat_Odiff__diff__eq,axiom,
! [N: nat,K: nat,M: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ) ) ).
thf(fact_1137_le__diff__iff,axiom,
! [N: nat,K: nat,M: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
<=> ( ord_less_eq_nat @ M @ N ) ) ) ) ).
thf(fact_1138_Zero__not__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
thf(fact_1139_nat_Osimps_I2_J,axiom,
! [Nat_3: nat] :
( zero_zero_nat
!= ( suc @ Nat_3 ) ) ).
thf(fact_1140_Suc__not__Zero,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) ).
thf(fact_1141_nat_Osimps_I3_J,axiom,
! [Nat_2: nat] :
( ( suc @ Nat_2 )
!= zero_zero_nat ) ).
thf(fact_1142_diff__Suc__Suc,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( minus_minus_nat @ M @ N ) ) ).
thf(fact_1143_Suc__diff__diff,axiom,
! [M: nat,N: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
= ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
thf(fact_1144_Zero__neq__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
thf(fact_1145_Suc__neq__Zero,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) ).
thf(fact_1146_diffs0__imp__equal,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ N @ M )
= zero_zero_nat )
=> ( M = N ) ) ) ).
thf(fact_1147_diff__commute,axiom,
! [I_1: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J ) @ K )
= ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ K ) @ J ) ) ).
thf(fact_1148_diff__self__eq__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) ).
thf(fact_1149_minus__nat_Odiff__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ zero_zero_nat )
= M ) ).
thf(fact_1150_diff__0__eq__0,axiom,
! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ).
thf(fact_1151_diff__Suc,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ M @ ( suc @ N ) )
= ( nat_case_nat @ zero_zero_nat
@ ^ [K_1: nat] : K_1
@ ( minus_minus_nat @ M @ N ) ) ) ).
thf(fact_1152_diff__add__assoc2,axiom,
! [I_1: nat,K: nat,J: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I_1 ) @ K )
= ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I_1 ) ) ) ).
thf(fact_1153_add__diff__assoc2,axiom,
! [I_1: nat,K: nat,J: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I_1 )
= ( minus_minus_nat @ ( plus_plus_nat @ J @ I_1 ) @ K ) ) ) ).
thf(fact_1154_diff__add__assoc,axiom,
! [I_1: nat,K: nat,J: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J ) @ K )
= ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
thf(fact_1155_le__imp__diff__is__add,axiom,
! [K: nat,I_1: nat,J: nat] :
( ( ord_less_eq_nat @ I_1 @ J )
=> ( ( ( minus_minus_nat @ J @ I_1 )
= K )
<=> ( J
= ( plus_plus_nat @ K @ I_1 ) ) ) ) ).
thf(fact_1156_le__add__diff__inverse2,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ M @ N ) @ N )
= M ) ) ).
thf(fact_1157_le__diff__conv2,axiom,
! [I_1: nat,K: nat,J: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_eq_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
<=> ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ) ).
thf(fact_1158_add__diff__assoc,axiom,
! [I_1: nat,K: nat,J: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J ) @ K ) ) ) ).
thf(fact_1159_le__add__diff__inverse,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
= M ) ) ).
thf(fact_1160_le__add__diff,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ K @ N )
=> ( ord_less_eq_nat @ M @ ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ K ) ) ) ).
thf(fact_1161_le__diff__conv,axiom,
! [J: nat,K: nat,I_1: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I_1 )
<=> ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I_1 @ K ) ) ) ).
thf(fact_1162_diff__diff__right,axiom,
! [I_1: nat,K: nat,J: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ) ).
thf(fact_1163_diff__less__mono,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
thf(fact_1164_less__diff__iff,axiom,
! [N: nat,K: nat,M: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
<=> ( ord_less_nat @ M @ N ) ) ) ) ).
thf(fact_1165_Suc__diff__le,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( minus_minus_nat @ ( suc @ M ) @ N )
= ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
thf(fact_1166_less__diff__conv,axiom,
! [I_1: nat,J: nat,K: nat] :
( ( ord_less_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
<=> ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ).
thf(fact_1167_add__diff__inverse,axiom,
! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
=> ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
= M ) ) ).
thf(fact_1168_diff__less__Suc,axiom,
! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
thf(fact_1169_less__Suc__eq__0__disj,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
<=> ( ( M = zero_zero_nat )
| ? [J_1: nat] :
( ( M
= ( suc @ J_1 ) )
& ( ord_less_nat @ J_1 @ N ) ) ) ) ).
thf(fact_1170_less__Suc0,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
<=> ( N = zero_zero_nat ) ) ).
thf(fact_1171_gr0__conv__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
<=> ? [M_1: nat] :
( N
= ( suc @ M_1 ) ) ) ).
thf(fact_1172_one__is__add,axiom,
! [M: nat,N: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ M @ N ) )
<=> ( ( ( M
= ( suc @ zero_zero_nat ) )
& ( N = zero_zero_nat ) )
| ( ( M = zero_zero_nat )
& ( N
= ( suc @ zero_zero_nat ) ) ) ) ) ).
thf(fact_1173_add__is__1,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= ( suc @ zero_zero_nat ) )
<=> ( ( ( M
= ( suc @ zero_zero_nat ) )
& ( N = zero_zero_nat ) )
| ( ( M = zero_zero_nat )
& ( N
= ( suc @ zero_zero_nat ) ) ) ) ) ).
thf(fact_1174_add__gr__0,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ M )
| ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
thf(fact_1175_min__Suc1,axiom,
! [N: nat,M: nat] :
( ( ord_min_nat @ ( suc @ N ) @ M )
= ( nat_case_nat @ zero_zero_nat
@ ^ [M_2: nat] : ( suc @ ( ord_min_nat @ N @ M_2 ) )
@ M ) ) ).
