TPTP Problem File: SCT171^3.p
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%------------------------------------------------------------------------------
% File : SCT171^3 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 309, 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_l309 [Bla11]
% Status : ContradictoryAxioms
% Rating : 0.40 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% Syntax : Number of formulae : 1366 ( 128 unt; 162 typ; 0 def)
% Number of atoms : 4053 ( 520 equ; 6 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 11191 ( 319 ~; 51 |; 97 &;8542 @)
% ( 243 <=>;1939 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 5404 (5404 >; 0 *; 0 +; 0 <<)
% Number of symbols : 161 ( 157 usr; 12 con; 0-4 aty)
% Number of variables : 3694 ( 90 ^;3583 !; 21 ?;3694 :)
% SPC : TH0_CAX_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 19:54:54
%------------------------------------------------------------------------------
%----Should-be-implicit typings (5)
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__Nat__Onat,type,
nat: $tType ).
thf(ty_ty_tc__Product____Type__Ounit,type,
product_unit: $tType ).
thf(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_Mtc__Arrow__,type,
produc1572197287le_alt: $tType ).
%----Explicit typings (157)
thf(sy_c_All,type,
all: ( produc1572197287le_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_Big__Operators_Ocomm__monoid__add__class_Osetsum_000tc__Nat__Onat_000tc__Na,type,
big_co387207925at_nat: ( nat > nat ) > ( nat > $o ) > nat ).
thf(sy_c_Finite__Set_Ocard_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
finite2011930979e_indi: ( arrow_1196572341e_indi > $o ) > nat ).
thf(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
finite_card_nat: ( nat > $o ) > nat ).
thf(sy_c_Finite__Set_Ocard_000tc__Product____Type__Ounit,type,
finite1949902593t_unit: ( product_unit > $o ) > nat ).
thf(sy_c_Finite__Set_Ofinite_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi,type,
finite431949602e_indi: ( arrow_1196572341e_indi > $o ) > $o ).
thf(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
finite_finite_nat: ( nat > $o ) > $o ).
thf(sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000tc_,type,
inj_on1505595958di_nat: ( arrow_1196572341e_indi > nat ) > ( arrow_1196572341e_indi > $o ) > $o ).
thf(sy_c_Fun_Oinj__on_000tc__Nat__Onat_000tc__Nat__Onat,type,
inj_on_nat_nat: ( nat > nat ) > ( nat > $o ) > $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_001,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_002,type,
pi_Arr2096782767t_unit: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit ) > $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_003,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_004,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_005,type,
pi_Arr509685723t_unit: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit ) > $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_006,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_007,type,
pi_Pro30504752t_unit: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( produc1572197287le_alt > $o ) > product_unit ) > $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__Nat__Onat,type,
pi_o_nat: ( $o > $o ) > ( $o > nat > $o ) > ( $o > nat ) > $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__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_008,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_009,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_Arr778514268di_nat: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > nat > $o ) > ( arrow_1196572341e_indi > nat ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000tc___010,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_Eo,type,
pi_nat_o: ( nat > $o ) > ( nat > $o > $o ) > ( nat > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____piyeccgg,type,
pi_nat986275508e_indi: ( nat > $o ) > ( nat > arrow_1196572341e_indi > $o ) > ( nat > arrow_1196572341e_indi ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Product____Type__Ounit,type,
pi_nat_Product_unit: ( nat > $o ) > ( nat > product_unit > $o ) > ( nat > product_unit ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_I_062_Itc__Arrow____Order,type,
pi_Pro443817391_alt_o: ( product_unit > $o ) > ( product_unit > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_Itc__Arrow____Order____Mi,type,
pi_Pro1959068871_alt_o: ( product_unit > $o ) > ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_Itc__prod_Itc__Arrow____O,type,
pi_Pro29851292_alt_o: ( product_unit > $o ) > ( product_unit > ( produc1572197287le_alt > $o ) > $o ) > ( product_unit > produc1572197287le_alt > $o ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__Nat__Onat,type,
pi_Product_unit_nat: ( product_unit > $o ) > ( product_unit > nat > $o ) > ( product_unit > nat ) > $o ).
thf(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__prod_Itc__Arrow____Order__,type,
pi_Pro772884595le_alt: ( product_unit > $o ) > ( product_unit > produc1572197287le_alt > $o ) > ( product_unit > 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_011,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_012,type,
pi_Pro926528371t_unit: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > product_unit > $o ) > ( produc1572197287le_alt > product_unit ) > $o ).
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_Otimes__class_Otimes_000tc__Nat__Onat,type,
times_times_nat: nat > nat > nat ).
thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
zero_zero_nat: nat ).
thf(sy_c_HOL_Obool_Obool__size,type,
bool_size: $o > nat ).
thf(sy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____piyeccggrh,type,
hilber1125280539di_nat: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > nat ) > nat > arrow_1196572341e_indi ).
thf(sy_c_Hilbert__Choice_Oinv__into_000tc__Nat__Onat_000tc__Nat__Onat,type,
hilber195283148at_nat: ( nat > $o ) > ( nat > nat ) > nat > nat ).
thf(sy_c_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_M,type,
if_Pro278423000_alt_o: $o > ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Nat__Onat_M_Eo_J,type,
semila848761471_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
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__size,type,
nat_size: nat > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__Nat__Onat,type,
size_size_nat: nat > nat ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_I_062_I_062_Itc__Arrow____Order____Mira,type,
ord_le1382328578lt_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_000_062_I_062_Itc__Arrow____Order____Mirabelle_,type,
ord_le914873172lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__prod_Itc__Arrow____Order____,type,
ord_le874404799lt_o_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Arrow____Order____Mirabelle____piy,type,
ord_le1339521307_alt_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Arrow____Order____Mirabelle____piy_013,type,
ord_le1991507760indi_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Nat__Onat_M_Eo_J,type,
ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Product____Type__Ounit_M_Eo_J,type,
ord_le232288914unit_o: ( product_unit > $o ) > ( product_unit > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__prod_Itc__Arrow____Order____Mirabe,type,
ord_le1852932542_alt_o: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_000_Eo,type,
ord_less_o: $o > $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 ).
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thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle____014,type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle____015,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,
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thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Product____Type__Ounit_M_Eo_J,type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__Arrow____Order____Mi,type,
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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_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,
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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_to1627321279_alt_o: arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____piye_016,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__Product____Type__Ounit_M_Eo_J,type,
top_to1984820022unit_o: product_unit > $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_Eo,type,
top_top_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_SetInterval_Oord__class_OatLeastAtMost_000tc__Nat__Onat,type,
ord_at238088361st_nat: nat > nat > nat > $o ).
thf(sy_c_SetInterval_Oord__class_OatLeastLessThan_000tc__Nat__Onat,type,
ord_at4362885an_nat: nat > nat > nat > $o ).
thf(sy_c_SetInterval_Oord__class_OatLeast_000tc__Nat__Onat,type,
ord_atLeast_nat: nat > nat > $o ).
thf(sy_c_SetInterval_Oord__class_OgreaterThanAtMost_000tc__Nat__Onat,type,
ord_gr375877188st_nat: nat > nat > nat > $o ).
thf(sy_c_SetInterval_Oord__class_OgreaterThanLessThan_000tc__Nat__Onat,type,
ord_gr660468384an_nat: nat > nat > nat > $o ).
thf(sy_c_SetInterval_Oord__class_OgreaterThan_000tc__Nat__Onat,type,
ord_greaterThan_nat: nat > nat > $o ).
thf(sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
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thf(sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_,type,
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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__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__Product____Type__Ounit,type,
collect_Product_unit: ( product_unit > $o ) > product_unit > $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_Set_Oimage_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000tc__N,type,
image_1011045538di_nat: ( arrow_1196572341e_indi > nat ) > ( arrow_1196572341e_indi > $o ) > nat > $o ).
thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Nat__Onat,type,
image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__,type,
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thf(sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh___017,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___018,type,
member1043380889t_unit: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit ) > $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__019,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__020,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__021,type,
member1537523201t_unit: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit ) > $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_022,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_023,type,
member1092867670t_unit: ( ( produc1572197287le_alt > $o ) > product_unit ) > ( ( ( produc1572197287le_alt > $o ) > product_unit ) > $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__Nat__Onat_J,type,
member_o_nat: ( $o > nat ) > ( ( $o > nat ) > $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__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__024,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__025,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__N,type,
member1842285448di_nat: ( arrow_1196572341e_indi > nat ) > ( ( arrow_1196572341e_indi > nat ) > $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_Eo_J,type,
member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle____piyeccggr,type,
member1113138010e_indi: ( nat > arrow_1196572341e_indi ) > ( ( nat > arrow_1196572341e_indi ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J,type,
member616671224t_unit: ( nat > product_unit ) > ( ( nat > product_unit ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_I_062_Itc__Arrow____Order_,type,
member1888392857_alt_o: ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_Itc__Arrow____Order____Mir,type,
member2021528307_alt_o: ( product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_Itc__prod_Itc__Arrow____Or,type,
member1295651272_alt_o: ( product_unit > produc1572197287le_alt > $o ) > ( ( product_unit > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J,type,
member1827227242it_nat: ( product_unit > nat ) > ( ( product_unit > nat ) > $o ) > $o ).
thf(sy_c_member_000_062_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow____Order___,type,
member1161214429le_alt: ( product_unit > produc1572197287le_alt ) > ( ( product_unit > 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_026,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_027,type,
member44534621t_unit: ( produc1572197287le_alt > product_unit ) > ( ( produc1572197287le_alt > product_unit ) > $o ) > $o ).
thf(sy_c_member_000_Eo,type,
member_o: $o > ( $o > $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__Nat__Onat,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(sy_c_member_000tc__Product____Type__Ounit,type,
member_Product_unit: product_unit > ( product_unit > $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_v_F,type,
f: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(sy_v_Lab____,type,
lab: produc1572197287le_alt > $o ).
thf(sy_v_Lba____,type,
lba: 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 ).
thf(sy_v_d____,type,
d: arrow_1389031998le_alt ).
thf(sy_v_e____,type,
e: arrow_1389031998le_alt ).
thf(sy_v_h____,type,
h: arrow_1196572341e_indi > nat ).
thf(sy_v_n____,type,
n: nat ).
%----Relevant facts (1200)
thf(fact_0_assms_I3_J,axiom,
arrow_1955289568le_IIA @ f ).
thf(fact_1_u,axiom,
arrow_1282657667nimity @ f ).
thf(fact_2__096c_A_126_061_Ad_096,axiom,
c != d ).
thf(fact_3__096P_A_058_AProf_096,axiom,
member822980838_alt_o @ p @ arrow_1647925946e_Prof ).
thf(fact_4_in__mkbot,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_2: produc1572197287le_alt > $o,Z: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_1821416136_mkbot @ L_2 @ Z ) )
<=> ( ( Y != Z )
& ( ( X = Z )
=> ( X != Y ) )
& ( ( X != Z )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_2 ) ) ) ) ).
thf(fact_5_in__mktop,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_2: produc1572197287le_alt > $o,Z: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_1970123222_mktop @ L_2 @ Z ) )
<=> ( ( X != Z )
& ( ( Y = Z )
=> ( X != Y ) )
& ( ( Y != Z )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_2 ) ) ) ) ).
thf(fact_6__C2_C,axiom,
! [P_8: arrow_1196572341e_indi > produc1572197287le_alt > $o,P_7: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_91: arrow_1389031998le_alt,B_72: arrow_1389031998le_alt,A_90: arrow_1389031998le_alt,B_71: arrow_1389031998le_alt] :
( ( A_90 != B_71 )
=> ( ( A_91 != B_72 )
=> ( ( A_90 != B_72 )
=> ( ( B_71 != A_91 )
=> ( ( member822980838_alt_o @ P_7 @ arrow_1647925946e_Prof )
=> ( ( member822980838_alt_o @ P_8 @ arrow_1647925946e_Prof )
=> ( ! [I_1: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( P_7 @ I_1 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_91 @ B_72 ) @ ( P_8 @ I_1 ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( f @ P_7 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_91 @ B_72 ) @ ( f @ P_8 ) ) ) ) ) ) ) ) ) ) ).
thf(fact_7__C1_C,axiom,
! [P_8: arrow_1196572341e_indi > produc1572197287le_alt > $o,P_7: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_91: arrow_1389031998le_alt,B_72: arrow_1389031998le_alt,A_90: arrow_1389031998le_alt,B_71: arrow_1389031998le_alt] :
( ( A_90 != B_71 )
=> ( ( A_91 != B_72 )
=> ( ( A_90 != B_72 )
=> ( ( B_71 != A_91 )
=> ( ( member822980838_alt_o @ P_7 @ arrow_1647925946e_Prof )
=> ( ( member822980838_alt_o @ P_8 @ arrow_1647925946e_Prof )
=> ( ! [I_1: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( P_7 @ I_1 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_91 @ B_72 ) @ ( P_8 @ I_1 ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( f @ P_7 ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_91 @ B_72 ) @ ( f @ P_8 ) ) ) ) ) ) ) ) ) ) ).
thf(fact_8__C4_C,axiom,
! [P_8: arrow_1196572341e_indi > produc1572197287le_alt > $o,P_7: arrow_1196572341e_indi > produc1572197287le_alt > $o,C_42: arrow_1389031998le_alt,A_90: arrow_1389031998le_alt,B_71: arrow_1389031998le_alt] :
( ( A_90 != B_71 )
=> ( ( B_71 != C_42 )
=> ( ( A_90 != C_42 )
=> ( ( member822980838_alt_o @ P_7 @ arrow_1647925946e_Prof )
=> ( ( member822980838_alt_o @ P_8 @ arrow_1647925946e_Prof )
=> ( ! [I_1: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( P_7 @ I_1 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ B_71 @ C_42 ) @ ( P_8 @ I_1 ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( f @ P_7 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ B_71 @ C_42 ) @ ( f @ P_8 ) ) ) ) ) ) ) ) ) ).
thf(fact_9_pairwise__neutrality,axiom,
! [P_8: arrow_1196572341e_indi > produc1572197287le_alt > $o,P_7: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_91: arrow_1389031998le_alt,B_72: arrow_1389031998le_alt,A_90: arrow_1389031998le_alt,B_71: arrow_1389031998le_alt] :
( ( A_90 != B_71 )
=> ( ( A_91 != B_72 )
=> ( ( member822980838_alt_o @ P_7 @ arrow_1647925946e_Prof )
=> ( ( member822980838_alt_o @ P_8 @ arrow_1647925946e_Prof )
=> ( ! [I_1: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( P_7 @ I_1 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_91 @ B_72 ) @ ( P_8 @ I_1 ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( f @ P_7 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_91 @ B_72 ) @ ( f @ P_8 ) ) ) ) ) ) ) ) ).
thf(fact_10__C3_C,axiom,
! [P_8: arrow_1196572341e_indi > produc1572197287le_alt > $o,P_7: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_90: arrow_1389031998le_alt,B_71: arrow_1389031998le_alt] :
( ( A_90 != B_71 )
=> ( ( member822980838_alt_o @ P_7 @ arrow_1647925946e_Prof )
=> ( ( member822980838_alt_o @ P_8 @ arrow_1647925946e_Prof )
=> ( ! [I_1: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( P_7 @ I_1 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ B_71 @ A_90 ) @ ( P_8 @ I_1 ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_90 @ B_71 ) @ ( f @ P_7 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ B_71 @ A_90 ) @ ( f @ P_8 ) ) ) ) ) ) ) ).
thf(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
! [I_1: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( p @ I_1 ) )
<=> ( ( ( ord_less_nat @ ( h @ I_1 ) @ n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ I_1 ) @ n )
=> ( ( ( ( h @ I_1 )
= n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e ) ) )
& ( ( ( h @ I_1 )
!= n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) ) ) ) ).
thf(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( p @ ( hilber1125280539di_nat @ top_to54564308indi_o @ h @ n ) ) ).
thf(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ I_1 )
= n )
@ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) ) ).
thf(fact_14_PW,axiom,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ I_1 )
= n )
@ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) ) ) ).
thf(fact_15_split__paired__All,axiom,
! [P_6: produc1572197287le_alt > $o] :
( ( all @ P_6 )
<=> ! [A_76: arrow_1389031998le_alt,B_60: arrow_1389031998le_alt] : ( P_6 @ ( produc897867031le_alt @ A_76 @ B_60 ) ) ) ).
thf(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
( member822980838_alt_o
@ ^ [I_1: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ I_1 )
= n )
@ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) )
@ arrow_1647925946e_Prof ) ).
thf(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
( member285112084le_alt @ ( produc897867031le_alt @ c @ e )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ I_1 )
= n )
@ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) ) ).
thf(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
( member285112084le_alt @ ( produc897867031le_alt @ e @ d )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ I_1 )
= n )
@ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) ) ).
thf(fact_19_n_I1_J,axiom,
ord_less_nat @ n @ ( finite2011930979e_indi @ top_to54564308indi_o ) ).
thf(fact_20_injh,axiom,
inj_on1505595958di_nat @ h @ top_to54564308indi_o ).
thf(fact_21_Pair__inject,axiom,
! [A_89: arrow_1389031998le_alt,B_70: arrow_1389031998le_alt,A_88: arrow_1389031998le_alt,B_69: arrow_1389031998le_alt] :
( ( ( produc897867031le_alt @ A_89 @ B_70 )
= ( produc897867031le_alt @ A_88 @ B_69 ) )
=> ~ ( ( A_89 = A_88 )
=> ( B_70 != B_69 ) ) ) ).
thf(fact_22_Pair__eq,axiom,
! [A_87: arrow_1389031998le_alt,B_68: arrow_1389031998le_alt,A_86: arrow_1389031998le_alt,B_67: arrow_1389031998le_alt] :
( ( ( produc897867031le_alt @ A_87 @ B_68 )
= ( produc897867031le_alt @ A_86 @ B_67 ) )
<=> ( ( A_87 = A_86 )
& ( B_68 = B_67 ) ) ) ).
thf(fact_23_IIA__def,axiom,
! [F_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( arrow_1955289568le_IIA @ F_31 )
<=> ! [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_76: arrow_1389031998le_alt,B_60: arrow_1389031998le_alt] :
( ! [I_1: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ A_76 @ B_60 ) @ ( X_1 @ I_1 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_76 @ B_60 ) @ ( Xa @ I_1 ) ) )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_76 @ B_60 ) @ ( F_31 @ X_1 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ A_76 @ B_60 ) @ ( F_31 @ Xa ) ) ) ) ) ) ) ).
thf(fact_24_unanimity__def,axiom,
! [F_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( arrow_1282657667nimity @ F_31 )
<=> ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ arrow_1647925946e_Prof )
=> ! [A_76: arrow_1389031998le_alt,B_60: arrow_1389031998le_alt] :
( ! [I_1: arrow_1196572341e_indi] : ( member285112084le_alt @ ( produc897867031le_alt @ A_76 @ B_60 ) @ ( X_1 @ I_1 ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_76 @ B_60 ) @ ( F_31 @ X_1 ) ) ) ) ) ).
thf(fact_25_top1I,axiom,
! [X_69: produc1572197287le_alt > $o] : ( top_to1806834203lt_o_o @ X_69 ) ).
thf(fact_26_top1I,axiom,
! [X_69: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( top_to732317616lt_o_o @ X_69 ) ).
thf(fact_27_top1I,axiom,
! [X_69: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( top_to1492351398lt_o_o @ X_69 ) ).
thf(fact_28_top1I,axiom,
! [X_69: produc1572197287le_alt] : ( top_to558618722_alt_o @ X_69 ) ).
thf(fact_29_top1I,axiom,
! [X_69: arrow_1196572341e_indi] : ( top_to54564308indi_o @ X_69 ) ).
thf(fact_30_top1I,axiom,
! [X_69: nat] : ( top_top_nat_o @ X_69 ) ).
thf(fact_31_top1I,axiom,
! [X_69: product_unit] : ( top_to1984820022unit_o @ X_69 ) ).
thf(fact_32_UNIV__I,axiom,
! [X_68: $o] : ( member_o @ X_68 @ top_top_o_o ) ).
thf(fact_33_UNIV__I,axiom,
! [X_68: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_68 @ top_to54564308indi_o ) ).
thf(fact_34_UNIV__I,axiom,
! [X_68: product_unit] : ( member_Product_unit @ X_68 @ top_to1984820022unit_o ) ).
thf(fact_35_UNIV__I,axiom,
! [X_68: produc1572197287le_alt] : ( member285112084le_alt @ X_68 @ top_to558618722_alt_o ) ).
thf(fact_36_UNIV__I,axiom,
! [X_68: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( member822980838_alt_o @ X_68 @ top_to732317616lt_o_o ) ).
thf(fact_37_UNIV__I,axiom,
! [X_68: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( member1425217232_alt_o @ X_68 @ top_to1492351398lt_o_o ) ).
thf(fact_38_UNIV__I,axiom,
! [X_68: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ X_68 @ top_to1806834203lt_o_o ) ).
thf(fact_39_UNIV__I,axiom,
! [X_68: nat] : ( member_nat @ X_68 @ top_top_nat_o ) ).
thf(fact_40_iso__tuple__UNIV__I,axiom,
! [X_67: $o] : ( member_o @ X_67 @ top_top_o_o ) ).
thf(fact_41_iso__tuple__UNIV__I,axiom,
! [X_67: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_67 @ top_to54564308indi_o ) ).
thf(fact_42_iso__tuple__UNIV__I,axiom,
! [X_67: product_unit] : ( member_Product_unit @ X_67 @ top_to1984820022unit_o ) ).
thf(fact_43_iso__tuple__UNIV__I,axiom,
! [X_67: produc1572197287le_alt] : ( member285112084le_alt @ X_67 @ top_to558618722_alt_o ) ).
thf(fact_44_iso__tuple__UNIV__I,axiom,
! [X_67: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( member822980838_alt_o @ X_67 @ top_to732317616lt_o_o ) ).
thf(fact_45_iso__tuple__UNIV__I,axiom,
! [X_67: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( member1425217232_alt_o @ X_67 @ top_to1492351398lt_o_o ) ).
thf(fact_46_iso__tuple__UNIV__I,axiom,
! [X_67: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ X_67 @ top_to1806834203lt_o_o ) ).
thf(fact_47_iso__tuple__UNIV__I,axiom,
! [X_67: nat] : ( member_nat @ X_67 @ top_top_nat_o ) ).
thf(fact_48_top__apply,axiom,
! [X_66: produc1572197287le_alt > $o] :
( ( top_to1806834203lt_o_o @ X_66 )
<=> top_top_o ) ).
thf(fact_49_top__apply,axiom,
! [X_66: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( top_to732317616lt_o_o @ X_66 )
<=> top_top_o ) ).
thf(fact_50_top__apply,axiom,
! [X_66: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( top_to1492351398lt_o_o @ X_66 )
<=> top_top_o ) ).
thf(fact_51_top__apply,axiom,
! [X_66: produc1572197287le_alt] :
( ( top_to558618722_alt_o @ X_66 )
<=> top_top_o ) ).
thf(fact_52_top__apply,axiom,
! [X_66: arrow_1196572341e_indi] :
( ( top_to54564308indi_o @ X_66 )
<=> top_top_o ) ).
thf(fact_53_top__apply,axiom,
! [X_66: nat] :
( ( top_top_nat_o @ X_66 )
<=> top_top_o ) ).
thf(fact_54_top__apply,axiom,
! [X_66: product_unit] :
( ( top_to1984820022unit_o @ X_66 )
<=> top_top_o ) ).
thf(fact_55_not__top__less,axiom,
! [A_85: ( produc1572197287le_alt > $o ) > $o] :
~ ( ord_le874404799lt_o_o @ top_to1806834203lt_o_o @ A_85 ) ).
thf(fact_56_not__top__less,axiom,
! [A_85: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
~ ( ord_le914873172lt_o_o @ top_to732317616lt_o_o @ A_85 ) ).
thf(fact_57_not__top__less,axiom,
! [A_85: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
~ ( ord_le1382328578lt_o_o @ top_to1492351398lt_o_o @ A_85 ) ).
thf(fact_58_not__top__less,axiom,
! [A_85: $o] :
~ ( ord_less_o @ top_top_o @ A_85 ) ).
thf(fact_59_not__top__less,axiom,
! [A_85: produc1572197287le_alt > $o] :
~ ( ord_le1852932542_alt_o @ top_to558618722_alt_o @ A_85 ) ).
thf(fact_60_not__top__less,axiom,
! [A_85: arrow_1196572341e_indi > $o] :
~ ( ord_le1991507760indi_o @ top_to54564308indi_o @ A_85 ) ).
thf(fact_61_not__top__less,axiom,
! [A_85: nat > $o] :
~ ( ord_less_nat_o @ top_top_nat_o @ A_85 ) ).
thf(fact_62_not__top__less,axiom,
! [A_85: product_unit > $o] :
~ ( ord_le232288914unit_o @ top_to1984820022unit_o @ A_85 ) ).
thf(fact_63_less__top,axiom,
! [A_84: ( produc1572197287le_alt > $o ) > $o] :
( ( A_84 != top_to1806834203lt_o_o )
<=> ( ord_le874404799lt_o_o @ A_84 @ top_to1806834203lt_o_o ) ) ).
thf(fact_64_less__top,axiom,
! [A_84: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( A_84 != top_to732317616lt_o_o )
<=> ( ord_le914873172lt_o_o @ A_84 @ top_to732317616lt_o_o ) ) ).
thf(fact_65_less__top,axiom,
! [A_84: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( A_84 != top_to1492351398lt_o_o )
<=> ( ord_le1382328578lt_o_o @ A_84 @ top_to1492351398lt_o_o ) ) ).
thf(fact_66_less__top,axiom,
! [A_84: $o] :
( ~ ( A_84
<=> top_top_o )
<=> ( ord_less_o @ A_84 @ top_top_o ) ) ).
thf(fact_67_less__top,axiom,
! [A_84: produc1572197287le_alt > $o] :
( ( A_84 != top_to558618722_alt_o )
<=> ( ord_le1852932542_alt_o @ A_84 @ top_to558618722_alt_o ) ) ).
thf(fact_68_less__top,axiom,
! [A_84: arrow_1196572341e_indi > $o] :
( ( A_84 != top_to54564308indi_o )
<=> ( ord_le1991507760indi_o @ A_84 @ top_to54564308indi_o ) ) ).
thf(fact_69_less__top,axiom,
! [A_84: nat > $o] :
( ( A_84 != top_top_nat_o )
<=> ( ord_less_nat_o @ A_84 @ top_top_nat_o ) ) ).
thf(fact_70_less__top,axiom,
! [A_84: product_unit > $o] :
( ( A_84 != top_to1984820022unit_o )
<=> ( ord_le232288914unit_o @ A_84 @ top_to1984820022unit_o ) ) ).
thf(fact_71_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_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
( ( member285112084le_alt @ ( produc897867031le_alt @ e @ d )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ I_1 )
= n )
@ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ b @ a )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ n ) @ lab @ lba ) ) ) ) ).
thf(fact_73_dictator__def,axiom,
! [F_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,I: arrow_1196572341e_indi] :
( ( arrow_968343245ctator @ F_31 @ I )
<=> ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ arrow_1647925946e_Prof )
=> ( ( F_31 @ X_1 )
= ( X_1 @ I ) ) ) ) ).
thf(fact_74__096Lab_A_058_ALin_096,axiom,
member1241905979_alt_o @ lab @ arrow_1982173296le_Lin ).
thf(fact_75__096Lba_A_058_ALin_096,axiom,
member1241905979_alt_o @ lba @ arrow_1982173296le_Lin ).
thf(fact_76__096a_A_126_061_Ab_096,axiom,
a != b ).
thf(fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ lab ).
thf(fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
member285112084le_alt @ ( produc897867031le_alt @ b @ a ) @ lba ).
thf(fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ lba ) ).
thf(fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ ( member285112084le_alt @ ( produc897867031le_alt @ b @ a ) @ lab ) ).
thf(fact_81_PiProf,axiom,
! [N_1: nat] :
( member822980838_alt_o
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ N_1 ) @ lab @ lba )
@ arrow_1647925946e_Prof ) ).
thf(fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
~ ! [Lab: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ Lab )
=> ~ ( member1241905979_alt_o @ Lab @ arrow_1982173296le_Lin ) ) ).
thf(fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
~ ! [Lba: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ ( produc897867031le_alt @ b @ a ) @ Lba )
=> ~ ( member1241905979_alt_o @ Lba @ arrow_1982173296le_Lin ) ) ).
thf(fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
! [I_1: arrow_1196572341e_indi] :
( ( ( ( ord_less_nat @ ( h @ I_1 ) @ n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ e @ d ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ I_1 ) @ n )
=> ( ( ( ( h @ I_1 )
= n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ e @ d ) @ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e ) ) )
& ( ( ( h @ I_1 )
!= n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ e @ d ) @ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) ) )
<=> ( ( ( ord_less_nat @ ( h @ I_1 ) @ n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ b @ a ) @ lab ) )
& ( ~ ( ord_less_nat @ ( h @ I_1 ) @ n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ b @ a ) @ lba ) ) ) ) ).
thf(fact_85_n_I2_J,axiom,
! [M: nat] :
( ( ord_less_eq_nat @ M @ n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ b @ a )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ M ) @ lab @ lba ) ) ) ) ).
thf(fact_86_notin__Lin__iff,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_2: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( ( X != Y )
=> ( ~ ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_2 )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ Y @ X ) @ L_2 ) ) ) ) ).
thf(fact_87_Lin__irrefl,axiom,
! [A_73: arrow_1389031998le_alt,B_58: arrow_1389031998le_alt,L_2: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_73 @ B_58 ) @ L_2 )
=> ~ ( member285112084le_alt @ ( produc897867031le_alt @ B_58 @ A_73 ) @ L_2 ) ) ) ).
thf(fact_88_mktop__Lin,axiom,
! [X: arrow_1389031998le_alt,L_2: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( member1241905979_alt_o @ ( arrow_1970123222_mktop @ L_2 @ X ) @ arrow_1982173296le_Lin ) ) ).
thf(fact_89_mkbot__Lin,axiom,
! [X: arrow_1389031998le_alt,L_2: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( member1241905979_alt_o @ ( arrow_1821416136_mkbot @ L_2 @ X ) @ arrow_1982173296le_Lin ) ) ).
thf(fact_90_above__Lin,axiom,
! [L_2: produc1572197287le_alt > $o,X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt] :
( ( X != Y )
=> ( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( member1241905979_alt_o @ ( arrow_556571452_above @ L_2 @ X @ Y ) @ arrow_1982173296le_Lin ) ) ) ).
thf(fact_91_const__Lin__Prof,axiom,
! [L_2: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( member822980838_alt_o
@ ^ [P_5: arrow_1196572341e_indi] : L_2
@ arrow_1647925946e_Prof ) ) ).
thf(fact_92_linorder__cases,axiom,
! [X_65: nat,Y_49: nat] :
( ~ ( ord_less_nat @ X_65 @ Y_49 )
=> ( ( X_65 != Y_49 )
=> ( ord_less_nat @ Y_49 @ X_65 ) ) ) ).
thf(fact_93_order__less__asym,axiom,
! [X_64: nat > $o,Y_48: nat > $o] :
( ( ord_less_nat_o @ X_64 @ Y_48 )
=> ~ ( ord_less_nat_o @ Y_48 @ X_64 ) ) ).
thf(fact_94_order__less__asym,axiom,
! [X_64: product_unit > $o,Y_48: product_unit > $o] :
( ( ord_le232288914unit_o @ X_64 @ Y_48 )
=> ~ ( ord_le232288914unit_o @ Y_48 @ X_64 ) ) ).
thf(fact_95_order__less__asym,axiom,
! [X_64: arrow_1196572341e_indi > $o,Y_48: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_64 @ Y_48 )
=> ~ ( ord_le1991507760indi_o @ Y_48 @ X_64 ) ) ).
thf(fact_96_order__less__asym,axiom,
! [X_64: nat,Y_48: nat] :
( ( ord_less_nat @ X_64 @ Y_48 )
=> ~ ( ord_less_nat @ Y_48 @ X_64 ) ) ).
thf(fact_97_xt1_I10_J,axiom,
! [Z_8: nat > $o,Y_47: nat > $o,X_63: nat > $o] :
( ( ord_less_nat_o @ Y_47 @ X_63 )
=> ( ( ord_less_nat_o @ Z_8 @ Y_47 )
=> ( ord_less_nat_o @ Z_8 @ X_63 ) ) ) ).
thf(fact_98_xt1_I10_J,axiom,
! [Z_8: product_unit > $o,Y_47: product_unit > $o,X_63: product_unit > $o] :
( ( ord_le232288914unit_o @ Y_47 @ X_63 )
=> ( ( ord_le232288914unit_o @ Z_8 @ Y_47 )
=> ( ord_le232288914unit_o @ Z_8 @ X_63 ) ) ) ).
thf(fact_99_xt1_I10_J,axiom,
! [Z_8: arrow_1196572341e_indi > $o,Y_47: arrow_1196572341e_indi > $o,X_63: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ Y_47 @ X_63 )
=> ( ( ord_le1991507760indi_o @ Z_8 @ Y_47 )
=> ( ord_le1991507760indi_o @ Z_8 @ X_63 ) ) ) ).
thf(fact_100_xt1_I10_J,axiom,
! [Z_8: nat,Y_47: nat,X_63: nat] :
( ( ord_less_nat @ Y_47 @ X_63 )
=> ( ( ord_less_nat @ Z_8 @ Y_47 )
=> ( ord_less_nat @ Z_8 @ X_63 ) ) ) ).
thf(fact_101_order__less__trans,axiom,
! [Z_7: nat > $o,X_62: nat > $o,Y_46: nat > $o] :
( ( ord_less_nat_o @ X_62 @ Y_46 )
=> ( ( ord_less_nat_o @ Y_46 @ Z_7 )
=> ( ord_less_nat_o @ X_62 @ Z_7 ) ) ) ).
thf(fact_102_order__less__trans,axiom,
! [Z_7: product_unit > $o,X_62: product_unit > $o,Y_46: product_unit > $o] :
( ( ord_le232288914unit_o @ X_62 @ Y_46 )
=> ( ( ord_le232288914unit_o @ Y_46 @ Z_7 )
=> ( ord_le232288914unit_o @ X_62 @ Z_7 ) ) ) ).
thf(fact_103_order__less__trans,axiom,
! [Z_7: arrow_1196572341e_indi > $o,X_62: arrow_1196572341e_indi > $o,Y_46: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_62 @ Y_46 )
=> ( ( ord_le1991507760indi_o @ Y_46 @ Z_7 )
=> ( ord_le1991507760indi_o @ X_62 @ Z_7 ) ) ) ).
thf(fact_104_order__less__trans,axiom,
! [Z_7: nat,X_62: nat,Y_46: nat] :
( ( ord_less_nat @ X_62 @ Y_46 )
=> ( ( ord_less_nat @ Y_46 @ Z_7 )
=> ( ord_less_nat @ X_62 @ Z_7 ) ) ) ).
thf(fact_105_xt1_I2_J,axiom,
! [C_41: nat > $o,B_66: nat > $o,A_83: nat > $o] :
( ( ord_less_nat_o @ B_66 @ A_83 )
=> ( ( B_66 = C_41 )
=> ( ord_less_nat_o @ C_41 @ A_83 ) ) ) ).
thf(fact_106_xt1_I2_J,axiom,
! [C_41: product_unit > $o,B_66: product_unit > $o,A_83: product_unit > $o] :
( ( ord_le232288914unit_o @ B_66 @ A_83 )
=> ( ( B_66 = C_41 )
=> ( ord_le232288914unit_o @ C_41 @ A_83 ) ) ) ).
thf(fact_107_xt1_I2_J,axiom,
! [C_41: arrow_1196572341e_indi > $o,B_66: arrow_1196572341e_indi > $o,A_83: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ B_66 @ A_83 )
=> ( ( B_66 = C_41 )
=> ( ord_le1991507760indi_o @ C_41 @ A_83 ) ) ) ).
thf(fact_108_xt1_I2_J,axiom,
! [C_41: nat,B_66: nat,A_83: nat] :
( ( ord_less_nat @ B_66 @ A_83 )
=> ( ( B_66 = C_41 )
=> ( ord_less_nat @ C_41 @ A_83 ) ) ) ).
thf(fact_109_ord__less__eq__trans,axiom,
! [C_40: nat > $o,A_82: nat > $o,B_65: nat > $o] :
( ( ord_less_nat_o @ A_82 @ B_65 )
=> ( ( B_65 = C_40 )
=> ( ord_less_nat_o @ A_82 @ C_40 ) ) ) ).
thf(fact_110_ord__less__eq__trans,axiom,
! [C_40: product_unit > $o,A_82: product_unit > $o,B_65: product_unit > $o] :
( ( ord_le232288914unit_o @ A_82 @ B_65 )
=> ( ( B_65 = C_40 )
=> ( ord_le232288914unit_o @ A_82 @ C_40 ) ) ) ).
thf(fact_111_ord__less__eq__trans,axiom,
! [C_40: arrow_1196572341e_indi > $o,A_82: arrow_1196572341e_indi > $o,B_65: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ A_82 @ B_65 )
=> ( ( B_65 = C_40 )
=> ( ord_le1991507760indi_o @ A_82 @ C_40 ) ) ) ).
thf(fact_112_ord__less__eq__trans,axiom,
! [C_40: nat,A_82: nat,B_65: nat] :
( ( ord_less_nat @ A_82 @ B_65 )
=> ( ( B_65 = C_40 )
=> ( ord_less_nat @ A_82 @ C_40 ) ) ) ).
thf(fact_113_xt1_I1_J,axiom,
! [C_39: nat > $o,A_81: nat > $o,B_64: nat > $o] :
( ( A_81 = B_64 )
=> ( ( ord_less_nat_o @ C_39 @ B_64 )
=> ( ord_less_nat_o @ C_39 @ A_81 ) ) ) ).
thf(fact_114_xt1_I1_J,axiom,
! [C_39: product_unit > $o,A_81: product_unit > $o,B_64: product_unit > $o] :
( ( A_81 = B_64 )
=> ( ( ord_le232288914unit_o @ C_39 @ B_64 )
=> ( ord_le232288914unit_o @ C_39 @ A_81 ) ) ) ).
thf(fact_115_xt1_I1_J,axiom,
! [C_39: arrow_1196572341e_indi > $o,A_81: arrow_1196572341e_indi > $o,B_64: arrow_1196572341e_indi > $o] :
( ( A_81 = B_64 )
=> ( ( ord_le1991507760indi_o @ C_39 @ B_64 )
=> ( ord_le1991507760indi_o @ C_39 @ A_81 ) ) ) ).
thf(fact_116_xt1_I1_J,axiom,
! [C_39: nat,A_81: nat,B_64: nat] :
( ( A_81 = B_64 )
=> ( ( ord_less_nat @ C_39 @ B_64 )
=> ( ord_less_nat @ C_39 @ A_81 ) ) ) ).
thf(fact_117_ord__eq__less__trans,axiom,
! [C_38: nat > $o,A_80: nat > $o,B_63: nat > $o] :
( ( A_80 = B_63 )
=> ( ( ord_less_nat_o @ B_63 @ C_38 )
=> ( ord_less_nat_o @ A_80 @ C_38 ) ) ) ).
thf(fact_118_ord__eq__less__trans,axiom,
! [C_38: product_unit > $o,A_80: product_unit > $o,B_63: product_unit > $o] :
( ( A_80 = B_63 )
=> ( ( ord_le232288914unit_o @ B_63 @ C_38 )
=> ( ord_le232288914unit_o @ A_80 @ C_38 ) ) ) ).
thf(fact_119_ord__eq__less__trans,axiom,
! [C_38: arrow_1196572341e_indi > $o,A_80: arrow_1196572341e_indi > $o,B_63: arrow_1196572341e_indi > $o] :
( ( A_80 = B_63 )
=> ( ( ord_le1991507760indi_o @ B_63 @ C_38 )
=> ( ord_le1991507760indi_o @ A_80 @ C_38 ) ) ) ).
thf(fact_120_ord__eq__less__trans,axiom,
! [C_38: nat,A_80: nat,B_63: nat] :
( ( A_80 = B_63 )
=> ( ( ord_less_nat @ B_63 @ C_38 )
=> ( ord_less_nat @ A_80 @ C_38 ) ) ) ).
thf(fact_121_xt1_I9_J,axiom,
! [B_62: nat > $o,A_79: nat > $o] :
( ( ord_less_nat_o @ B_62 @ A_79 )
=> ~ ( ord_less_nat_o @ A_79 @ B_62 ) ) ).
thf(fact_122_xt1_I9_J,axiom,
! [B_62: product_unit > $o,A_79: product_unit > $o] :
( ( ord_le232288914unit_o @ B_62 @ A_79 )
=> ~ ( ord_le232288914unit_o @ A_79 @ B_62 ) ) ).
thf(fact_123_xt1_I9_J,axiom,
! [B_62: arrow_1196572341e_indi > $o,A_79: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ B_62 @ A_79 )
=> ~ ( ord_le1991507760indi_o @ A_79 @ B_62 ) ) ).
thf(fact_124_xt1_I9_J,axiom,
! [B_62: nat,A_79: nat] :
( ( ord_less_nat @ B_62 @ A_79 )
=> ~ ( ord_less_nat @ A_79 @ B_62 ) ) ).
thf(fact_125_order__less__asym_H,axiom,
! [A_78: nat > $o,B_61: nat > $o] :
( ( ord_less_nat_o @ A_78 @ B_61 )
=> ~ ( ord_less_nat_o @ B_61 @ A_78 ) ) ).
thf(fact_126_order__less__asym_H,axiom,
! [A_78: product_unit > $o,B_61: product_unit > $o] :
( ( ord_le232288914unit_o @ A_78 @ B_61 )
=> ~ ( ord_le232288914unit_o @ B_61 @ A_78 ) ) ).
thf(fact_127_order__less__asym_H,axiom,
! [A_78: arrow_1196572341e_indi > $o,B_61: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ A_78 @ B_61 )
=> ~ ( ord_le1991507760indi_o @ B_61 @ A_78 ) ) ).
thf(fact_128_order__less__asym_H,axiom,
! [A_78: nat,B_61: nat] :
( ( ord_less_nat @ A_78 @ B_61 )
=> ~ ( ord_less_nat @ B_61 @ A_78 ) ) ).
thf(fact_129_order__less__imp__triv,axiom,
! [P_4: $o,X_61: nat > $o,Y_45: nat > $o] :
( ( ord_less_nat_o @ X_61 @ Y_45 )
=> ( ( ord_less_nat_o @ Y_45 @ X_61 )
=> P_4 ) ) ).