thf(fact_1176_min__Suc2,axiom,
! [M: nat,N: nat] :
( ( ord_min_nat @ M @ ( suc @ N ) )
= ( nat_case_nat @ zero_zero_nat
@ ^ [M_2: nat] : ( suc @ ( ord_min_nat @ M_2 @ N ) )
@ M ) ) ).
thf(fact_1177_diff__Suc__diff__eq1,axiom,
! [M: nat,K: nat,J: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ M @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
= ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( suc @ J ) ) ) ) ).
thf(fact_1178_diff__Suc__diff__eq2,axiom,
! [M: nat,K: nat,J: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ M )
= ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ M ) ) ) ) ).
thf(fact_1179_ex__least__nat__le,axiom,
! [N: nat,P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ( P @ N )
=> ? [K_1: nat] :
( ( ord_less_eq_nat @ K_1 @ N )
& ! [I: nat] :
( ( ord_less_nat @ I @ K_1 )
=> ~ ( P @ I ) )
& ( P @ K_1 ) ) ) ) ).
thf(fact_1180_less__imp__add__positive,axiom,
! [I_1: nat,J: nat] :
( ( ord_less_nat @ I_1 @ J )
=> ? [K_1: nat] :
( ( ord_less_nat @ zero_zero_nat @ K_1 )
& ( ( plus_plus_nat @ I_1 @ K_1 )
= J ) ) ) ).
thf(fact_1181_gr0__implies__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M_1: nat] :
( N
= ( suc @ M_1 ) ) ) ).
thf(fact_1182_nat_Osize_I2_J,axiom,
! [Nat: nat] :
( ( nat_size @ ( suc @ Nat ) )
= ( plus_plus_nat @ ( nat_size @ Nat ) @ ( suc @ zero_zero_nat ) ) ) ).
thf(fact_1183_nat_Osize_I1_J,axiom,
( ( nat_size @ zero_zero_nat )
= zero_zero_nat ) ).
thf(fact_1184_zero__induct__lemma,axiom,
! [I_1: nat,P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N_1: nat] :
( ( P @ ( suc @ N_1 ) )
=> ( P @ N_1 ) )
=> ( P @ ( minus_minus_nat @ K @ I_1 ) ) ) ) ).
thf(fact_1185_not0__implies__Suc,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M_1: nat] :
( N
= ( suc @ M_1 ) ) ) ).
thf(fact_1186_nat__induct,axiom,
! [N: nat,P: nat > $o] :
( ( P @ zero_zero_nat )
=> ( ! [N_1: nat] :
( ( P @ N_1 )
=> ( P @ ( suc @ N_1 ) ) )
=> ( P @ N ) ) ) ).
thf(fact_1187_nat_Oexhaust,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat_1: nat] :
( Y
!= ( suc @ Nat_1 ) ) ) ).
thf(fact_1188_zero__induct,axiom,
! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N_1: nat] :
( ( P @ ( suc @ N_1 ) )
=> ( P @ N_1 ) )
=> ( P @ zero_zero_nat ) ) ) ).
thf(fact_1189_nat_Osize_I4_J,axiom,
! [Nat: nat] :
( ( size_size_nat @ ( suc @ Nat ) )
= ( plus_plus_nat @ ( size_size_nat @ Nat ) @ ( suc @ zero_zero_nat ) ) ) ).
thf(fact_1190_nat_Osize_I3_J,axiom,
( ( size_size_nat @ zero_zero_nat )
= zero_zero_nat ) ).
thf(fact_1191_nat__size,axiom,
! [N: nat] :
( ( size_size_nat @ N )
= N ) ).
thf(fact_1192_One__nat__def,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ) ).
thf(fact_1193_Suc__eq__plus1,axiom,
! [N: nat] :
( ( suc @ N )
= ( plus_plus_nat @ N @ one_one_nat ) ) ).
thf(fact_1194_Suc__eq__plus1__left,axiom,
! [N: nat] :
( ( suc @ N )
= ( plus_plus_nat @ one_one_nat @ N ) ) ).
thf(fact_1195_diff__Suc__1,axiom,
! [N: nat] :
( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
= N ) ).
thf(fact_1196_diff__Suc__eq__diff__pred,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ M @ ( suc @ N ) )
= ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
thf(fact_1197_Suc__pred_H,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( N
= ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
thf(fact_1198_Suc__diff__1,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
= N ) ) ).
thf(fact_1199_add__eq__if,axiom,
! [N: nat,M: nat] :
( ( ( M = zero_zero_nat )
=> ( ( plus_plus_nat @ M @ N )
= N ) )
& ( ( M != zero_zero_nat )
=> ( ( plus_plus_nat @ M @ N )
= ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ) ) ) ).
%----Helper facts (5)
thf(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____pi,axiom,
! [X: list_A1402527603le_alt,Y: list_A1402527603le_alt] :
( ~ ( fequal68576820le_alt @ X @ Y )
| ( X = Y ) ) ).
thf(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____pi,axiom,
! [X: list_A1402527603le_alt,Y: list_A1402527603le_alt] :
( ( X != Y )
| ( fequal68576820le_alt @ X @ Y ) ) ).
thf(help_If_1_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
! [X: produc2069254453le_alt,Y: produc2069254453le_alt] :
( ( if_Pro1021494213le_alt @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
! [X: produc2069254453le_alt,Y: produc2069254453le_alt] :
( ( if_Pro1021494213le_alt @ $false @ X @ Y )
= Y ) ).
thf(help_If_3_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
! [I: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ ( p @ I ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ a @ c ) @ ( arrow_1865170000_below @ ( p @ I ) @ c @ b ) ) ) ).
%------------------------------------------------------------------------------