thf(fact_130_order__less__imp__triv,axiom,
! [P_4: $o,X_61: product_unit > $o,Y_45: product_unit > $o] :
( ( ord_le232288914unit_o @ X_61 @ Y_45 )
=> ( ( ord_le232288914unit_o @ Y_45 @ X_61 )
=> P_4 ) ) ).
thf(fact_131_order__less__imp__triv,axiom,
! [P_4: $o,X_61: arrow_1196572341e_indi > $o,Y_45: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_61 @ Y_45 )
=> ( ( ord_le1991507760indi_o @ Y_45 @ X_61 )
=> P_4 ) ) ).
thf(fact_132_order__less__imp__triv,axiom,
! [P_4: $o,X_61: nat,Y_45: nat] :
( ( ord_less_nat @ X_61 @ Y_45 )
=> ( ( ord_less_nat @ Y_45 @ X_61 )
=> P_4 ) ) ).
thf(fact_133_order__less__imp__not__eq2,axiom,
! [X_60: nat > $o,Y_44: nat > $o] :
( ( ord_less_nat_o @ X_60 @ Y_44 )
=> ( Y_44 != X_60 ) ) ).
thf(fact_134_order__less__imp__not__eq2,axiom,
! [X_60: product_unit > $o,Y_44: product_unit > $o] :
( ( ord_le232288914unit_o @ X_60 @ Y_44 )
=> ( Y_44 != X_60 ) ) ).
thf(fact_135_order__less__imp__not__eq2,axiom,
! [X_60: arrow_1196572341e_indi > $o,Y_44: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_60 @ Y_44 )
=> ( Y_44 != X_60 ) ) ).
thf(fact_136_order__less__imp__not__eq2,axiom,
! [X_60: nat,Y_44: nat] :
( ( ord_less_nat @ X_60 @ Y_44 )
=> ( Y_44 != X_60 ) ) ).
thf(fact_137_order__less__imp__not__eq,axiom,
! [X_59: nat > $o,Y_43: nat > $o] :
( ( ord_less_nat_o @ X_59 @ Y_43 )
=> ( X_59 != Y_43 ) ) ).
thf(fact_138_order__less__imp__not__eq,axiom,
! [X_59: product_unit > $o,Y_43: product_unit > $o] :
( ( ord_le232288914unit_o @ X_59 @ Y_43 )
=> ( X_59 != Y_43 ) ) ).
thf(fact_139_order__less__imp__not__eq,axiom,
! [X_59: arrow_1196572341e_indi > $o,Y_43: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_59 @ Y_43 )
=> ( X_59 != Y_43 ) ) ).
thf(fact_140_order__less__imp__not__eq,axiom,
! [X_59: nat,Y_43: nat] :
( ( ord_less_nat @ X_59 @ Y_43 )
=> ( X_59 != Y_43 ) ) ).
thf(fact_141_order__less__imp__not__less,axiom,
! [X_58: nat > $o,Y_42: nat > $o] :
( ( ord_less_nat_o @ X_58 @ Y_42 )
=> ~ ( ord_less_nat_o @ Y_42 @ X_58 ) ) ).
thf(fact_142_order__less__imp__not__less,axiom,
! [X_58: product_unit > $o,Y_42: product_unit > $o] :
( ( ord_le232288914unit_o @ X_58 @ Y_42 )
=> ~ ( ord_le232288914unit_o @ Y_42 @ X_58 ) ) ).
thf(fact_143_order__less__imp__not__less,axiom,
! [X_58: arrow_1196572341e_indi > $o,Y_42: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_58 @ Y_42 )
=> ~ ( ord_le1991507760indi_o @ Y_42 @ X_58 ) ) ).
thf(fact_144_order__less__imp__not__less,axiom,
! [X_58: nat,Y_42: nat] :
( ( ord_less_nat @ X_58 @ Y_42 )
=> ~ ( ord_less_nat @ Y_42 @ X_58 ) ) ).
thf(fact_145_order__less__not__sym,axiom,
! [X_57: nat > $o,Y_41: nat > $o] :
( ( ord_less_nat_o @ X_57 @ Y_41 )
=> ~ ( ord_less_nat_o @ Y_41 @ X_57 ) ) ).
thf(fact_146_order__less__not__sym,axiom,
! [X_57: product_unit > $o,Y_41: product_unit > $o] :
( ( ord_le232288914unit_o @ X_57 @ Y_41 )
=> ~ ( ord_le232288914unit_o @ Y_41 @ X_57 ) ) ).
thf(fact_147_order__less__not__sym,axiom,
! [X_57: arrow_1196572341e_indi > $o,Y_41: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_57 @ Y_41 )
=> ~ ( ord_le1991507760indi_o @ Y_41 @ X_57 ) ) ).
thf(fact_148_order__less__not__sym,axiom,
! [X_57: nat,Y_41: nat] :
( ( ord_less_nat @ X_57 @ Y_41 )
=> ~ ( ord_less_nat @ Y_41 @ X_57 ) ) ).
thf(fact_149_less__imp__neq,axiom,
! [X_56: nat > $o,Y_40: nat > $o] :
( ( ord_less_nat_o @ X_56 @ Y_40 )
=> ( X_56 != Y_40 ) ) ).
thf(fact_150_less__imp__neq,axiom,
! [X_56: product_unit > $o,Y_40: product_unit > $o] :
( ( ord_le232288914unit_o @ X_56 @ Y_40 )
=> ( X_56 != Y_40 ) ) ).
thf(fact_151_less__imp__neq,axiom,
! [X_56: arrow_1196572341e_indi > $o,Y_40: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_56 @ Y_40 )
=> ( X_56 != Y_40 ) ) ).
thf(fact_152_less__imp__neq,axiom,
! [X_56: nat,Y_40: nat] :
( ( ord_less_nat @ X_56 @ Y_40 )
=> ( X_56 != Y_40 ) ) ).
thf(fact_153_linorder__neqE,axiom,
! [X_55: nat,Y_39: nat] :
( ( X_55 != Y_39 )
=> ( ~ ( ord_less_nat @ X_55 @ Y_39 )
=> ( ord_less_nat @ Y_39 @ X_55 ) ) ) ).
thf(fact_154_linorder__antisym__conv3,axiom,
! [Y_38: nat,X_54: nat] :
( ~ ( ord_less_nat @ Y_38 @ X_54 )
=> ( ~ ( ord_less_nat @ X_54 @ Y_38 )
<=> ( X_54 = Y_38 ) ) ) ).
thf(fact_155_linorder__less__linear,axiom,
! [X_53: nat,Y_37: nat] :
( ( ord_less_nat @ X_53 @ Y_37 )
| ( X_53 = Y_37 )
| ( ord_less_nat @ Y_37 @ X_53 ) ) ).
thf(fact_156_not__less__iff__gr__or__eq,axiom,
! [X_52: nat,Y_36: nat] :
( ~ ( ord_less_nat @ X_52 @ Y_36 )
<=> ( ( ord_less_nat @ Y_36 @ X_52 )
| ( X_52 = Y_36 ) ) ) ).
thf(fact_157_linorder__neq__iff,axiom,
! [X_51: nat,Y_35: nat] :
( ( X_51 != Y_35 )
<=> ( ( ord_less_nat @ X_51 @ Y_35 )
| ( ord_less_nat @ Y_35 @ X_51 ) ) ) ).
thf(fact_158_order__less__irrefl,axiom,
! [X_50: nat > $o] :
~ ( ord_less_nat_o @ X_50 @ X_50 ) ).
thf(fact_159_order__less__irrefl,axiom,
! [X_50: product_unit > $o] :
~ ( ord_le232288914unit_o @ X_50 @ X_50 ) ).
thf(fact_160_order__less__irrefl,axiom,
! [X_50: arrow_1196572341e_indi > $o] :
~ ( ord_le1991507760indi_o @ X_50 @ X_50 ) ).
thf(fact_161_order__less__irrefl,axiom,
! [X_50: nat] :
~ ( ord_less_nat @ X_50 @ X_50 ) ).
thf(fact_162_mem__def,axiom,
! [X_49: arrow_1196572341e_indi,A_77: arrow_1196572341e_indi > $o] :
( ( member1818997282e_indi @ X_49 @ A_77 )
<=> ( A_77 @ X_49 ) ) ).
thf(fact_163_mem__def,axiom,
! [X_49: $o,A_77: $o > $o] :
( ( member_o @ X_49 @ A_77 )
<=> ( A_77 @ X_49 ) ) ).
thf(fact_164_mem__def,axiom,
! [X_49: product_unit,A_77: product_unit > $o] :
( ( member_Product_unit @ X_49 @ A_77 )
<=> ( A_77 @ X_49 ) ) ).
thf(fact_165_mem__def,axiom,
! [X_49: produc1572197287le_alt,A_77: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X_49 @ A_77 )
<=> ( A_77 @ X_49 ) ) ).
thf(fact_166_mem__def,axiom,
! [X_49: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_77: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X_49 @ A_77 )
<=> ( A_77 @ X_49 ) ) ).
thf(fact_167_mem__def,axiom,
! [X_49: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_77: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ X_49 @ A_77 )
<=> ( A_77 @ X_49 ) ) ).
thf(fact_168_mem__def,axiom,
! [X_49: produc1572197287le_alt > $o,A_77: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ X_49 @ A_77 )
<=> ( A_77 @ X_49 ) ) ).
thf(fact_169_mem__def,axiom,
! [X_49: nat,A_77: nat > $o] :
( ( member_nat @ X_49 @ A_77 )
<=> ( A_77 @ X_49 ) ) ).
thf(fact_170_Collect__def,axiom,
! [P_3: product_unit > $o] :
( ( collect_Product_unit @ P_3 )
= P_3 ) ).
thf(fact_171_Collect__def,axiom,
! [P_3: arrow_1196572341e_indi > $o] :
( ( collec1936859488e_indi @ P_3 )
= P_3 ) ).
thf(fact_172_Collect__def,axiom,
! [P_3: nat > $o] :
( ( collect_nat @ P_3 )
= P_3 ) ).
thf(fact_173_UNIV__def,axiom,
( top_to1806834203lt_o_o
= ( collec958969213_alt_o
@ ^ [X_1: produc1572197287le_alt > $o] : $true ) ) ).
thf(fact_174_UNIV__def,axiom,
( top_to732317616lt_o_o
= ( collec979749928_alt_o
@ ^ [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] : $true ) ) ).
thf(fact_175_UNIV__def,axiom,
( top_to1492351398lt_o_o
= ( collec670126350_alt_o
@ ^ [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : $true ) ) ).
thf(fact_176_UNIV__def,axiom,
( top_to558618722_alt_o
= ( collec940901970le_alt
@ ^ [X_1: produc1572197287le_alt] : $true ) ) ).
thf(fact_177_UNIV__def,axiom,
( top_to54564308indi_o
= ( collec1936859488e_indi
@ ^ [X_1: arrow_1196572341e_indi] : $true ) ) ).
thf(fact_178_UNIV__def,axiom,
( top_to1984820022unit_o
= ( collect_Product_unit
@ ^ [X_1: product_unit] : $true ) ) ).
thf(fact_179_UNIV__def,axiom,
( top_top_nat_o
= ( collect_nat
@ ^ [X_1: nat] : $true ) ) ).
thf(fact_180_in__above,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_2: produc1572197287le_alt > $o,A_73: arrow_1389031998le_alt,B_58: arrow_1389031998le_alt] :
( ( A_73 != B_58 )
=> ( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_556571452_above @ L_2 @ A_73 @ B_58 ) )
<=> ( ( X != Y )
& ( ( X = B_58 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_73 @ Y ) @ L_2 ) )
& ( ( X != B_58 )
=> ( ( ( Y = B_58 )
=> ( ( X = A_73 )
| ( member285112084le_alt @ ( produc897867031le_alt @ X @ A_73 ) @ L_2 ) ) )
& ( ( Y != B_58 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_2 ) ) ) ) ) ) ) ) ).
thf(fact_181_pred__equals__eq2,axiom,
! [S_3: produc1572197287le_alt > $o,R_2: produc1572197287le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt,Xa: arrow_1389031998le_alt] :
( ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Xa ) @ R_2 )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Xa ) @ S_3 ) )
<=> ( R_2 = S_3 ) ) ).
thf(fact_182_dictatorI,axiom,
! [I: arrow_1196572341e_indi,F_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] :
( ( member1425217232_alt_o @ F_31
@ ( 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_76: arrow_1389031998le_alt,B_60: arrow_1389031998le_alt] :
( ( A_76 != B_60 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ A_76 @ B_60 ) @ ( X_1 @ I ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ A_76 @ B_60 ) @ ( F_31 @ X_1 ) ) ) ) )
=> ( arrow_968343245ctator @ F_31 @ I ) ) ) ).
thf(fact_183_n_I3_J,axiom,
( member285112084le_alt @ ( produc897867031le_alt @ a @ b )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ ( plus_plus_nat @ n @ one_one_nat ) ) @ lab @ lba ) ) ) ).
thf(fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ e )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ I_1 )
= n )
@ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ a @ b )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ ( plus_plus_nat @ n @ one_one_nat ) ) @ lab @ lba ) ) ) ) ).
thf(fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
! [I_1: arrow_1196572341e_indi] :
( ( ( ( ord_less_nat @ ( h @ I_1 ) @ n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ e ) @ ( arrow_1970123222_mktop @ ( p @ I_1 ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ I_1 ) @ n )
=> ( ( ( ( h @ I_1 )
= n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ e ) @ ( arrow_556571452_above @ ( p @ I_1 ) @ c @ e ) ) )
& ( ( ( h @ I_1 )
!= n )
=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ e ) @ ( arrow_1821416136_mkbot @ ( p @ I_1 ) @ e ) ) ) ) ) )
<=> ( ( ( ord_less_nat @ ( h @ I_1 ) @ ( plus_plus_nat @ n @ one_one_nat ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ lab ) )
& ( ~ ( ord_less_nat @ ( h @ I_1 ) @ ( plus_plus_nat @ n @ one_one_nat ) )
=> ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ lba ) ) ) ) ).
thf(fact_186_inv__f__eq,axiom,
! [X_48: arrow_1196572341e_indi,Y_34: nat,F_30: arrow_1196572341e_indi > nat] :
( ( inj_on1505595958di_nat @ F_30 @ top_to54564308indi_o )
=> ( ( ( F_30 @ X_48 )
= Y_34 )
=> ( ( hilber1125280539di_nat @ top_to54564308indi_o @ F_30 @ Y_34 )
= X_48 ) ) ) ).
thf(fact_187_inv__f__eq,axiom,
! [X_48: nat,Y_34: nat,F_30: nat > nat] :
( ( inj_on_nat_nat @ F_30 @ top_top_nat_o )
=> ( ( ( F_30 @ X_48 )
= Y_34 )
=> ( ( hilber195283148at_nat @ top_top_nat_o @ F_30 @ Y_34 )
= X_48 ) ) ) ).
thf(fact_188_inv__f__f,axiom,
! [X_47: arrow_1196572341e_indi,F_29: arrow_1196572341e_indi > nat] :
( ( inj_on1505595958di_nat @ F_29 @ top_to54564308indi_o )
=> ( ( hilber1125280539di_nat @ top_to54564308indi_o @ F_29 @ ( F_29 @ X_47 ) )
= X_47 ) ) ).
thf(fact_189_inv__f__f,axiom,
! [X_47: nat,F_29: nat > nat] :
( ( inj_on_nat_nat @ F_29 @ top_top_nat_o )
=> ( ( hilber195283148at_nat @ top_top_nat_o @ F_29 @ ( F_29 @ X_47 ) )
= X_47 ) ) ).
thf(fact_190_PiE,axiom,
! [X_46: produc1572197287le_alt,F_28: produc1572197287le_alt > $o,A_75: produc1572197287le_alt > $o,B_59: produc1572197287le_alt > $o > $o] :
( ( member1241905979_alt_o @ F_28 @ ( pi_Pro418549519_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member285112084le_alt @ X_46 @ A_75 ) ) ) ).
thf(fact_191_PiE,axiom,
! [X_46: arrow_1196572341e_indi,F_28: arrow_1196572341e_indi > produc1572197287le_alt,A_75: arrow_1196572341e_indi > $o,B_59: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member232085823le_alt @ F_28 @ ( pi_Arr1762714837le_alt @ A_75 @ B_59 ) )
=> ( ~ ( member285112084le_alt @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1818997282e_indi @ X_46 @ A_75 ) ) ) ).
thf(fact_192_PiE,axiom,
! [X_46: $o,F_28: $o > produc1572197287le_alt,A_75: $o > $o,B_59: $o > produc1572197287le_alt > $o] :
( ( member1158049649le_alt @ F_28 @ ( pi_o_P728361163le_alt @ A_75 @ B_59 ) )
=> ( ~ ( member285112084le_alt @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_o @ X_46 @ A_75 ) ) ) ).
thf(fact_193_PiE,axiom,
! [X_46: product_unit,F_28: product_unit > produc1572197287le_alt,A_75: product_unit > $o,B_59: product_unit > produc1572197287le_alt > $o] :
( ( member1161214429le_alt @ F_28 @ ( pi_Pro772884595le_alt @ A_75 @ B_59 ) )
=> ( ~ ( member285112084le_alt @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_Product_unit @ X_46 @ A_75 ) ) ) ).
thf(fact_194_PiE,axiom,
! [X_46: arrow_1196572341e_indi,F_28: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_75: arrow_1196572341e_indi > $o,B_59: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2071265553_alt_o @ F_28 @ ( pi_Arr456308197_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member822980838_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1818997282e_indi @ X_46 @ A_75 ) ) ) ).
thf(fact_195_PiE,axiom,
! [X_46: $o,F_28: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_75: $o > $o,B_59: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member984757343_alt_o @ F_28 @ ( pi_o_A1479825007_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member822980838_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_o @ X_46 @ A_75 ) ) ) ).
thf(fact_196_PiE,axiom,
! [X_46: product_unit,F_28: product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_75: product_unit > $o,B_59: product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2021528307_alt_o @ F_28 @ ( pi_Pro1959068871_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member822980838_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_Product_unit @ X_46 @ A_75 ) ) ) ).
thf(fact_197_PiE,axiom,
! [X_46: arrow_1196572341e_indi,F_28: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_75: arrow_1196572341e_indi > $o,B_59: arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1521294075_alt_o @ F_28 @ ( pi_Arr583278353_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member1425217232_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1818997282e_indi @ X_46 @ A_75 ) ) ) ).
thf(fact_198_PiE,axiom,
! [X_46: $o,F_28: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_75: $o > $o,B_59: $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member161783341_alt_o @ F_28 @ ( pi_o_A1994447367_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member1425217232_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_o @ X_46 @ A_75 ) ) ) ).
thf(fact_199_PiE,axiom,
! [X_46: product_unit,F_28: product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_75: product_unit > $o,B_59: product_unit > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1888392857_alt_o @ F_28 @ ( pi_Pro443817391_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member1425217232_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_Product_unit @ X_46 @ A_75 ) ) ) ).
thf(fact_200_PiE,axiom,
! [X_46: $o,F_28: $o > produc1572197287le_alt > $o,A_75: $o > $o,B_59: $o > ( produc1572197287le_alt > $o ) > $o] :
( ( member1495989556_alt_o @ F_28 @ ( pi_o_P1417870404_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_o @ X_46 @ A_75 ) ) ) ).
thf(fact_201_PiE,axiom,
! [X_46: product_unit,F_28: product_unit > produc1572197287le_alt > $o,A_75: product_unit > $o,B_59: product_unit > ( produc1572197287le_alt > $o ) > $o] :
( ( member1295651272_alt_o @ F_28 @ ( pi_Pro29851292_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_Product_unit @ X_46 @ A_75 ) ) ) ).
thf(fact_202_PiE,axiom,
! [X_46: arrow_1196572341e_indi,F_28: arrow_1196572341e_indi > nat,A_75: arrow_1196572341e_indi > $o,B_59: arrow_1196572341e_indi > nat > $o] :
( ( member1842285448di_nat @ F_28 @ ( pi_Arr778514268di_nat @ A_75 @ B_59 ) )
=> ( ~ ( member_nat @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1818997282e_indi @ X_46 @ A_75 ) ) ) ).
thf(fact_203_PiE,axiom,
! [X_46: $o,F_28: $o > nat,A_75: $o > $o,B_59: $o > nat > $o] :
( ( member_o_nat @ F_28 @ ( pi_o_nat @ A_75 @ B_59 ) )
=> ( ~ ( member_nat @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_o @ X_46 @ A_75 ) ) ) ).
thf(fact_204_PiE,axiom,
! [X_46: product_unit,F_28: product_unit > nat,A_75: product_unit > $o,B_59: product_unit > nat > $o] :
( ( member1827227242it_nat @ F_28 @ ( pi_Product_unit_nat @ A_75 @ B_59 ) )
=> ( ~ ( member_nat @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_Product_unit @ X_46 @ A_75 ) ) ) ).
thf(fact_205_PiE,axiom,
! [X_46: produc1572197287le_alt,F_28: produc1572197287le_alt > arrow_1196572341e_indi,A_75: produc1572197287le_alt > $o,B_59: produc1572197287le_alt > arrow_1196572341e_indi > $o] :
( ( member1074431551e_indi @ F_28 @ ( pi_Pro1246947541e_indi @ A_75 @ B_59 ) )
=> ( ~ ( member1818997282e_indi @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member285112084le_alt @ X_46 @ A_75 ) ) ) ).
thf(fact_206_PiE,axiom,
! [X_46: produc1572197287le_alt,F_28: produc1572197287le_alt > product_unit,A_75: produc1572197287le_alt > $o,B_59: produc1572197287le_alt > product_unit > $o] :
( ( member44534621t_unit @ F_28 @ ( pi_Pro926528371t_unit @ A_75 @ B_59 ) )
=> ( ~ ( member_Product_unit @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member285112084le_alt @ X_46 @ A_75 ) ) ) ).
thf(fact_207_PiE,axiom,
! [X_46: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_28: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_75: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_59: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1186582243e_indi @ F_28 @ ( pi_Arr272777533e_indi @ A_75 @ B_59 ) )
=> ( ~ ( member1818997282e_indi @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member822980838_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_208_PiE,axiom,
! [X_46: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_28: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_75: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_59: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o] :
( ( member1696373143lt_o_o @ F_28 @ ( pi_Arr1709554855lt_o_o @ A_75 @ B_59 ) )
=> ( ~ ( member_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member822980838_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_209_PiE,axiom,
! [X_46: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_28: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit,A_75: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_59: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit > $o] :
( ( member1537523201t_unit @ F_28 @ ( pi_Arr509685723t_unit @ A_75 @ B_59 ) )
=> ( ~ ( member_Product_unit @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member822980838_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_210_PiE,axiom,
! [X_46: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_28: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_75: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_59: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1539010427e_indi @ F_28 @ ( pi_Arr470535441e_indi @ A_75 @ B_59 ) )
=> ( ~ ( member1818997282e_indi @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1425217232_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_211_PiE,axiom,
! [X_46: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_28: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_75: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_59: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o] :
( ( member1346253567lt_o_o @ F_28 @ ( pi_Arr1865419731lt_o_o @ A_75 @ B_59 ) )
=> ( ~ ( member_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1425217232_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_212_PiE,axiom,
! [X_46: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_28: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit,A_75: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_59: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit > $o] :
( ( member1043380889t_unit @ F_28 @ ( pi_Arr2096782767t_unit @ A_75 @ B_59 ) )
=> ( ~ ( member_Product_unit @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1425217232_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_213_PiE,axiom,
! [X_46: produc1572197287le_alt > $o,F_28: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_75: ( produc1572197287le_alt > $o ) > $o,B_59: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1830244024e_indi @ F_28 @ ( pi_Pro2039443474e_indi @ A_75 @ B_59 ) )
=> ( ~ ( member1818997282e_indi @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1241905979_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_214_PiE,axiom,
! [X_46: produc1572197287le_alt > $o,F_28: ( produc1572197287le_alt > $o ) > $o,A_75: ( produc1572197287le_alt > $o ) > $o,B_59: ( produc1572197287le_alt > $o ) > $o > $o] :
( ( member1925470338lt_o_o @ F_28 @ ( pi_Pro386796690lt_o_o @ A_75 @ B_59 ) )
=> ( ~ ( member_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1241905979_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_215_PiE,axiom,
! [X_46: produc1572197287le_alt > $o,F_28: ( produc1572197287le_alt > $o ) > product_unit,A_75: ( produc1572197287le_alt > $o ) > $o,B_59: ( produc1572197287le_alt > $o ) > product_unit > $o] :
( ( member1092867670t_unit @ F_28 @ ( pi_Pro30504752t_unit @ A_75 @ B_59 ) )
=> ( ~ ( member_Product_unit @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1241905979_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_216_PiE,axiom,
! [X_46: nat,F_28: nat > arrow_1196572341e_indi,A_75: nat > $o,B_59: nat > arrow_1196572341e_indi > $o] :
( ( member1113138010e_indi @ F_28 @ ( pi_nat986275508e_indi @ A_75 @ B_59 ) )
=> ( ~ ( member1818997282e_indi @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_nat @ X_46 @ A_75 ) ) ) ).
thf(fact_217_PiE,axiom,
! [X_46: nat,F_28: nat > $o,A_75: nat > $o,B_59: nat > $o > $o] :
( ( member_nat_o @ F_28 @ ( pi_nat_o @ A_75 @ B_59 ) )
=> ( ~ ( member_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_nat @ X_46 @ A_75 ) ) ) ).
thf(fact_218_PiE,axiom,
! [X_46: nat,F_28: nat > product_unit,A_75: nat > $o,B_59: nat > product_unit > $o] :
( ( member616671224t_unit @ F_28 @ ( pi_nat_Product_unit @ A_75 @ B_59 ) )
=> ( ~ ( member_Product_unit @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member_nat @ X_46 @ A_75 ) ) ) ).
thf(fact_219_PiE,axiom,
! [X_46: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_28: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_75: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_59: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ F_28 @ ( pi_Arr1196397536_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member822980838_alt_o @ X_46 @ A_75 ) ) ) ).
thf(fact_220_PiE,axiom,
! [X_46: arrow_1196572341e_indi,F_28: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_75: arrow_1196572341e_indi > $o,B_59: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ F_28 @ ( pi_Arr1309696186_alt_o @ A_75 @ B_59 ) )
=> ( ~ ( member1241905979_alt_o @ ( F_28 @ X_46 ) @ ( B_59 @ X_46 ) )
=> ~ ( member1818997282e_indi @ X_46 @ A_75 ) ) ) ).
thf(fact_221_complete__Lin,axiom,
! [A_73: arrow_1389031998le_alt,B_58: arrow_1389031998le_alt] :
( ( A_73 != B_58 )
=> ? [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ arrow_1982173296le_Lin )
& ( member285112084le_alt @ ( produc897867031le_alt @ A_73 @ B_58 ) @ X_1 ) ) ) ).
thf(fact_222_Pi__UNIV,axiom,
! [A_74: produc1572197287le_alt > $o] :
( ( pi_Pro418549519_alt_o @ A_74
@ ^ [Uu: produc1572197287le_alt] : top_top_o_o )
= top_to1806834203lt_o_o ) ).
thf(fact_223_Pi__UNIV,axiom,
! [A_74: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( pi_Arr1196397536_alt_o @ A_74
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : top_to1806834203lt_o_o )
= top_to1492351398lt_o_o ) ).
thf(fact_224_Pi__UNIV,axiom,
! [A_74: arrow_1196572341e_indi > $o] :
( ( pi_Arr1309696186_alt_o @ A_74
@ ^ [Uu: arrow_1196572341e_indi] : top_to1806834203lt_o_o )
= top_to732317616lt_o_o ) ).
thf(fact_225_in__below,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_2: produc1572197287le_alt > $o,A_73: arrow_1389031998le_alt,B_58: arrow_1389031998le_alt] :
( ( A_73 != B_58 )
=> ( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_1865170000_below @ L_2 @ A_73 @ B_58 ) )
<=> ( ( X != Y )
& ( ( Y = A_73 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ B_58 ) @ L_2 ) )
& ( ( Y != A_73 )
=> ( ( ( X = A_73 )
=> ( ( Y = B_58 )
| ( member285112084le_alt @ ( produc897867031le_alt @ B_58 @ Y ) @ L_2 ) ) )
& ( ( X != A_73 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_2 ) ) ) ) ) ) ) ) ).
thf(fact_226_order__refl,axiom,
! [X_45: ( produc1572197287le_alt > $o ) > $o] : ( ord_le1027220427lt_o_o @ X_45 @ X_45 ) ).
thf(fact_227_order__refl,axiom,
! [X_45: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] : ( ord_le1805007862lt_o_o @ X_45 @ X_45 ) ).
thf(fact_228_order__refl,axiom,
! [X_45: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] : ( ord_le602483040lt_o_o @ X_45 @ X_45 ) ).
thf(fact_229_order__refl,axiom,
! [X_45: produc1572197287le_alt > $o] : ( ord_le962286258_alt_o @ X_45 @ X_45 ) ).
thf(fact_230_order__refl,axiom,
! [X_45: $o] : ( ord_less_eq_o @ X_45 @ X_45 ) ).
thf(fact_231_order__refl,axiom,
! [X_45: arrow_1196572341e_indi > $o] : ( ord_le865407012indi_o @ X_45 @ X_45 ) ).
thf(fact_232_order__refl,axiom,
! [X_45: product_unit > $o] : ( ord_le1511552390unit_o @ X_45 @ X_45 ) ).
thf(fact_233_order__refl,axiom,
! [X_45: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] : ( ord_le1463467535_alt_o @ X_45 @ X_45 ) ).
thf(fact_234_order__refl,axiom,
! [X_45: nat] : ( ord_less_eq_nat @ X_45 @ X_45 ) ).
thf(fact_235_order__refl,axiom,
! [X_45: nat > $o] : ( ord_less_eq_nat_o @ X_45 @ X_45 ) ).
thf(fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I,axiom,
? [N: nat] :
( ( ord_less_nat @ N @ ( finite2011930979e_indi @ top_to54564308indi_o ) )
& ! [M: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( member285112084le_alt @ ( produc897867031le_alt @ b @ a )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ M ) @ lab @ lba ) ) ) )
& ( member285112084le_alt @ ( produc897867031le_alt @ a @ b )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ ( plus_plus_nat @ N @ one_one_nat ) ) @ lab @ lba ) ) ) ) ).
thf(fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_,axiom,
~ ! [N: nat] :
( ( ord_less_nat @ N @ ( finite2011930979e_indi @ top_to54564308indi_o ) )
=> ( ! [M: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( member285112084le_alt @ ( produc897867031le_alt @ b @ a )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ M ) @ lab @ lba ) ) ) )
=> ~ ( member285112084le_alt @ ( produc897867031le_alt @ a @ b )
@ ( f
@ ^ [I_1: arrow_1196572341e_indi] : ( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ I_1 ) @ ( plus_plus_nat @ N @ one_one_nat ) ) @ lab @ lba ) ) ) ) ) ).
thf(fact_238_linorder__le__cases,axiom,
! [X_44: nat,Y_33: nat] :
( ~ ( ord_less_eq_nat @ X_44 @ Y_33 )
=> ( ord_less_eq_nat @ Y_33 @ X_44 ) ) ).
thf(fact_239_le__funE,axiom,
! [X_43: produc1572197287le_alt > $o,F_27: ( produc1572197287le_alt > $o ) > $o,G_5: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ F_27 @ G_5 )
=> ( ord_less_eq_o @ ( F_27 @ X_43 ) @ ( G_5 @ X_43 ) ) ) ).
thf(fact_240_le__funE,axiom,
! [X_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_27: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,G_5: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ F_27 @ G_5 )
=> ( ord_less_eq_o @ ( F_27 @ X_43 ) @ ( G_5 @ X_43 ) ) ) ).
thf(fact_241_le__funE,axiom,
! [X_43: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_27: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,G_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ F_27 @ G_5 )
=> ( ord_less_eq_o @ ( F_27 @ X_43 ) @ ( G_5 @ X_43 ) ) ) ).
thf(fact_242_le__funE,axiom,
! [X_43: produc1572197287le_alt,F_27: produc1572197287le_alt > $o,G_5: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ F_27 @ G_5 )
=> ( ord_less_eq_o @ ( F_27 @ X_43 ) @ ( G_5 @ X_43 ) ) ) ).
thf(fact_243_le__funE,axiom,
! [X_43: arrow_1196572341e_indi,F_27: arrow_1196572341e_indi > $o,G_5: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ F_27 @ G_5 )
=> ( ord_less_eq_o @ ( F_27 @ X_43 ) @ ( G_5 @ X_43 ) ) ) ).
thf(fact_244_le__funE,axiom,
! [X_43: product_unit,F_27: product_unit > $o,G_5: product_unit > $o] :
( ( ord_le1511552390unit_o @ F_27 @ G_5 )
=> ( ord_less_eq_o @ ( F_27 @ X_43 ) @ ( G_5 @ X_43 ) ) ) ).
thf(fact_245_le__funE,axiom,
! [X_43: arrow_1389031998le_alt,F_27: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,G_5: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ F_27 @ G_5 )
=> ( ord_le1423491573_alt_o @ ( F_27 @ X_43 ) @ ( G_5 @ X_43 ) ) ) ).
thf(fact_246_le__funE,axiom,
! [X_43: nat,F_27: nat > $o,G_5: nat > $o] :
( ( ord_less_eq_nat_o @ F_27 @ G_5 )
=> ( ord_less_eq_o @ ( F_27 @ X_43 ) @ ( G_5 @ X_43 ) ) ) ).
thf(fact_247_xt1_I6_J,axiom,
! [Z_6: ( produc1572197287le_alt > $o ) > $o,Y_32: ( produc1572197287le_alt > $o ) > $o,X_42: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ Y_32 @ X_42 )
=> ( ( ord_le1027220427lt_o_o @ Z_6 @ Y_32 )
=> ( ord_le1027220427lt_o_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_248_xt1_I6_J,axiom,
! [Z_6: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_32: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_42: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ Y_32 @ X_42 )
=> ( ( ord_le1805007862lt_o_o @ Z_6 @ Y_32 )
=> ( ord_le1805007862lt_o_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_249_xt1_I6_J,axiom,
! [Z_6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_32: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_42: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y_32 @ X_42 )
=> ( ( ord_le602483040lt_o_o @ Z_6 @ Y_32 )
=> ( ord_le602483040lt_o_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_250_xt1_I6_J,axiom,
! [Z_6: produc1572197287le_alt > $o,Y_32: produc1572197287le_alt > $o,X_42: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ Y_32 @ X_42 )
=> ( ( ord_le962286258_alt_o @ Z_6 @ Y_32 )
=> ( ord_le962286258_alt_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_251_xt1_I6_J,axiom,
! [Z_6: $o,Y_32: $o,X_42: $o] :
( ( ord_less_eq_o @ Y_32 @ X_42 )
=> ( ( ord_less_eq_o @ Z_6 @ Y_32 )
=> ( ord_less_eq_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_252_xt1_I6_J,axiom,
! [Z_6: arrow_1196572341e_indi > $o,Y_32: arrow_1196572341e_indi > $o,X_42: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y_32 @ X_42 )
=> ( ( ord_le865407012indi_o @ Z_6 @ Y_32 )
=> ( ord_le865407012indi_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_253_xt1_I6_J,axiom,
! [Z_6: product_unit > $o,Y_32: product_unit > $o,X_42: product_unit > $o] :
( ( ord_le1511552390unit_o @ Y_32 @ X_42 )
=> ( ( ord_le1511552390unit_o @ Z_6 @ Y_32 )
=> ( ord_le1511552390unit_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_254_xt1_I6_J,axiom,
! [Z_6: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_32: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_42: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ Y_32 @ X_42 )
=> ( ( ord_le1463467535_alt_o @ Z_6 @ Y_32 )
=> ( ord_le1463467535_alt_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_255_xt1_I6_J,axiom,
! [Z_6: nat,Y_32: nat,X_42: nat] :
( ( ord_less_eq_nat @ Y_32 @ X_42 )
=> ( ( ord_less_eq_nat @ Z_6 @ Y_32 )
=> ( ord_less_eq_nat @ Z_6 @ X_42 ) ) ) ).
thf(fact_256_xt1_I6_J,axiom,
! [Z_6: nat > $o,Y_32: nat > $o,X_42: nat > $o] :
( ( ord_less_eq_nat_o @ Y_32 @ X_42 )
=> ( ( ord_less_eq_nat_o @ Z_6 @ Y_32 )
=> ( ord_less_eq_nat_o @ Z_6 @ X_42 ) ) ) ).
thf(fact_257_xt1_I5_J,axiom,
! [Y_31: ( produc1572197287le_alt > $o ) > $o,X_41: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ Y_31 @ X_41 )
=> ( ( ord_le1027220427lt_o_o @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_258_xt1_I5_J,axiom,
! [Y_31: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_41: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ Y_31 @ X_41 )
=> ( ( ord_le1805007862lt_o_o @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_259_xt1_I5_J,axiom,
! [Y_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_41: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y_31 @ X_41 )
=> ( ( ord_le602483040lt_o_o @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_260_xt1_I5_J,axiom,
! [Y_31: produc1572197287le_alt > $o,X_41: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ Y_31 @ X_41 )
=> ( ( ord_le962286258_alt_o @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_261_xt1_I5_J,axiom,
! [Y_31: $o,X_41: $o] :
( ( ord_less_eq_o @ Y_31 @ X_41 )
=> ( ( ord_less_eq_o @ X_41 @ Y_31 )
=> ( X_41
<=> Y_31 ) ) ) ).
thf(fact_262_xt1_I5_J,axiom,
! [Y_31: arrow_1196572341e_indi > $o,X_41: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y_31 @ X_41 )
=> ( ( ord_le865407012indi_o @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_263_xt1_I5_J,axiom,
! [Y_31: product_unit > $o,X_41: product_unit > $o] :
( ( ord_le1511552390unit_o @ Y_31 @ X_41 )
=> ( ( ord_le1511552390unit_o @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_264_xt1_I5_J,axiom,
! [Y_31: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_41: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ Y_31 @ X_41 )
=> ( ( ord_le1463467535_alt_o @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_265_xt1_I5_J,axiom,
! [Y_31: nat,X_41: nat] :
( ( ord_less_eq_nat @ Y_31 @ X_41 )
=> ( ( ord_less_eq_nat @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_266_xt1_I5_J,axiom,
! [Y_31: nat > $o,X_41: nat > $o] :
( ( ord_less_eq_nat_o @ Y_31 @ X_41 )
=> ( ( ord_less_eq_nat_o @ X_41 @ Y_31 )
=> ( X_41 = Y_31 ) ) ) ).
thf(fact_267_order__trans,axiom,
! [Z_5: ( produc1572197287le_alt > $o ) > $o,X_40: ( produc1572197287le_alt > $o ) > $o,Y_30: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_40 @ Y_30 )
=> ( ( ord_le1027220427lt_o_o @ Y_30 @ Z_5 )
=> ( ord_le1027220427lt_o_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_268_order__trans,axiom,
! [Z_5: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_40: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_40 @ Y_30 )
=> ( ( ord_le1805007862lt_o_o @ Y_30 @ Z_5 )
=> ( ord_le1805007862lt_o_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_269_order__trans,axiom,
! [Z_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_40: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_40 @ Y_30 )
=> ( ( ord_le602483040lt_o_o @ Y_30 @ Z_5 )
=> ( ord_le602483040lt_o_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_270_order__trans,axiom,
! [Z_5: produc1572197287le_alt > $o,X_40: produc1572197287le_alt > $o,Y_30: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_40 @ Y_30 )
=> ( ( ord_le962286258_alt_o @ Y_30 @ Z_5 )
=> ( ord_le962286258_alt_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_271_order__trans,axiom,
! [Z_5: $o,X_40: $o,Y_30: $o] :
( ( ord_less_eq_o @ X_40 @ Y_30 )
=> ( ( ord_less_eq_o @ Y_30 @ Z_5 )
=> ( ord_less_eq_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_272_order__trans,axiom,
! [Z_5: arrow_1196572341e_indi > $o,X_40: arrow_1196572341e_indi > $o,Y_30: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_40 @ Y_30 )
=> ( ( ord_le865407012indi_o @ Y_30 @ Z_5 )
=> ( ord_le865407012indi_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_273_order__trans,axiom,
! [Z_5: product_unit > $o,X_40: product_unit > $o,Y_30: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_40 @ Y_30 )
=> ( ( ord_le1511552390unit_o @ Y_30 @ Z_5 )
=> ( ord_le1511552390unit_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_274_order__trans,axiom,
! [Z_5: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_40: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_30: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_40 @ Y_30 )
=> ( ( ord_le1463467535_alt_o @ Y_30 @ Z_5 )
=> ( ord_le1463467535_alt_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_275_order__trans,axiom,
! [Z_5: nat,X_40: nat,Y_30: nat] :
( ( ord_less_eq_nat @ X_40 @ Y_30 )
=> ( ( ord_less_eq_nat @ Y_30 @ Z_5 )
=> ( ord_less_eq_nat @ X_40 @ Z_5 ) ) ) ).
thf(fact_276_order__trans,axiom,
! [Z_5: nat > $o,X_40: nat > $o,Y_30: nat > $o] :
( ( ord_less_eq_nat_o @ X_40 @ Y_30 )
=> ( ( ord_less_eq_nat_o @ Y_30 @ Z_5 )
=> ( ord_less_eq_nat_o @ X_40 @ Z_5 ) ) ) ).
thf(fact_277_order__antisym,axiom,
! [X_39: ( produc1572197287le_alt > $o ) > $o,Y_29: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_39 @ Y_29 )
=> ( ( ord_le1027220427lt_o_o @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_278_order__antisym,axiom,
! [X_39: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_29: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_39 @ Y_29 )
=> ( ( ord_le1805007862lt_o_o @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_279_order__antisym,axiom,
! [X_39: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_29: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_39 @ Y_29 )
=> ( ( ord_le602483040lt_o_o @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_280_order__antisym,axiom,
! [X_39: produc1572197287le_alt > $o,Y_29: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_39 @ Y_29 )
=> ( ( ord_le962286258_alt_o @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_281_order__antisym,axiom,
! [X_39: $o,Y_29: $o] :
( ( ord_less_eq_o @ X_39 @ Y_29 )
=> ( ( ord_less_eq_o @ Y_29 @ X_39 )
=> ( X_39
<=> Y_29 ) ) ) ).
thf(fact_282_order__antisym,axiom,
! [X_39: arrow_1196572341e_indi > $o,Y_29: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_39 @ Y_29 )
=> ( ( ord_le865407012indi_o @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_283_order__antisym,axiom,
! [X_39: product_unit > $o,Y_29: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_39 @ Y_29 )
=> ( ( ord_le1511552390unit_o @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_284_order__antisym,axiom,
! [X_39: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_29: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_39 @ Y_29 )
=> ( ( ord_le1463467535_alt_o @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_285_order__antisym,axiom,
! [X_39: nat,Y_29: nat] :
( ( ord_less_eq_nat @ X_39 @ Y_29 )
=> ( ( ord_less_eq_nat @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_286_order__antisym,axiom,
! [X_39: nat > $o,Y_29: nat > $o] :
( ( ord_less_eq_nat_o @ X_39 @ Y_29 )
=> ( ( ord_less_eq_nat_o @ Y_29 @ X_39 )
=> ( X_39 = Y_29 ) ) ) ).
thf(fact_287_xt1_I4_J,axiom,
! [C_37: ( produc1572197287le_alt > $o ) > $o,B_57: ( produc1572197287le_alt > $o ) > $o,A_72: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_le1027220427lt_o_o @ C_37 @ A_72 ) ) ) ).
thf(fact_288_xt1_I4_J,axiom,
! [C_37: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_57: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_72: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_le1805007862lt_o_o @ C_37 @ A_72 ) ) ) ).
thf(fact_289_xt1_I4_J,axiom,
! [C_37: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_57: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_72: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_le602483040lt_o_o @ C_37 @ A_72 ) ) ) ).
thf(fact_290_xt1_I4_J,axiom,
! [C_37: produc1572197287le_alt > $o,B_57: produc1572197287le_alt > $o,A_72: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_le962286258_alt_o @ C_37 @ A_72 ) ) ) ).
thf(fact_291_xt1_I4_J,axiom,
! [C_37: $o,B_57: $o,A_72: $o] :
( ( ord_less_eq_o @ B_57 @ A_72 )
=> ( ( B_57
<=> C_37 )
=> ( ord_less_eq_o @ C_37 @ A_72 ) ) ) ).
thf(fact_292_xt1_I4_J,axiom,
! [C_37: arrow_1196572341e_indi > $o,B_57: arrow_1196572341e_indi > $o,A_72: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_le865407012indi_o @ C_37 @ A_72 ) ) ) ).
thf(fact_293_xt1_I4_J,axiom,
! [C_37: product_unit > $o,B_57: product_unit > $o,A_72: product_unit > $o] :
( ( ord_le1511552390unit_o @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_le1511552390unit_o @ C_37 @ A_72 ) ) ) ).
thf(fact_294_xt1_I4_J,axiom,
! [C_37: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_57: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_72: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_le1463467535_alt_o @ C_37 @ A_72 ) ) ) ).
thf(fact_295_xt1_I4_J,axiom,
! [C_37: nat,B_57: nat,A_72: nat] :
( ( ord_less_eq_nat @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_less_eq_nat @ C_37 @ A_72 ) ) ) ).
thf(fact_296_xt1_I4_J,axiom,
! [C_37: nat > $o,B_57: nat > $o,A_72: nat > $o] :
( ( ord_less_eq_nat_o @ B_57 @ A_72 )
=> ( ( B_57 = C_37 )
=> ( ord_less_eq_nat_o @ C_37 @ A_72 ) ) ) ).
thf(fact_297_ord__le__eq__trans,axiom,
! [C_36: ( produc1572197287le_alt > $o ) > $o,A_71: ( produc1572197287le_alt > $o ) > $o,B_56: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_le1027220427lt_o_o @ A_71 @ C_36 ) ) ) ).
thf(fact_298_ord__le__eq__trans,axiom,
! [C_36: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_71: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_56: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_le1805007862lt_o_o @ A_71 @ C_36 ) ) ) ).
thf(fact_299_ord__le__eq__trans,axiom,
! [C_36: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_71: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_56: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_le602483040lt_o_o @ A_71 @ C_36 ) ) ) ).
thf(fact_300_ord__le__eq__trans,axiom,
! [C_36: produc1572197287le_alt > $o,A_71: produc1572197287le_alt > $o,B_56: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_le962286258_alt_o @ A_71 @ C_36 ) ) ) ).
thf(fact_301_ord__le__eq__trans,axiom,
! [C_36: $o,A_71: $o,B_56: $o] :
( ( ord_less_eq_o @ A_71 @ B_56 )
=> ( ( B_56
<=> C_36 )
=> ( ord_less_eq_o @ A_71 @ C_36 ) ) ) ).
thf(fact_302_ord__le__eq__trans,axiom,
! [C_36: arrow_1196572341e_indi > $o,A_71: arrow_1196572341e_indi > $o,B_56: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_le865407012indi_o @ A_71 @ C_36 ) ) ) ).
thf(fact_303_ord__le__eq__trans,axiom,
! [C_36: product_unit > $o,A_71: product_unit > $o,B_56: product_unit > $o] :
( ( ord_le1511552390unit_o @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_le1511552390unit_o @ A_71 @ C_36 ) ) ) ).
thf(fact_304_ord__le__eq__trans,axiom,
! [C_36: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_71: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_56: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_le1463467535_alt_o @ A_71 @ C_36 ) ) ) ).
thf(fact_305_ord__le__eq__trans,axiom,
! [C_36: nat,A_71: nat,B_56: nat] :
( ( ord_less_eq_nat @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_less_eq_nat @ A_71 @ C_36 ) ) ) ).
thf(fact_306_ord__le__eq__trans,axiom,
! [C_36: nat > $o,A_71: nat > $o,B_56: nat > $o] :
( ( ord_less_eq_nat_o @ A_71 @ B_56 )
=> ( ( B_56 = C_36 )
=> ( ord_less_eq_nat_o @ A_71 @ C_36 ) ) ) ).
thf(fact_307_xt1_I3_J,axiom,
! [C_35: ( produc1572197287le_alt > $o ) > $o,A_70: ( produc1572197287le_alt > $o ) > $o,B_55: ( produc1572197287le_alt > $o ) > $o] :
( ( A_70 = B_55 )
=> ( ( ord_le1027220427lt_o_o @ C_35 @ B_55 )
=> ( ord_le1027220427lt_o_o @ C_35 @ A_70 ) ) ) ).
thf(fact_308_xt1_I3_J,axiom,
! [C_35: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_70: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_55: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( A_70 = B_55 )
=> ( ( ord_le1805007862lt_o_o @ C_35 @ B_55 )
=> ( ord_le1805007862lt_o_o @ C_35 @ A_70 ) ) ) ).
thf(fact_309_xt1_I3_J,axiom,
! [C_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_70: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_55: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( A_70 = B_55 )
=> ( ( ord_le602483040lt_o_o @ C_35 @ B_55 )
=> ( ord_le602483040lt_o_o @ C_35 @ A_70 ) ) ) ).
thf(fact_310_xt1_I3_J,axiom,
! [C_35: produc1572197287le_alt > $o,A_70: produc1572197287le_alt > $o,B_55: produc1572197287le_alt > $o] :
( ( A_70 = B_55 )
=> ( ( ord_le962286258_alt_o @ C_35 @ B_55 )
=> ( ord_le962286258_alt_o @ C_35 @ A_70 ) ) ) ).
thf(fact_311_xt1_I3_J,axiom,
! [C_35: $o,B_55: $o,A_70: $o] :
( ( A_70
<=> B_55 )
=> ( ( ord_less_eq_o @ C_35 @ B_55 )
=> ( ord_less_eq_o @ C_35 @ A_70 ) ) ) ).
thf(fact_312_xt1_I3_J,axiom,
! [C_35: arrow_1196572341e_indi > $o,A_70: arrow_1196572341e_indi > $o,B_55: arrow_1196572341e_indi > $o] :
( ( A_70 = B_55 )
=> ( ( ord_le865407012indi_o @ C_35 @ B_55 )
=> ( ord_le865407012indi_o @ C_35 @ A_70 ) ) ) ).
thf(fact_313_xt1_I3_J,axiom,
! [C_35: product_unit > $o,A_70: product_unit > $o,B_55: product_unit > $o] :
( ( A_70 = B_55 )
=> ( ( ord_le1511552390unit_o @ C_35 @ B_55 )
=> ( ord_le1511552390unit_o @ C_35 @ A_70 ) ) ) ).
thf(fact_314_xt1_I3_J,axiom,
! [C_35: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_70: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_55: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( A_70 = B_55 )
=> ( ( ord_le1463467535_alt_o @ C_35 @ B_55 )
=> ( ord_le1463467535_alt_o @ C_35 @ A_70 ) ) ) ).
thf(fact_315_xt1_I3_J,axiom,
! [C_35: nat,A_70: nat,B_55: nat] :
( ( A_70 = B_55 )
=> ( ( ord_less_eq_nat @ C_35 @ B_55 )
=> ( ord_less_eq_nat @ C_35 @ A_70 ) ) ) ).
thf(fact_316_xt1_I3_J,axiom,
! [C_35: nat > $o,A_70: nat > $o,B_55: nat > $o] :
( ( A_70 = B_55 )
=> ( ( ord_less_eq_nat_o @ C_35 @ B_55 )
=> ( ord_less_eq_nat_o @ C_35 @ A_70 ) ) ) ).
thf(fact_317_ord__eq__le__trans,axiom,
! [C_34: ( produc1572197287le_alt > $o ) > $o,A_69: ( produc1572197287le_alt > $o ) > $o,B_54: ( produc1572197287le_alt > $o ) > $o] :
( ( A_69 = B_54 )
=> ( ( ord_le1027220427lt_o_o @ B_54 @ C_34 )
=> ( ord_le1027220427lt_o_o @ A_69 @ C_34 ) ) ) ).
thf(fact_318_ord__eq__le__trans,axiom,
! [C_34: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_69: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_54: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( A_69 = B_54 )
=> ( ( ord_le1805007862lt_o_o @ B_54 @ C_34 )
=> ( ord_le1805007862lt_o_o @ A_69 @ C_34 ) ) ) ).
thf(fact_319_ord__eq__le__trans,axiom,
! [C_34: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_69: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_54: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( A_69 = B_54 )
=> ( ( ord_le602483040lt_o_o @ B_54 @ C_34 )
=> ( ord_le602483040lt_o_o @ A_69 @ C_34 ) ) ) ).
thf(fact_320_ord__eq__le__trans,axiom,
! [C_34: produc1572197287le_alt > $o,A_69: produc1572197287le_alt > $o,B_54: produc1572197287le_alt > $o] :
( ( A_69 = B_54 )
=> ( ( ord_le962286258_alt_o @ B_54 @ C_34 )
=> ( ord_le962286258_alt_o @ A_69 @ C_34 ) ) ) ).
thf(fact_321_ord__eq__le__trans,axiom,
! [C_34: $o,B_54: $o,A_69: $o] :
( ( A_69
<=> B_54 )
=> ( ( ord_less_eq_o @ B_54 @ C_34 )
=> ( ord_less_eq_o @ A_69 @ C_34 ) ) ) ).
thf(fact_322_ord__eq__le__trans,axiom,
! [C_34: arrow_1196572341e_indi > $o,A_69: arrow_1196572341e_indi > $o,B_54: arrow_1196572341e_indi > $o] :
( ( A_69 = B_54 )
=> ( ( ord_le865407012indi_o @ B_54 @ C_34 )
=> ( ord_le865407012indi_o @ A_69 @ C_34 ) ) ) ).
thf(fact_323_ord__eq__le__trans,axiom,
! [C_34: product_unit > $o,A_69: product_unit > $o,B_54: product_unit > $o] :
( ( A_69 = B_54 )
=> ( ( ord_le1511552390unit_o @ B_54 @ C_34 )
=> ( ord_le1511552390unit_o @ A_69 @ C_34 ) ) ) ).
thf(fact_324_ord__eq__le__trans,axiom,
! [C_34: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_69: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_54: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( A_69 = B_54 )
=> ( ( ord_le1463467535_alt_o @ B_54 @ C_34 )
=> ( ord_le1463467535_alt_o @ A_69 @ C_34 ) ) ) ).
thf(fact_325_ord__eq__le__trans,axiom,
! [C_34: nat,A_69: nat,B_54: nat] :
( ( A_69 = B_54 )
=> ( ( ord_less_eq_nat @ B_54 @ C_34 )
=> ( ord_less_eq_nat @ A_69 @ C_34 ) ) ) ).
thf(fact_326_ord__eq__le__trans,axiom,
! [C_34: nat > $o,A_69: nat > $o,B_54: nat > $o] :
( ( A_69 = B_54 )
=> ( ( ord_less_eq_nat_o @ B_54 @ C_34 )
=> ( ord_less_eq_nat_o @ A_69 @ C_34 ) ) ) ).
thf(fact_327_order__antisym__conv,axiom,
! [Y_28: ( produc1572197287le_alt > $o ) > $o,X_38: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ Y_28 @ X_38 )
=> ( ( ord_le1027220427lt_o_o @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_328_order__antisym__conv,axiom,
! [Y_28: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_38: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ Y_28 @ X_38 )
=> ( ( ord_le1805007862lt_o_o @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_329_order__antisym__conv,axiom,
! [Y_28: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_38: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y_28 @ X_38 )
=> ( ( ord_le602483040lt_o_o @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_330_order__antisym__conv,axiom,
! [Y_28: produc1572197287le_alt > $o,X_38: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ Y_28 @ X_38 )
=> ( ( ord_le962286258_alt_o @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_331_order__antisym__conv,axiom,
! [Y_28: $o,X_38: $o] :
( ( ord_less_eq_o @ Y_28 @ X_38 )
=> ( ( ord_less_eq_o @ X_38 @ Y_28 )
<=> ( X_38
<=> Y_28 ) ) ) ).
thf(fact_332_order__antisym__conv,axiom,
! [Y_28: arrow_1196572341e_indi > $o,X_38: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y_28 @ X_38 )
=> ( ( ord_le865407012indi_o @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_333_order__antisym__conv,axiom,
! [Y_28: product_unit > $o,X_38: product_unit > $o] :
( ( ord_le1511552390unit_o @ Y_28 @ X_38 )
=> ( ( ord_le1511552390unit_o @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_334_order__antisym__conv,axiom,
! [Y_28: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_38: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ Y_28 @ X_38 )
=> ( ( ord_le1463467535_alt_o @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_335_order__antisym__conv,axiom,
! [Y_28: nat,X_38: nat] :
( ( ord_less_eq_nat @ Y_28 @ X_38 )
=> ( ( ord_less_eq_nat @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_336_order__antisym__conv,axiom,
! [Y_28: nat > $o,X_38: nat > $o] :
( ( ord_less_eq_nat_o @ Y_28 @ X_38 )
=> ( ( ord_less_eq_nat_o @ X_38 @ Y_28 )
<=> ( X_38 = Y_28 ) ) ) ).
thf(fact_337_le__funD,axiom,
! [X_37: produc1572197287le_alt > $o,F_26: ( produc1572197287le_alt > $o ) > $o,G_4: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ F_26 @ G_4 )
=> ( ord_less_eq_o @ ( F_26 @ X_37 ) @ ( G_4 @ X_37 ) ) ) ).
thf(fact_338_le__funD,axiom,
! [X_37: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_26: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,G_4: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ F_26 @ G_4 )
=> ( ord_less_eq_o @ ( F_26 @ X_37 ) @ ( G_4 @ X_37 ) ) ) ).
thf(fact_339_le__funD,axiom,
! [X_37: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_26: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,G_4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ F_26 @ G_4 )
=> ( ord_less_eq_o @ ( F_26 @ X_37 ) @ ( G_4 @ X_37 ) ) ) ).
thf(fact_340_le__funD,axiom,
! [X_37: produc1572197287le_alt,F_26: produc1572197287le_alt > $o,G_4: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ F_26 @ G_4 )
=> ( ord_less_eq_o @ ( F_26 @ X_37 ) @ ( G_4 @ X_37 ) ) ) ).
thf(fact_341_le__funD,axiom,
! [X_37: arrow_1196572341e_indi,F_26: arrow_1196572341e_indi > $o,G_4: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ F_26 @ G_4 )
=> ( ord_less_eq_o @ ( F_26 @ X_37 ) @ ( G_4 @ X_37 ) ) ) ).
thf(fact_342_le__funD,axiom,
! [X_37: product_unit,F_26: product_unit > $o,G_4: product_unit > $o] :
( ( ord_le1511552390unit_o @ F_26 @ G_4 )
=> ( ord_less_eq_o @ ( F_26 @ X_37 ) @ ( G_4 @ X_37 ) ) ) ).
thf(fact_343_le__funD,axiom,
! [X_37: arrow_1389031998le_alt,F_26: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,G_4: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ F_26 @ G_4 )
=> ( ord_le1423491573_alt_o @ ( F_26 @ X_37 ) @ ( G_4 @ X_37 ) ) ) ).
thf(fact_344_le__funD,axiom,
! [X_37: nat,F_26: nat > $o,G_4: nat > $o] :
( ( ord_less_eq_nat_o @ F_26 @ G_4 )
=> ( ord_less_eq_o @ ( F_26 @ X_37 ) @ ( G_4 @ X_37 ) ) ) ).
thf(fact_345_order__eq__refl,axiom,
! [X_36: ( produc1572197287le_alt > $o ) > $o,Y_27: ( produc1572197287le_alt > $o ) > $o] :
( ( X_36 = Y_27 )
=> ( ord_le1027220427lt_o_o @ X_36 @ Y_27 ) ) ).
thf(fact_346_order__eq__refl,axiom,
! [X_36: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_27: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( X_36 = Y_27 )
=> ( ord_le1805007862lt_o_o @ X_36 @ Y_27 ) ) ).
thf(fact_347_order__eq__refl,axiom,
! [X_36: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_27: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( X_36 = Y_27 )
=> ( ord_le602483040lt_o_o @ X_36 @ Y_27 ) ) ).
thf(fact_348_order__eq__refl,axiom,
! [X_36: produc1572197287le_alt > $o,Y_27: produc1572197287le_alt > $o] :
( ( X_36 = Y_27 )
=> ( ord_le962286258_alt_o @ X_36 @ Y_27 ) ) ).
thf(fact_349_order__eq__refl,axiom,
! [Y_27: $o,X_36: $o] :
( ( X_36
<=> Y_27 )
=> ( ord_less_eq_o @ X_36 @ Y_27 ) ) ).
thf(fact_350_order__eq__refl,axiom,
! [X_36: arrow_1196572341e_indi > $o,Y_27: arrow_1196572341e_indi > $o] :
( ( X_36 = Y_27 )
=> ( ord_le865407012indi_o @ X_36 @ Y_27 ) ) ).
thf(fact_351_order__eq__refl,axiom,
! [X_36: product_unit > $o,Y_27: product_unit > $o] :
( ( X_36 = Y_27 )
=> ( ord_le1511552390unit_o @ X_36 @ Y_27 ) ) ).
thf(fact_352_order__eq__refl,axiom,
! [X_36: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_27: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( X_36 = Y_27 )
=> ( ord_le1463467535_alt_o @ X_36 @ Y_27 ) ) ).
thf(fact_353_order__eq__refl,axiom,
! [X_36: nat,Y_27: nat] :
( ( X_36 = Y_27 )
=> ( ord_less_eq_nat @ X_36 @ Y_27 ) ) ).
thf(fact_354_order__eq__refl,axiom,
! [X_36: nat > $o,Y_27: nat > $o] :
( ( X_36 = Y_27 )
=> ( ord_less_eq_nat_o @ X_36 @ Y_27 ) ) ).
thf(fact_355_order__eq__iff,axiom,
! [X_35: ( produc1572197287le_alt > $o ) > $o,Y_26: ( produc1572197287le_alt > $o ) > $o] :
( ( X_35 = Y_26 )
<=> ( ( ord_le1027220427lt_o_o @ X_35 @ Y_26 )
& ( ord_le1027220427lt_o_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_356_order__eq__iff,axiom,
! [X_35: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_26: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( X_35 = Y_26 )
<=> ( ( ord_le1805007862lt_o_o @ X_35 @ Y_26 )
& ( ord_le1805007862lt_o_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_357_order__eq__iff,axiom,
! [X_35: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_26: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( X_35 = Y_26 )
<=> ( ( ord_le602483040lt_o_o @ X_35 @ Y_26 )
& ( ord_le602483040lt_o_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_358_order__eq__iff,axiom,
! [X_35: produc1572197287le_alt > $o,Y_26: produc1572197287le_alt > $o] :
( ( X_35 = Y_26 )
<=> ( ( ord_le962286258_alt_o @ X_35 @ Y_26 )
& ( ord_le962286258_alt_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_359_order__eq__iff,axiom,
! [Y_26: $o,X_35: $o] :
( ( X_35
<=> Y_26 )
<=> ( ( ord_less_eq_o @ X_35 @ Y_26 )
& ( ord_less_eq_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_360_order__eq__iff,axiom,
! [X_35: arrow_1196572341e_indi > $o,Y_26: arrow_1196572341e_indi > $o] :
( ( X_35 = Y_26 )
<=> ( ( ord_le865407012indi_o @ X_35 @ Y_26 )
& ( ord_le865407012indi_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_361_order__eq__iff,axiom,
! [X_35: product_unit > $o,Y_26: product_unit > $o] :
( ( X_35 = Y_26 )
<=> ( ( ord_le1511552390unit_o @ X_35 @ Y_26 )
& ( ord_le1511552390unit_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_362_order__eq__iff,axiom,
! [X_35: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_26: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( X_35 = Y_26 )
<=> ( ( ord_le1463467535_alt_o @ X_35 @ Y_26 )
& ( ord_le1463467535_alt_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_363_order__eq__iff,axiom,
! [X_35: nat,Y_26: nat] :
( ( X_35 = Y_26 )
<=> ( ( ord_less_eq_nat @ X_35 @ Y_26 )
& ( ord_less_eq_nat @ Y_26 @ X_35 ) ) ) ).
thf(fact_364_order__eq__iff,axiom,
! [X_35: nat > $o,Y_26: nat > $o] :
( ( X_35 = Y_26 )
<=> ( ( ord_less_eq_nat_o @ X_35 @ Y_26 )
& ( ord_less_eq_nat_o @ Y_26 @ X_35 ) ) ) ).
thf(fact_365_linorder__linear,axiom,
! [X_34: nat,Y_25: nat] :
( ( ord_less_eq_nat @ X_34 @ Y_25 )
| ( ord_less_eq_nat @ Y_25 @ X_34 ) ) ).
thf(fact_366_le__fun__def,axiom,
! [F_25: ( produc1572197287le_alt > $o ) > $o,G_3: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ F_25 @ G_3 )
<=> ! [X_1: produc1572197287le_alt > $o] : ( ord_less_eq_o @ ( F_25 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
thf(fact_367_le__fun__def,axiom,
! [F_25: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,G_3: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ F_25 @ G_3 )
<=> ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( ord_less_eq_o @ ( F_25 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
thf(fact_368_le__fun__def,axiom,
! [F_25: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,G_3: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ F_25 @ G_3 )
<=> ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( ord_less_eq_o @ ( F_25 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
thf(fact_369_le__fun__def,axiom,
! [F_25: produc1572197287le_alt > $o,G_3: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ F_25 @ G_3 )
<=> ! [X_1: produc1572197287le_alt] : ( ord_less_eq_o @ ( F_25 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
thf(fact_370_le__fun__def,axiom,
! [F_25: arrow_1196572341e_indi > $o,G_3: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ F_25 @ G_3 )
<=> ! [X_1: arrow_1196572341e_indi] : ( ord_less_eq_o @ ( F_25 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
thf(fact_371_le__fun__def,axiom,
! [F_25: product_unit > $o,G_3: product_unit > $o] :
( ( ord_le1511552390unit_o @ F_25 @ G_3 )
<=> ! [X_1: product_unit] : ( ord_less_eq_o @ ( F_25 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
thf(fact_372_le__fun__def,axiom,
! [F_25: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,G_3: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ F_25 @ G_3 )
<=> ! [X_1: arrow_1389031998le_alt] : ( ord_le1423491573_alt_o @ ( F_25 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
thf(fact_373_le__fun__def,axiom,
! [F_25: nat > $o,G_3: nat > $o] :
( ( ord_less_eq_nat_o @ F_25 @ G_3 )
<=> ! [X_1: nat] : ( ord_less_eq_o @ ( F_25 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
thf(fact_374_linorder__not__less,axiom,
! [X_33: nat,Y_24: nat] :
( ~ ( ord_less_nat @ X_33 @ Y_24 )
<=> ( ord_less_eq_nat @ Y_24 @ X_33 ) ) ).
thf(fact_375_linorder__not__le,axiom,
! [X_32: nat,Y_23: nat] :
( ~ ( ord_less_eq_nat @ X_32 @ Y_23 )
<=> ( ord_less_nat @ Y_23 @ X_32 ) ) ).
thf(fact_376_linorder__le__less__linear,axiom,
! [X_31: nat,Y_22: nat] :
( ( ord_less_eq_nat @ X_31 @ Y_22 )
| ( ord_less_nat @ Y_22 @ X_31 ) ) ).
thf(fact_377_order__less__le,axiom,
! [X_30: product_unit > $o,Y_21: product_unit > $o] :
( ( ord_le232288914unit_o @ X_30 @ Y_21 )
<=> ( ( ord_le1511552390unit_o @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_378_order__less__le,axiom,
! [X_30: arrow_1196572341e_indi > $o,Y_21: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_30 @ Y_21 )
<=> ( ( ord_le865407012indi_o @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_379_order__less__le,axiom,
! [X_30: ( produc1572197287le_alt > $o ) > $o,Y_21: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ X_30 @ Y_21 )
<=> ( ( ord_le1027220427lt_o_o @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_380_order__less__le,axiom,
! [X_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ X_30 @ Y_21 )
<=> ( ( ord_le1805007862lt_o_o @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_381_order__less__le,axiom,
! [X_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ X_30 @ Y_21 )
<=> ( ( ord_le602483040lt_o_o @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_382_order__less__le,axiom,
! [X_30: produc1572197287le_alt > $o,Y_21: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ X_30 @ Y_21 )
<=> ( ( ord_le962286258_alt_o @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_383_order__less__le,axiom,
! [X_30: $o,Y_21: $o] :
( ( ord_less_o @ X_30 @ Y_21 )
<=> ( ( ord_less_eq_o @ X_30 @ Y_21 )
& ~ ( X_30
<=> Y_21 ) ) ) ).
thf(fact_384_order__less__le,axiom,
! [X_30: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_21: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1339521307_alt_o @ X_30 @ Y_21 )
<=> ( ( ord_le1463467535_alt_o @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_385_order__less__le,axiom,
! [X_30: nat > $o,Y_21: nat > $o] :
( ( ord_less_nat_o @ X_30 @ Y_21 )
<=> ( ( ord_less_eq_nat_o @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_386_order__less__le,axiom,
! [X_30: nat,Y_21: nat] :
( ( ord_less_nat @ X_30 @ Y_21 )
<=> ( ( ord_less_eq_nat @ X_30 @ Y_21 )
& ( X_30 != Y_21 ) ) ) ).
thf(fact_387_less__le__not__le,axiom,
! [X_29: product_unit > $o,Y_20: product_unit > $o] :
( ( ord_le232288914unit_o @ X_29 @ Y_20 )
<=> ( ( ord_le1511552390unit_o @ X_29 @ Y_20 )
& ~ ( ord_le1511552390unit_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_388_less__le__not__le,axiom,
! [X_29: arrow_1196572341e_indi > $o,Y_20: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_29 @ Y_20 )
<=> ( ( ord_le865407012indi_o @ X_29 @ Y_20 )
& ~ ( ord_le865407012indi_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_389_less__le__not__le,axiom,
! [X_29: ( produc1572197287le_alt > $o ) > $o,Y_20: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ X_29 @ Y_20 )
<=> ( ( ord_le1027220427lt_o_o @ X_29 @ Y_20 )
& ~ ( ord_le1027220427lt_o_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_390_less__le__not__le,axiom,
! [X_29: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ X_29 @ Y_20 )
<=> ( ( ord_le1805007862lt_o_o @ X_29 @ Y_20 )
& ~ ( ord_le1805007862lt_o_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_391_less__le__not__le,axiom,
! [X_29: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ X_29 @ Y_20 )
<=> ( ( ord_le602483040lt_o_o @ X_29 @ Y_20 )
& ~ ( ord_le602483040lt_o_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_392_less__le__not__le,axiom,
! [X_29: produc1572197287le_alt > $o,Y_20: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ X_29 @ Y_20 )
<=> ( ( ord_le962286258_alt_o @ X_29 @ Y_20 )
& ~ ( ord_le962286258_alt_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_393_less__le__not__le,axiom,
! [X_29: $o,Y_20: $o] :
( ( ord_less_o @ X_29 @ Y_20 )
<=> ( ( ord_less_eq_o @ X_29 @ Y_20 )
& ~ ( ord_less_eq_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_394_less__le__not__le,axiom,
! [X_29: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_20: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1339521307_alt_o @ X_29 @ Y_20 )
<=> ( ( ord_le1463467535_alt_o @ X_29 @ Y_20 )
& ~ ( ord_le1463467535_alt_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_395_less__le__not__le,axiom,
! [X_29: nat > $o,Y_20: nat > $o] :
( ( ord_less_nat_o @ X_29 @ Y_20 )
<=> ( ( ord_less_eq_nat_o @ X_29 @ Y_20 )
& ~ ( ord_less_eq_nat_o @ Y_20 @ X_29 ) ) ) ).
thf(fact_396_less__le__not__le,axiom,
! [X_29: nat,Y_20: nat] :
( ( ord_less_nat @ X_29 @ Y_20 )
<=> ( ( ord_less_eq_nat @ X_29 @ Y_20 )
& ~ ( ord_less_eq_nat @ Y_20 @ X_29 ) ) ) ).
thf(fact_397_order__le__less,axiom,
! [X_28: product_unit > $o,Y_19: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_28 @ Y_19 )
<=> ( ( ord_le232288914unit_o @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_398_order__le__less,axiom,
! [X_28: arrow_1196572341e_indi > $o,Y_19: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_28 @ Y_19 )
<=> ( ( ord_le1991507760indi_o @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_399_order__le__less,axiom,
! [X_28: ( produc1572197287le_alt > $o ) > $o,Y_19: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_28 @ Y_19 )
<=> ( ( ord_le874404799lt_o_o @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_400_order__le__less,axiom,
! [X_28: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_28 @ Y_19 )
<=> ( ( ord_le1382328578lt_o_o @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_401_order__le__less,axiom,
! [X_28: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_28 @ Y_19 )
<=> ( ( ord_le914873172lt_o_o @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_402_order__le__less,axiom,
! [X_28: produc1572197287le_alt > $o,Y_19: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_28 @ Y_19 )
<=> ( ( ord_le1852932542_alt_o @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_403_order__le__less,axiom,
! [X_28: $o,Y_19: $o] :
( ( ord_less_eq_o @ X_28 @ Y_19 )
<=> ( ( ord_less_o @ X_28 @ Y_19 )
| ( X_28
<=> Y_19 ) ) ) ).
thf(fact_404_order__le__less,axiom,
! [X_28: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_19: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_28 @ Y_19 )
<=> ( ( ord_le1339521307_alt_o @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_405_order__le__less,axiom,
! [X_28: nat > $o,Y_19: nat > $o] :
( ( ord_less_eq_nat_o @ X_28 @ Y_19 )
<=> ( ( ord_less_nat_o @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_406_order__le__less,axiom,
! [X_28: nat,Y_19: nat] :
( ( ord_less_eq_nat @ X_28 @ Y_19 )
<=> ( ( ord_less_nat @ X_28 @ Y_19 )
| ( X_28 = Y_19 ) ) ) ).
thf(fact_407_leI,axiom,
! [X_27: nat,Y_18: nat] :
( ~ ( ord_less_nat @ X_27 @ Y_18 )
=> ( ord_less_eq_nat @ Y_18 @ X_27 ) ) ).
thf(fact_408_not__leE,axiom,
! [Y_17: nat,X_26: nat] :
( ~ ( ord_less_eq_nat @ Y_17 @ X_26 )
=> ( ord_less_nat @ X_26 @ Y_17 ) ) ).
thf(fact_409_linorder__antisym__conv1,axiom,
! [X_25: nat,Y_16: nat] :
( ~ ( ord_less_nat @ X_25 @ Y_16 )
=> ( ( ord_less_eq_nat @ X_25 @ Y_16 )
<=> ( X_25 = Y_16 ) ) ) ).
thf(fact_410_order__neq__le__trans,axiom,
! [A_68: product_unit > $o,B_53: product_unit > $o] :
( ( A_68 != B_53 )
=> ( ( ord_le1511552390unit_o @ A_68 @ B_53 )
=> ( ord_le232288914unit_o @ A_68 @ B_53 ) ) ) ).
thf(fact_411_order__neq__le__trans,axiom,
! [A_68: arrow_1196572341e_indi > $o,B_53: arrow_1196572341e_indi > $o] :
( ( A_68 != B_53 )
=> ( ( ord_le865407012indi_o @ A_68 @ B_53 )
=> ( ord_le1991507760indi_o @ A_68 @ B_53 ) ) ) ).
thf(fact_412_order__neq__le__trans,axiom,
! [A_68: ( produc1572197287le_alt > $o ) > $o,B_53: ( produc1572197287le_alt > $o ) > $o] :
( ( A_68 != B_53 )
=> ( ( ord_le1027220427lt_o_o @ A_68 @ B_53 )
=> ( ord_le874404799lt_o_o @ A_68 @ B_53 ) ) ) ).
thf(fact_413_order__neq__le__trans,axiom,
! [A_68: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_53: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( A_68 != B_53 )
=> ( ( ord_le1805007862lt_o_o @ A_68 @ B_53 )
=> ( ord_le1382328578lt_o_o @ A_68 @ B_53 ) ) ) ).
thf(fact_414_order__neq__le__trans,axiom,
! [A_68: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_53: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( A_68 != B_53 )
=> ( ( ord_le602483040lt_o_o @ A_68 @ B_53 )
=> ( ord_le914873172lt_o_o @ A_68 @ B_53 ) ) ) ).
thf(fact_415_order__neq__le__trans,axiom,
! [A_68: produc1572197287le_alt > $o,B_53: produc1572197287le_alt > $o] :
( ( A_68 != B_53 )
=> ( ( ord_le962286258_alt_o @ A_68 @ B_53 )
=> ( ord_le1852932542_alt_o @ A_68 @ B_53 ) ) ) ).
thf(fact_416_order__neq__le__trans,axiom,
! [B_53: $o,A_68: $o] :
( ~ ( A_68
<=> B_53 )
=> ( ( ord_less_eq_o @ A_68 @ B_53 )
=> ( ord_less_o @ A_68 @ B_53 ) ) ) ).
thf(fact_417_order__neq__le__trans,axiom,
! [A_68: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_53: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( A_68 != B_53 )
=> ( ( ord_le1463467535_alt_o @ A_68 @ B_53 )
=> ( ord_le1339521307_alt_o @ A_68 @ B_53 ) ) ) ).
thf(fact_418_order__neq__le__trans,axiom,
! [A_68: nat > $o,B_53: nat > $o] :
( ( A_68 != B_53 )
=> ( ( ord_less_eq_nat_o @ A_68 @ B_53 )
=> ( ord_less_nat_o @ A_68 @ B_53 ) ) ) ).
thf(fact_419_order__neq__le__trans,axiom,
! [A_68: nat,B_53: nat] :
( ( A_68 != B_53 )
=> ( ( ord_less_eq_nat @ A_68 @ B_53 )
=> ( ord_less_nat @ A_68 @ B_53 ) ) ) ).
thf(fact_420_xt1_I12_J,axiom,
! [A_67: product_unit > $o,B_52: product_unit > $o] :
( ( A_67 != B_52 )
=> ( ( ord_le1511552390unit_o @ B_52 @ A_67 )
=> ( ord_le232288914unit_o @ B_52 @ A_67 ) ) ) ).
thf(fact_421_xt1_I12_J,axiom,
! [A_67: arrow_1196572341e_indi > $o,B_52: arrow_1196572341e_indi > $o] :
( ( A_67 != B_52 )
=> ( ( ord_le865407012indi_o @ B_52 @ A_67 )
=> ( ord_le1991507760indi_o @ B_52 @ A_67 ) ) ) ).
thf(fact_422_xt1_I12_J,axiom,
! [A_67: ( produc1572197287le_alt > $o ) > $o,B_52: ( produc1572197287le_alt > $o ) > $o] :
( ( A_67 != B_52 )
=> ( ( ord_le1027220427lt_o_o @ B_52 @ A_67 )
=> ( ord_le874404799lt_o_o @ B_52 @ A_67 ) ) ) ).
thf(fact_423_xt1_I12_J,axiom,
! [A_67: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_52: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( A_67 != B_52 )
=> ( ( ord_le1805007862lt_o_o @ B_52 @ A_67 )
=> ( ord_le1382328578lt_o_o @ B_52 @ A_67 ) ) ) ).
thf(fact_424_xt1_I12_J,axiom,
! [A_67: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_52: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( A_67 != B_52 )
=> ( ( ord_le602483040lt_o_o @ B_52 @ A_67 )
=> ( ord_le914873172lt_o_o @ B_52 @ A_67 ) ) ) ).
thf(fact_425_xt1_I12_J,axiom,
! [A_67: produc1572197287le_alt > $o,B_52: produc1572197287le_alt > $o] :
( ( A_67 != B_52 )
=> ( ( ord_le962286258_alt_o @ B_52 @ A_67 )
=> ( ord_le1852932542_alt_o @ B_52 @ A_67 ) ) ) ).
thf(fact_426_xt1_I12_J,axiom,
! [B_52: $o,A_67: $o] :
( ~ ( A_67
<=> B_52 )
=> ( ( ord_less_eq_o @ B_52 @ A_67 )
=> ( ord_less_o @ B_52 @ A_67 ) ) ) ).
thf(fact_427_xt1_I12_J,axiom,
! [A_67: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_52: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( A_67 != B_52 )
=> ( ( ord_le1463467535_alt_o @ B_52 @ A_67 )
=> ( ord_le1339521307_alt_o @ B_52 @ A_67 ) ) ) ).
thf(fact_428_xt1_I12_J,axiom,
! [A_67: nat > $o,B_52: nat > $o] :
( ( A_67 != B_52 )
=> ( ( ord_less_eq_nat_o @ B_52 @ A_67 )
=> ( ord_less_nat_o @ B_52 @ A_67 ) ) ) ).
thf(fact_429_xt1_I12_J,axiom,
! [A_67: nat,B_52: nat] :
( ( A_67 != B_52 )
=> ( ( ord_less_eq_nat @ B_52 @ A_67 )
=> ( ord_less_nat @ B_52 @ A_67 ) ) ) ).
thf(fact_430_leD,axiom,
! [Y_15: nat,X_24: nat] :
( ( ord_less_eq_nat @ Y_15 @ X_24 )
=> ~ ( ord_less_nat @ X_24 @ Y_15 ) ) ).
thf(fact_431_order__less__imp__le,axiom,
! [X_23: product_unit > $o,Y_14: product_unit > $o] :
( ( ord_le232288914unit_o @ X_23 @ Y_14 )
=> ( ord_le1511552390unit_o @ X_23 @ Y_14 ) ) ).
thf(fact_432_order__less__imp__le,axiom,
! [X_23: arrow_1196572341e_indi > $o,Y_14: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_23 @ Y_14 )
=> ( ord_le865407012indi_o @ X_23 @ Y_14 ) ) ).
thf(fact_433_order__less__imp__le,axiom,
! [X_23: ( produc1572197287le_alt > $o ) > $o,Y_14: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ X_23 @ Y_14 )
=> ( ord_le1027220427lt_o_o @ X_23 @ Y_14 ) ) ).
thf(fact_434_order__less__imp__le,axiom,
! [X_23: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_14: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ X_23 @ Y_14 )
=> ( ord_le1805007862lt_o_o @ X_23 @ Y_14 ) ) ).
thf(fact_435_order__less__imp__le,axiom,
! [X_23: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_14: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ X_23 @ Y_14 )
=> ( ord_le602483040lt_o_o @ X_23 @ Y_14 ) ) ).
thf(fact_436_order__less__imp__le,axiom,
! [X_23: produc1572197287le_alt > $o,Y_14: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ X_23 @ Y_14 )
=> ( ord_le962286258_alt_o @ X_23 @ Y_14 ) ) ).
thf(fact_437_order__less__imp__le,axiom,
! [X_23: $o,Y_14: $o] :
( ( ord_less_o @ X_23 @ Y_14 )
=> ( ord_less_eq_o @ X_23 @ Y_14 ) ) ).
thf(fact_438_order__less__imp__le,axiom,
! [X_23: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_14: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1339521307_alt_o @ X_23 @ Y_14 )
=> ( ord_le1463467535_alt_o @ X_23 @ Y_14 ) ) ).
thf(fact_439_order__less__imp__le,axiom,
! [X_23: nat > $o,Y_14: nat > $o] :
( ( ord_less_nat_o @ X_23 @ Y_14 )
=> ( ord_less_eq_nat_o @ X_23 @ Y_14 ) ) ).
thf(fact_440_order__less__imp__le,axiom,
! [X_23: nat,Y_14: nat] :
( ( ord_less_nat @ X_23 @ Y_14 )
=> ( ord_less_eq_nat @ X_23 @ Y_14 ) ) ).
thf(fact_441_linorder__antisym__conv2,axiom,
! [X_22: nat,Y_13: nat] :
( ( ord_less_eq_nat @ X_22 @ Y_13 )
=> ( ~ ( ord_less_nat @ X_22 @ Y_13 )
<=> ( X_22 = Y_13 ) ) ) ).
thf(fact_442_order__le__imp__less__or__eq,axiom,
! [X_21: product_unit > $o,Y_12: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_21 @ Y_12 )
=> ( ( ord_le232288914unit_o @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_443_order__le__imp__less__or__eq,axiom,
! [X_21: arrow_1196572341e_indi > $o,Y_12: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_21 @ Y_12 )
=> ( ( ord_le1991507760indi_o @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_444_order__le__imp__less__or__eq,axiom,
! [X_21: ( produc1572197287le_alt > $o ) > $o,Y_12: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_21 @ Y_12 )
=> ( ( ord_le874404799lt_o_o @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_445_order__le__imp__less__or__eq,axiom,
! [X_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_12: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_21 @ Y_12 )
=> ( ( ord_le1382328578lt_o_o @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_446_order__le__imp__less__or__eq,axiom,
! [X_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_12: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_21 @ Y_12 )
=> ( ( ord_le914873172lt_o_o @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_447_order__le__imp__less__or__eq,axiom,
! [X_21: produc1572197287le_alt > $o,Y_12: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_21 @ Y_12 )
=> ( ( ord_le1852932542_alt_o @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_448_order__le__imp__less__or__eq,axiom,
! [X_21: $o,Y_12: $o] :
( ( ord_less_eq_o @ X_21 @ Y_12 )
=> ( ( ord_less_o @ X_21 @ Y_12 )
| ( X_21
<=> Y_12 ) ) ) ).
thf(fact_449_order__le__imp__less__or__eq,axiom,
! [X_21: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_12: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_21 @ Y_12 )
=> ( ( ord_le1339521307_alt_o @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_450_order__le__imp__less__or__eq,axiom,
! [X_21: nat > $o,Y_12: nat > $o] :
( ( ord_less_eq_nat_o @ X_21 @ Y_12 )
=> ( ( ord_less_nat_o @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_451_order__le__imp__less__or__eq,axiom,
! [X_21: nat,Y_12: nat] :
( ( ord_less_eq_nat @ X_21 @ Y_12 )
=> ( ( ord_less_nat @ X_21 @ Y_12 )
| ( X_21 = Y_12 ) ) ) ).
thf(fact_452_order__le__neq__trans,axiom,
! [A_66: product_unit > $o,B_51: product_unit > $o] :
( ( ord_le1511552390unit_o @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_le232288914unit_o @ A_66 @ B_51 ) ) ) ).
thf(fact_453_order__le__neq__trans,axiom,
! [A_66: arrow_1196572341e_indi > $o,B_51: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_le1991507760indi_o @ A_66 @ B_51 ) ) ) ).
thf(fact_454_order__le__neq__trans,axiom,
! [A_66: ( produc1572197287le_alt > $o ) > $o,B_51: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_le874404799lt_o_o @ A_66 @ B_51 ) ) ) ).
thf(fact_455_order__le__neq__trans,axiom,
! [A_66: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_51: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_le1382328578lt_o_o @ A_66 @ B_51 ) ) ) ).
thf(fact_456_order__le__neq__trans,axiom,
! [A_66: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_51: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_le914873172lt_o_o @ A_66 @ B_51 ) ) ) ).
thf(fact_457_order__le__neq__trans,axiom,
! [A_66: produc1572197287le_alt > $o,B_51: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_le1852932542_alt_o @ A_66 @ B_51 ) ) ) ).
thf(fact_458_order__le__neq__trans,axiom,
! [A_66: $o,B_51: $o] :
( ( ord_less_eq_o @ A_66 @ B_51 )
=> ( ~ ( A_66
<=> B_51 )
=> ( ord_less_o @ A_66 @ B_51 ) ) ) ).
thf(fact_459_order__le__neq__trans,axiom,
! [A_66: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_51: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_le1339521307_alt_o @ A_66 @ B_51 ) ) ) ).
thf(fact_460_order__le__neq__trans,axiom,
! [A_66: nat > $o,B_51: nat > $o] :
( ( ord_less_eq_nat_o @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_less_nat_o @ A_66 @ B_51 ) ) ) ).
thf(fact_461_order__le__neq__trans,axiom,
! [A_66: nat,B_51: nat] :
( ( ord_less_eq_nat @ A_66 @ B_51 )
=> ( ( A_66 != B_51 )
=> ( ord_less_nat @ A_66 @ B_51 ) ) ) ).
thf(fact_462_xt1_I11_J,axiom,
! [B_50: product_unit > $o,A_65: product_unit > $o] :
( ( ord_le1511552390unit_o @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_le232288914unit_o @ B_50 @ A_65 ) ) ) ).
thf(fact_463_xt1_I11_J,axiom,
! [B_50: arrow_1196572341e_indi > $o,A_65: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_le1991507760indi_o @ B_50 @ A_65 ) ) ) ).
thf(fact_464_xt1_I11_J,axiom,
! [B_50: ( produc1572197287le_alt > $o ) > $o,A_65: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_le874404799lt_o_o @ B_50 @ A_65 ) ) ) ).
thf(fact_465_xt1_I11_J,axiom,
! [B_50: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_65: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_le1382328578lt_o_o @ B_50 @ A_65 ) ) ) ).
thf(fact_466_xt1_I11_J,axiom,
! [B_50: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_65: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_le914873172lt_o_o @ B_50 @ A_65 ) ) ) ).
thf(fact_467_xt1_I11_J,axiom,
! [B_50: produc1572197287le_alt > $o,A_65: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_le1852932542_alt_o @ B_50 @ A_65 ) ) ) ).
thf(fact_468_xt1_I11_J,axiom,
! [B_50: $o,A_65: $o] :
( ( ord_less_eq_o @ B_50 @ A_65 )
=> ( ~ ( A_65
<=> B_50 )
=> ( ord_less_o @ B_50 @ A_65 ) ) ) ).
thf(fact_469_xt1_I11_J,axiom,
! [B_50: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_65: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_le1339521307_alt_o @ B_50 @ A_65 ) ) ) ).
thf(fact_470_xt1_I11_J,axiom,
! [B_50: nat > $o,A_65: nat > $o] :
( ( ord_less_eq_nat_o @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_less_nat_o @ B_50 @ A_65 ) ) ) ).
thf(fact_471_xt1_I11_J,axiom,
! [B_50: nat,A_65: nat] :
( ( ord_less_eq_nat @ B_50 @ A_65 )
=> ( ( A_65 != B_50 )
=> ( ord_less_nat @ B_50 @ A_65 ) ) ) ).
thf(fact_472_order__less__le__trans,axiom,
! [Z_4: product_unit > $o,X_20: product_unit > $o,Y_11: product_unit > $o] :
( ( ord_le232288914unit_o @ X_20 @ Y_11 )
=> ( ( ord_le1511552390unit_o @ Y_11 @ Z_4 )
=> ( ord_le232288914unit_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_473_order__less__le__trans,axiom,
! [Z_4: arrow_1196572341e_indi > $o,X_20: arrow_1196572341e_indi > $o,Y_11: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_20 @ Y_11 )
=> ( ( ord_le865407012indi_o @ Y_11 @ Z_4 )
=> ( ord_le1991507760indi_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_474_order__less__le__trans,axiom,
! [Z_4: ( produc1572197287le_alt > $o ) > $o,X_20: ( produc1572197287le_alt > $o ) > $o,Y_11: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ X_20 @ Y_11 )
=> ( ( ord_le1027220427lt_o_o @ Y_11 @ Z_4 )
=> ( ord_le874404799lt_o_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_475_order__less__le__trans,axiom,
! [Z_4: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_11: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ X_20 @ Y_11 )
=> ( ( ord_le1805007862lt_o_o @ Y_11 @ Z_4 )
=> ( ord_le1382328578lt_o_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_476_order__less__le__trans,axiom,
! [Z_4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_11: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ X_20 @ Y_11 )
=> ( ( ord_le602483040lt_o_o @ Y_11 @ Z_4 )
=> ( ord_le914873172lt_o_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_477_order__less__le__trans,axiom,
! [Z_4: produc1572197287le_alt > $o,X_20: produc1572197287le_alt > $o,Y_11: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ X_20 @ Y_11 )
=> ( ( ord_le962286258_alt_o @ Y_11 @ Z_4 )
=> ( ord_le1852932542_alt_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_478_order__less__le__trans,axiom,
! [Z_4: $o,X_20: $o,Y_11: $o] :
( ( ord_less_o @ X_20 @ Y_11 )
=> ( ( ord_less_eq_o @ Y_11 @ Z_4 )
=> ( ord_less_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_479_order__less__le__trans,axiom,
! [Z_4: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_20: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_11: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1339521307_alt_o @ X_20 @ Y_11 )
=> ( ( ord_le1463467535_alt_o @ Y_11 @ Z_4 )
=> ( ord_le1339521307_alt_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_480_order__less__le__trans,axiom,
! [Z_4: nat > $o,X_20: nat > $o,Y_11: nat > $o] :
( ( ord_less_nat_o @ X_20 @ Y_11 )
=> ( ( ord_less_eq_nat_o @ Y_11 @ Z_4 )
=> ( ord_less_nat_o @ X_20 @ Z_4 ) ) ) ).
thf(fact_481_order__less__le__trans,axiom,
! [Z_4: nat,X_20: nat,Y_11: nat] :
( ( ord_less_nat @ X_20 @ Y_11 )
=> ( ( ord_less_eq_nat @ Y_11 @ Z_4 )
=> ( ord_less_nat @ X_20 @ Z_4 ) ) ) ).
thf(fact_482_xt1_I7_J,axiom,
! [Z_3: product_unit > $o,Y_10: product_unit > $o,X_19: product_unit > $o] :
( ( ord_le232288914unit_o @ Y_10 @ X_19 )
=> ( ( ord_le1511552390unit_o @ Z_3 @ Y_10 )
=> ( ord_le232288914unit_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_483_xt1_I7_J,axiom,
! [Z_3: arrow_1196572341e_indi > $o,Y_10: arrow_1196572341e_indi > $o,X_19: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ Y_10 @ X_19 )
=> ( ( ord_le865407012indi_o @ Z_3 @ Y_10 )
=> ( ord_le1991507760indi_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_484_xt1_I7_J,axiom,
! [Z_3: ( produc1572197287le_alt > $o ) > $o,Y_10: ( produc1572197287le_alt > $o ) > $o,X_19: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ Y_10 @ X_19 )
=> ( ( ord_le1027220427lt_o_o @ Z_3 @ Y_10 )
=> ( ord_le874404799lt_o_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_485_xt1_I7_J,axiom,
! [Z_3: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_10: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ Y_10 @ X_19 )
=> ( ( ord_le1805007862lt_o_o @ Z_3 @ Y_10 )
=> ( ord_le1382328578lt_o_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_486_xt1_I7_J,axiom,
! [Z_3: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_10: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ Y_10 @ X_19 )
=> ( ( ord_le602483040lt_o_o @ Z_3 @ Y_10 )
=> ( ord_le914873172lt_o_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_487_xt1_I7_J,axiom,
! [Z_3: produc1572197287le_alt > $o,Y_10: produc1572197287le_alt > $o,X_19: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ Y_10 @ X_19 )
=> ( ( ord_le962286258_alt_o @ Z_3 @ Y_10 )
=> ( ord_le1852932542_alt_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_488_xt1_I7_J,axiom,
! [Z_3: $o,Y_10: $o,X_19: $o] :
( ( ord_less_o @ Y_10 @ X_19 )
=> ( ( ord_less_eq_o @ Z_3 @ Y_10 )
=> ( ord_less_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_489_xt1_I7_J,axiom,
! [Z_3: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_10: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_19: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1339521307_alt_o @ Y_10 @ X_19 )
=> ( ( ord_le1463467535_alt_o @ Z_3 @ Y_10 )
=> ( ord_le1339521307_alt_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_490_xt1_I7_J,axiom,
! [Z_3: nat > $o,Y_10: nat > $o,X_19: nat > $o] :
( ( ord_less_nat_o @ Y_10 @ X_19 )
=> ( ( ord_less_eq_nat_o @ Z_3 @ Y_10 )
=> ( ord_less_nat_o @ Z_3 @ X_19 ) ) ) ).
thf(fact_491_xt1_I7_J,axiom,
! [Z_3: nat,Y_10: nat,X_19: nat] :
( ( ord_less_nat @ Y_10 @ X_19 )
=> ( ( ord_less_eq_nat @ Z_3 @ Y_10 )
=> ( ord_less_nat @ Z_3 @ X_19 ) ) ) ).
thf(fact_492_order__le__less__trans,axiom,
! [Z_2: product_unit > $o,X_18: product_unit > $o,Y_9: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_18 @ Y_9 )
=> ( ( ord_le232288914unit_o @ Y_9 @ Z_2 )
=> ( ord_le232288914unit_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_493_order__le__less__trans,axiom,
! [Z_2: arrow_1196572341e_indi > $o,X_18: arrow_1196572341e_indi > $o,Y_9: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_18 @ Y_9 )
=> ( ( ord_le1991507760indi_o @ Y_9 @ Z_2 )
=> ( ord_le1991507760indi_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_494_order__le__less__trans,axiom,
! [Z_2: ( produc1572197287le_alt > $o ) > $o,X_18: ( produc1572197287le_alt > $o ) > $o,Y_9: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_18 @ Y_9 )
=> ( ( ord_le874404799lt_o_o @ Y_9 @ Z_2 )
=> ( ord_le874404799lt_o_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_495_order__le__less__trans,axiom,
! [Z_2: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_18: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_9: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_18 @ Y_9 )
=> ( ( ord_le1382328578lt_o_o @ Y_9 @ Z_2 )
=> ( ord_le1382328578lt_o_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_496_order__le__less__trans,axiom,
! [Z_2: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_9: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_18 @ Y_9 )
=> ( ( ord_le914873172lt_o_o @ Y_9 @ Z_2 )
=> ( ord_le914873172lt_o_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_497_order__le__less__trans,axiom,
! [Z_2: produc1572197287le_alt > $o,X_18: produc1572197287le_alt > $o,Y_9: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_18 @ Y_9 )
=> ( ( ord_le1852932542_alt_o @ Y_9 @ Z_2 )
=> ( ord_le1852932542_alt_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_498_order__le__less__trans,axiom,
! [Z_2: $o,X_18: $o,Y_9: $o] :
( ( ord_less_eq_o @ X_18 @ Y_9 )
=> ( ( ord_less_o @ Y_9 @ Z_2 )
=> ( ord_less_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_499_order__le__less__trans,axiom,
! [Z_2: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_18: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_9: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_18 @ Y_9 )
=> ( ( ord_le1339521307_alt_o @ Y_9 @ Z_2 )
=> ( ord_le1339521307_alt_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_500_order__le__less__trans,axiom,
! [Z_2: nat > $o,X_18: nat > $o,Y_9: nat > $o] :
( ( ord_less_eq_nat_o @ X_18 @ Y_9 )
=> ( ( ord_less_nat_o @ Y_9 @ Z_2 )
=> ( ord_less_nat_o @ X_18 @ Z_2 ) ) ) ).
thf(fact_501_order__le__less__trans,axiom,
! [Z_2: nat,X_18: nat,Y_9: nat] :
( ( ord_less_eq_nat @ X_18 @ Y_9 )
=> ( ( ord_less_nat @ Y_9 @ Z_2 )
=> ( ord_less_nat @ X_18 @ Z_2 ) ) ) ).
thf(fact_502_xt1_I8_J,axiom,
! [Z_1: product_unit > $o,Y_8: product_unit > $o,X_17: product_unit > $o] :
( ( ord_le1511552390unit_o @ Y_8 @ X_17 )
=> ( ( ord_le232288914unit_o @ Z_1 @ Y_8 )
=> ( ord_le232288914unit_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_503_xt1_I8_J,axiom,
! [Z_1: arrow_1196572341e_indi > $o,Y_8: arrow_1196572341e_indi > $o,X_17: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y_8 @ X_17 )
=> ( ( ord_le1991507760indi_o @ Z_1 @ Y_8 )
=> ( ord_le1991507760indi_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_504_xt1_I8_J,axiom,
! [Z_1: ( produc1572197287le_alt > $o ) > $o,Y_8: ( produc1572197287le_alt > $o ) > $o,X_17: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ Y_8 @ X_17 )
=> ( ( ord_le874404799lt_o_o @ Z_1 @ Y_8 )
=> ( ord_le874404799lt_o_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_505_xt1_I8_J,axiom,
! [Z_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_8: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ Y_8 @ X_17 )
=> ( ( ord_le1382328578lt_o_o @ Z_1 @ Y_8 )
=> ( ord_le1382328578lt_o_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_506_xt1_I8_J,axiom,
! [Z_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_8: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y_8 @ X_17 )
=> ( ( ord_le914873172lt_o_o @ Z_1 @ Y_8 )
=> ( ord_le914873172lt_o_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_507_xt1_I8_J,axiom,
! [Z_1: produc1572197287le_alt > $o,Y_8: produc1572197287le_alt > $o,X_17: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ Y_8 @ X_17 )
=> ( ( ord_le1852932542_alt_o @ Z_1 @ Y_8 )
=> ( ord_le1852932542_alt_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_508_xt1_I8_J,axiom,
! [Z_1: $o,Y_8: $o,X_17: $o] :
( ( ord_less_eq_o @ Y_8 @ X_17 )
=> ( ( ord_less_o @ Z_1 @ Y_8 )
=> ( ord_less_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_509_xt1_I8_J,axiom,
! [Z_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_8: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,X_17: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ Y_8 @ X_17 )
=> ( ( ord_le1339521307_alt_o @ Z_1 @ Y_8 )
=> ( ord_le1339521307_alt_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_510_xt1_I8_J,axiom,
! [Z_1: nat > $o,Y_8: nat > $o,X_17: nat > $o] :
( ( ord_less_eq_nat_o @ Y_8 @ X_17 )
=> ( ( ord_less_nat_o @ Z_1 @ Y_8 )
=> ( ord_less_nat_o @ Z_1 @ X_17 ) ) ) ).
thf(fact_511_xt1_I8_J,axiom,
! [Z_1: nat,Y_8: nat,X_17: nat] :
( ( ord_less_eq_nat @ Y_8 @ X_17 )
=> ( ( ord_less_nat @ Z_1 @ Y_8 )
=> ( ord_less_nat @ Z_1 @ X_17 ) ) ) ).
thf(fact_512_top__greatest,axiom,
! [A_64: ( produc1572197287le_alt > $o ) > $o] : ( ord_le1027220427lt_o_o @ A_64 @ top_to1806834203lt_o_o ) ).
thf(fact_513_top__greatest,axiom,
! [A_64: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] : ( ord_le602483040lt_o_o @ A_64 @ top_to732317616lt_o_o ) ).
thf(fact_514_top__greatest,axiom,
! [A_64: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] : ( ord_le1805007862lt_o_o @ A_64 @ top_to1492351398lt_o_o ) ).
thf(fact_515_top__greatest,axiom,
! [A_64: $o] : ( ord_less_eq_o @ A_64 @ top_top_o ) ).
thf(fact_516_top__greatest,axiom,
! [A_64: produc1572197287le_alt > $o] : ( ord_le962286258_alt_o @ A_64 @ top_to558618722_alt_o ) ).
thf(fact_517_top__greatest,axiom,
! [A_64: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] : ( ord_le1463467535_alt_o @ A_64 @ top_to1627321279_alt_o ) ).
thf(fact_518_top__greatest,axiom,
! [A_64: arrow_1196572341e_indi > $o] : ( ord_le865407012indi_o @ A_64 @ top_to54564308indi_o ) ).
thf(fact_519_top__greatest,axiom,
! [A_64: nat > $o] : ( ord_less_eq_nat_o @ A_64 @ top_top_nat_o ) ).
thf(fact_520_top__greatest,axiom,
! [A_64: product_unit > $o] : ( ord_le1511552390unit_o @ A_64 @ top_to1984820022unit_o ) ).
thf(fact_521_top__unique,axiom,
! [A_63: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ top_to1806834203lt_o_o @ A_63 )
<=> ( A_63 = top_to1806834203lt_o_o ) ) ).
thf(fact_522_top__unique,axiom,
! [A_63: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ top_to732317616lt_o_o @ A_63 )
<=> ( A_63 = top_to732317616lt_o_o ) ) ).
thf(fact_523_top__unique,axiom,
! [A_63: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ top_to1492351398lt_o_o @ A_63 )
<=> ( A_63 = top_to1492351398lt_o_o ) ) ).
thf(fact_524_top__unique,axiom,
! [A_63: $o] :
( ( ord_less_eq_o @ top_top_o @ A_63 )
<=> ( A_63
<=> top_top_o ) ) ).
thf(fact_525_top__unique,axiom,
! [A_63: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ top_to558618722_alt_o @ A_63 )
<=> ( A_63 = top_to558618722_alt_o ) ) ).
thf(fact_526_top__unique,axiom,
! [A_63: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ top_to1627321279_alt_o @ A_63 )
<=> ( A_63 = top_to1627321279_alt_o ) ) ).
thf(fact_527_top__unique,axiom,
! [A_63: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ top_to54564308indi_o @ A_63 )
<=> ( A_63 = top_to54564308indi_o ) ) ).
thf(fact_528_top__unique,axiom,
! [A_63: nat > $o] :
( ( ord_less_eq_nat_o @ top_top_nat_o @ A_63 )
<=> ( A_63 = top_top_nat_o ) ) ).
thf(fact_529_top__unique,axiom,
! [A_63: product_unit > $o] :
( ( ord_le1511552390unit_o @ top_to1984820022unit_o @ A_63 )
<=> ( A_63 = top_to1984820022unit_o ) ) ).
thf(fact_530_top__le,axiom,
! [A_62: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ top_to1806834203lt_o_o @ A_62 )
=> ( A_62 = top_to1806834203lt_o_o ) ) ).
thf(fact_531_top__le,axiom,
! [A_62: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ top_to732317616lt_o_o @ A_62 )
=> ( A_62 = top_to732317616lt_o_o ) ) ).
thf(fact_532_top__le,axiom,
! [A_62: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ top_to1492351398lt_o_o @ A_62 )
=> ( A_62 = top_to1492351398lt_o_o ) ) ).
thf(fact_533_top__le,axiom,
! [A_62: $o] :
( ( ord_less_eq_o @ top_top_o @ A_62 )
=> ( A_62
<=> top_top_o ) ) ).
thf(fact_534_top__le,axiom,
! [A_62: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ top_to558618722_alt_o @ A_62 )
=> ( A_62 = top_to558618722_alt_o ) ) ).
thf(fact_535_top__le,axiom,
! [A_62: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ top_to1627321279_alt_o @ A_62 )
=> ( A_62 = top_to1627321279_alt_o ) ) ).
thf(fact_536_top__le,axiom,
! [A_62: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ top_to54564308indi_o @ A_62 )
=> ( A_62 = top_to54564308indi_o ) ) ).
thf(fact_537_top__le,axiom,
! [A_62: nat > $o] :
( ( ord_less_eq_nat_o @ top_top_nat_o @ A_62 )
=> ( A_62 = top_top_nat_o ) ) ).
thf(fact_538_top__le,axiom,
! [A_62: product_unit > $o] :
( ( ord_le1511552390unit_o @ top_to1984820022unit_o @ A_62 )
=> ( A_62 = top_to1984820022unit_o ) ) ).
thf(fact_539_inj__on__def,axiom,
! [F_24: arrow_1196572341e_indi > nat,A_61: arrow_1196572341e_indi > $o] :
( ( inj_on1505595958di_nat @ F_24 @ A_61 )
<=> ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_61 )
=> ! [Xa: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ Xa @ A_61 )
=> ( ( ( F_24 @ X_1 )
= ( F_24 @ Xa ) )
=> ( X_1 = Xa ) ) ) ) ) ).
thf(fact_540_inj__on__def,axiom,
! [F_24: nat > nat,A_61: nat > $o] :
( ( inj_on_nat_nat @ F_24 @ A_61 )
<=> ! [X_1: nat] :
( ( member_nat @ X_1 @ A_61 )
=> ! [Xa: nat] :
( ( member_nat @ Xa @ A_61 )
=> ( ( ( F_24 @ X_1 )
= ( F_24 @ Xa ) )
=> ( X_1 = Xa ) ) ) ) ) ).
thf(fact_541_inj__on__contraD,axiom,
! [X_16: arrow_1196572341e_indi,Y_7: arrow_1196572341e_indi,F_23: arrow_1196572341e_indi > nat,A_60: arrow_1196572341e_indi > $o] :
( ( inj_on1505595958di_nat @ F_23 @ A_60 )
=> ( ( X_16 != Y_7 )
=> ( ( member1818997282e_indi @ X_16 @ A_60 )
=> ( ( member1818997282e_indi @ Y_7 @ A_60 )
=> ( ( F_23 @ X_16 )
!= ( F_23 @ Y_7 ) ) ) ) ) ) ).
thf(fact_542_inj__on__contraD,axiom,
! [X_16: nat,Y_7: nat,F_23: nat > nat,A_60: nat > $o] :
( ( inj_on_nat_nat @ F_23 @ A_60 )
=> ( ( X_16 != Y_7 )
=> ( ( member_nat @ X_16 @ A_60 )
=> ( ( member_nat @ Y_7 @ A_60 )
=> ( ( F_23 @ X_16 )
!= ( F_23 @ Y_7 ) ) ) ) ) ) ).
thf(fact_543_inj__on__iff,axiom,
! [Y_6: arrow_1196572341e_indi,X_15: arrow_1196572341e_indi,F_22: arrow_1196572341e_indi > nat,A_59: arrow_1196572341e_indi > $o] :
( ( inj_on1505595958di_nat @ F_22 @ A_59 )
=> ( ( member1818997282e_indi @ X_15 @ A_59 )
=> ( ( member1818997282e_indi @ Y_6 @ A_59 )
=> ( ( ( F_22 @ X_15 )
= ( F_22 @ Y_6 ) )
<=> ( X_15 = Y_6 ) ) ) ) ) ).
thf(fact_544_inj__on__iff,axiom,
! [Y_6: nat,X_15: nat,F_22: nat > nat,A_59: nat > $o] :
( ( inj_on_nat_nat @ F_22 @ A_59 )
=> ( ( member_nat @ X_15 @ A_59 )
=> ( ( member_nat @ Y_6 @ A_59 )
=> ( ( ( F_22 @ X_15 )
= ( F_22 @ Y_6 ) )
<=> ( X_15 = Y_6 ) ) ) ) ) ).
thf(fact_545_inj__onD,axiom,
! [X_14: arrow_1196572341e_indi,Y_5: arrow_1196572341e_indi,F_21: arrow_1196572341e_indi > nat,A_58: arrow_1196572341e_indi > $o] :
( ( inj_on1505595958di_nat @ F_21 @ A_58 )
=> ( ( ( F_21 @ X_14 )
= ( F_21 @ Y_5 ) )
=> ( ( member1818997282e_indi @ X_14 @ A_58 )
=> ( ( member1818997282e_indi @ Y_5 @ A_58 )
=> ( X_14 = Y_5 ) ) ) ) ) ).
thf(fact_546_inj__onD,axiom,
! [X_14: nat,Y_5: nat,F_21: nat > nat,A_58: nat > $o] :
( ( inj_on_nat_nat @ F_21 @ A_58 )
=> ( ( ( F_21 @ X_14 )
= ( F_21 @ Y_5 ) )
=> ( ( member_nat @ X_14 @ A_58 )
=> ( ( member_nat @ Y_5 @ A_58 )
=> ( X_14 = Y_5 ) ) ) ) ) ).
thf(fact_547_Pi__mem,axiom,
! [X_13: produc1572197287le_alt,F_20: produc1572197287le_alt > $o,A_57: produc1572197287le_alt > $o,B_49: produc1572197287le_alt > $o > $o] :
( ( member1241905979_alt_o @ F_20 @ ( pi_Pro418549519_alt_o @ A_57 @ B_49 ) )
=> ( ( member285112084le_alt @ X_13 @ A_57 )
=> ( member_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_548_Pi__mem,axiom,
! [X_13: produc1572197287le_alt,F_20: produc1572197287le_alt > arrow_1196572341e_indi,A_57: produc1572197287le_alt > $o,B_49: produc1572197287le_alt > arrow_1196572341e_indi > $o] :
( ( member1074431551e_indi @ F_20 @ ( pi_Pro1246947541e_indi @ A_57 @ B_49 ) )
=> ( ( member285112084le_alt @ X_13 @ A_57 )
=> ( member1818997282e_indi @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_549_Pi__mem,axiom,
! [X_13: produc1572197287le_alt,F_20: produc1572197287le_alt > product_unit,A_57: produc1572197287le_alt > $o,B_49: produc1572197287le_alt > product_unit > $o] :
( ( member44534621t_unit @ F_20 @ ( pi_Pro926528371t_unit @ A_57 @ B_49 ) )
=> ( ( member285112084le_alt @ X_13 @ A_57 )
=> ( member_Product_unit @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_550_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_57: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_49: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1186582243e_indi @ F_20 @ ( pi_Arr272777533e_indi @ A_57 @ B_49 ) )
=> ( ( member822980838_alt_o @ X_13 @ A_57 )
=> ( member1818997282e_indi @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_551_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_57: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_49: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o] :
( ( member1696373143lt_o_o @ F_20 @ ( pi_Arr1709554855lt_o_o @ A_57 @ B_49 ) )
=> ( ( member822980838_alt_o @ X_13 @ A_57 )
=> ( member_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_552_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit,A_57: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_49: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit > $o] :
( ( member1537523201t_unit @ F_20 @ ( pi_Arr509685723t_unit @ A_57 @ B_49 ) )
=> ( ( member822980838_alt_o @ X_13 @ A_57 )
=> ( member_Product_unit @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_553_Pi__mem,axiom,
! [X_13: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_57: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_49: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1539010427e_indi @ F_20 @ ( pi_Arr470535441e_indi @ A_57 @ B_49 ) )
=> ( ( member1425217232_alt_o @ X_13 @ A_57 )
=> ( member1818997282e_indi @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_554_Pi__mem,axiom,
! [X_13: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_57: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_49: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o] :
( ( member1346253567lt_o_o @ F_20 @ ( pi_Arr1865419731lt_o_o @ A_57 @ B_49 ) )
=> ( ( member1425217232_alt_o @ X_13 @ A_57 )
=> ( member_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_555_Pi__mem,axiom,
! [X_13: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit,A_57: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_49: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit > $o] :
( ( member1043380889t_unit @ F_20 @ ( pi_Arr2096782767t_unit @ A_57 @ B_49 ) )
=> ( ( member1425217232_alt_o @ X_13 @ A_57 )
=> ( member_Product_unit @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_556_Pi__mem,axiom,
! [X_13: produc1572197287le_alt > $o,F_20: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_57: ( produc1572197287le_alt > $o ) > $o,B_49: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o] :
( ( member1830244024e_indi @ F_20 @ ( pi_Pro2039443474e_indi @ A_57 @ B_49 ) )
=> ( ( member1241905979_alt_o @ X_13 @ A_57 )
=> ( member1818997282e_indi @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_557_Pi__mem,axiom,
! [X_13: produc1572197287le_alt > $o,F_20: ( produc1572197287le_alt > $o ) > $o,A_57: ( produc1572197287le_alt > $o ) > $o,B_49: ( produc1572197287le_alt > $o ) > $o > $o] :
( ( member1925470338lt_o_o @ F_20 @ ( pi_Pro386796690lt_o_o @ A_57 @ B_49 ) )
=> ( ( member1241905979_alt_o @ X_13 @ A_57 )
=> ( member_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_558_Pi__mem,axiom,
! [X_13: produc1572197287le_alt > $o,F_20: ( produc1572197287le_alt > $o ) > product_unit,A_57: ( produc1572197287le_alt > $o ) > $o,B_49: ( produc1572197287le_alt > $o ) > product_unit > $o] :
( ( member1092867670t_unit @ F_20 @ ( pi_Pro30504752t_unit @ A_57 @ B_49 ) )
=> ( ( member1241905979_alt_o @ X_13 @ A_57 )
=> ( member_Product_unit @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_559_Pi__mem,axiom,
! [X_13: nat,F_20: nat > arrow_1196572341e_indi,A_57: nat > $o,B_49: nat > arrow_1196572341e_indi > $o] :
( ( member1113138010e_indi @ F_20 @ ( pi_nat986275508e_indi @ A_57 @ B_49 ) )
=> ( ( member_nat @ X_13 @ A_57 )
=> ( member1818997282e_indi @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_560_Pi__mem,axiom,
! [X_13: nat,F_20: nat > $o,A_57: nat > $o,B_49: nat > $o > $o] :
( ( member_nat_o @ F_20 @ ( pi_nat_o @ A_57 @ B_49 ) )
=> ( ( member_nat @ X_13 @ A_57 )
=> ( member_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_561_Pi__mem,axiom,
! [X_13: nat,F_20: nat > product_unit,A_57: nat > $o,B_49: nat > product_unit > $o] :
( ( member616671224t_unit @ F_20 @ ( pi_nat_Product_unit @ A_57 @ B_49 ) )
=> ( ( member_nat @ X_13 @ A_57 )
=> ( member_Product_unit @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_562_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > produc1572197287le_alt,A_57: arrow_1196572341e_indi > $o,B_49: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member232085823le_alt @ F_20 @ ( pi_Arr1762714837le_alt @ A_57 @ B_49 ) )
=> ( ( member1818997282e_indi @ X_13 @ A_57 )
=> ( member285112084le_alt @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_563_Pi__mem,axiom,
! [X_13: $o,F_20: $o > produc1572197287le_alt,A_57: $o > $o,B_49: $o > produc1572197287le_alt > $o] :
( ( member1158049649le_alt @ F_20 @ ( pi_o_P728361163le_alt @ A_57 @ B_49 ) )
=> ( ( member_o @ X_13 @ A_57 )
=> ( member285112084le_alt @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_564_Pi__mem,axiom,
! [X_13: product_unit,F_20: product_unit > produc1572197287le_alt,A_57: product_unit > $o,B_49: product_unit > produc1572197287le_alt > $o] :
( ( member1161214429le_alt @ F_20 @ ( pi_Pro772884595le_alt @ A_57 @ B_49 ) )
=> ( ( member_Product_unit @ X_13 @ A_57 )
=> ( member285112084le_alt @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_565_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_57: arrow_1196572341e_indi > $o,B_49: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2071265553_alt_o @ F_20 @ ( pi_Arr456308197_alt_o @ A_57 @ B_49 ) )
=> ( ( member1818997282e_indi @ X_13 @ A_57 )
=> ( member822980838_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_566_Pi__mem,axiom,
! [X_13: $o,F_20: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_57: $o > $o,B_49: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member984757343_alt_o @ F_20 @ ( pi_o_A1479825007_alt_o @ A_57 @ B_49 ) )
=> ( ( member_o @ X_13 @ A_57 )
=> ( member822980838_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_567_Pi__mem,axiom,
! [X_13: product_unit,F_20: product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_57: product_unit > $o,B_49: product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2021528307_alt_o @ F_20 @ ( pi_Pro1959068871_alt_o @ A_57 @ B_49 ) )
=> ( ( member_Product_unit @ X_13 @ A_57 )
=> ( member822980838_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_568_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_57: arrow_1196572341e_indi > $o,B_49: arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1521294075_alt_o @ F_20 @ ( pi_Arr583278353_alt_o @ A_57 @ B_49 ) )
=> ( ( member1818997282e_indi @ X_13 @ A_57 )
=> ( member1425217232_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_569_Pi__mem,axiom,
! [X_13: $o,F_20: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_57: $o > $o,B_49: $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member161783341_alt_o @ F_20 @ ( pi_o_A1994447367_alt_o @ A_57 @ B_49 ) )
=> ( ( member_o @ X_13 @ A_57 )
=> ( member1425217232_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_570_Pi__mem,axiom,
! [X_13: product_unit,F_20: product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_57: product_unit > $o,B_49: product_unit > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1888392857_alt_o @ F_20 @ ( pi_Pro443817391_alt_o @ A_57 @ B_49 ) )
=> ( ( member_Product_unit @ X_13 @ A_57 )
=> ( member1425217232_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_571_Pi__mem,axiom,
! [X_13: $o,F_20: $o > produc1572197287le_alt > $o,A_57: $o > $o,B_49: $o > ( produc1572197287le_alt > $o ) > $o] :
( ( member1495989556_alt_o @ F_20 @ ( pi_o_P1417870404_alt_o @ A_57 @ B_49 ) )
=> ( ( member_o @ X_13 @ A_57 )
=> ( member1241905979_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_572_Pi__mem,axiom,
! [X_13: product_unit,F_20: product_unit > produc1572197287le_alt > $o,A_57: product_unit > $o,B_49: product_unit > ( produc1572197287le_alt > $o ) > $o] :
( ( member1295651272_alt_o @ F_20 @ ( pi_Pro29851292_alt_o @ A_57 @ B_49 ) )
=> ( ( member_Product_unit @ X_13 @ A_57 )
=> ( member1241905979_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_573_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > nat,A_57: arrow_1196572341e_indi > $o,B_49: arrow_1196572341e_indi > nat > $o] :
( ( member1842285448di_nat @ F_20 @ ( pi_Arr778514268di_nat @ A_57 @ B_49 ) )
=> ( ( member1818997282e_indi @ X_13 @ A_57 )
=> ( member_nat @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_574_Pi__mem,axiom,
! [X_13: $o,F_20: $o > nat,A_57: $o > $o,B_49: $o > nat > $o] :
( ( member_o_nat @ F_20 @ ( pi_o_nat @ A_57 @ B_49 ) )
=> ( ( member_o @ X_13 @ A_57 )
=> ( member_nat @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_575_Pi__mem,axiom,
! [X_13: product_unit,F_20: product_unit > nat,A_57: product_unit > $o,B_49: product_unit > nat > $o] :
( ( member1827227242it_nat @ F_20 @ ( pi_Product_unit_nat @ A_57 @ B_49 ) )
=> ( ( member_Product_unit @ X_13 @ A_57 )
=> ( member_nat @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_576_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_57: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_49: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ F_20 @ ( pi_Arr1196397536_alt_o @ A_57 @ B_49 ) )
=> ( ( member822980838_alt_o @ X_13 @ A_57 )
=> ( member1241905979_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_577_Pi__mem,axiom,
! [X_13: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_57: arrow_1196572341e_indi > $o,B_49: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ F_20 @ ( pi_Arr1309696186_alt_o @ A_57 @ B_49 ) )
=> ( ( member1818997282e_indi @ X_13 @ A_57 )
=> ( member1241905979_alt_o @ ( F_20 @ X_13 ) @ ( B_49 @ X_13 ) ) ) ) ).
thf(fact_578_below__Lin,axiom,
! [L_2: produc1572197287le_alt > $o,X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt] :
( ( X != Y )
=> ( ( member1241905979_alt_o @ L_2 @ arrow_1982173296le_Lin )
=> ( member1241905979_alt_o @ ( arrow_1865170000_below @ L_2 @ X @ Y ) @ arrow_1982173296le_Lin ) ) ) ).
thf(fact_579_Prof__def,axiom,
( arrow_1647925946e_Prof
= ( pi_Arr1309696186_alt_o @ top_to54564308indi_o
@ ^ [Uu: arrow_1196572341e_indi] : arrow_1982173296le_Lin ) ) ).
thf(fact_580_inj__on__id2,axiom,
! [A_56: nat > $o] :
( inj_on_nat_nat
@ ^ [X_1: nat] : X_1
@ A_56 ) ).
thf(fact_581_funcset__mem,axiom,
! [X_12: produc1572197287le_alt,F_19: produc1572197287le_alt > $o,A_55: produc1572197287le_alt > $o,B_48: $o > $o] :
( ( member1241905979_alt_o @ F_19
@ ( pi_Pro418549519_alt_o @ A_55
@ ^ [Uu: produc1572197287le_alt] : B_48 ) )
=> ( ( member285112084le_alt @ X_12 @ A_55 )
=> ( member_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_582_funcset__mem,axiom,
! [X_12: produc1572197287le_alt,F_19: produc1572197287le_alt > arrow_1196572341e_indi,A_55: produc1572197287le_alt > $o,B_48: arrow_1196572341e_indi > $o] :
( ( member1074431551e_indi @ F_19
@ ( pi_Pro1246947541e_indi @ A_55
@ ^ [Uu: produc1572197287le_alt] : B_48 ) )
=> ( ( member285112084le_alt @ X_12 @ A_55 )
=> ( member1818997282e_indi @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_583_funcset__mem,axiom,
! [X_12: produc1572197287le_alt,F_19: produc1572197287le_alt > product_unit,A_55: produc1572197287le_alt > $o,B_48: product_unit > $o] :
( ( member44534621t_unit @ F_19
@ ( pi_Pro926528371t_unit @ A_55
@ ^ [Uu: produc1572197287le_alt] : B_48 ) )
=> ( ( member285112084le_alt @ X_12 @ A_55 )
=> ( member_Product_unit @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_584_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_55: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_48: arrow_1196572341e_indi > $o] :
( ( member1186582243e_indi @ F_19
@ ( pi_Arr272777533e_indi @ A_55
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member822980838_alt_o @ X_12 @ A_55 )
=> ( member1818997282e_indi @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_585_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_55: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_48: $o > $o] :
( ( member1696373143lt_o_o @ F_19
@ ( pi_Arr1709554855lt_o_o @ A_55
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member822980838_alt_o @ X_12 @ A_55 )
=> ( member_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_586_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit,A_55: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_48: product_unit > $o] :
( ( member1537523201t_unit @ F_19
@ ( pi_Arr509685723t_unit @ A_55
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member822980838_alt_o @ X_12 @ A_55 )
=> ( member_Product_unit @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_587_funcset__mem,axiom,
! [X_12: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_55: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_48: arrow_1196572341e_indi > $o] :
( ( member1539010427e_indi @ F_19
@ ( pi_Arr470535441e_indi @ A_55
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member1425217232_alt_o @ X_12 @ A_55 )
=> ( member1818997282e_indi @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_588_funcset__mem,axiom,
! [X_12: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_55: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_48: $o > $o] :
( ( member1346253567lt_o_o @ F_19
@ ( pi_Arr1865419731lt_o_o @ A_55
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member1425217232_alt_o @ X_12 @ A_55 )
=> ( member_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_589_funcset__mem,axiom,
! [X_12: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,F_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit,A_55: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_48: product_unit > $o] :
( ( member1043380889t_unit @ F_19
@ ( pi_Arr2096782767t_unit @ A_55
@ ^ [Uu: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member1425217232_alt_o @ X_12 @ A_55 )
=> ( member_Product_unit @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_590_funcset__mem,axiom,
! [X_12: produc1572197287le_alt > $o,F_19: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,A_55: ( produc1572197287le_alt > $o ) > $o,B_48: arrow_1196572341e_indi > $o] :
( ( member1830244024e_indi @ F_19
@ ( pi_Pro2039443474e_indi @ A_55
@ ^ [Uu: produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member1241905979_alt_o @ X_12 @ A_55 )
=> ( member1818997282e_indi @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_591_funcset__mem,axiom,
! [X_12: produc1572197287le_alt > $o,F_19: ( produc1572197287le_alt > $o ) > $o,A_55: ( produc1572197287le_alt > $o ) > $o,B_48: $o > $o] :
( ( member1925470338lt_o_o @ F_19
@ ( pi_Pro386796690lt_o_o @ A_55
@ ^ [Uu: produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member1241905979_alt_o @ X_12 @ A_55 )
=> ( member_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_592_funcset__mem,axiom,
! [X_12: produc1572197287le_alt > $o,F_19: ( produc1572197287le_alt > $o ) > product_unit,A_55: ( produc1572197287le_alt > $o ) > $o,B_48: product_unit > $o] :
( ( member1092867670t_unit @ F_19
@ ( pi_Pro30504752t_unit @ A_55
@ ^ [Uu: produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member1241905979_alt_o @ X_12 @ A_55 )
=> ( member_Product_unit @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_593_funcset__mem,axiom,
! [X_12: nat,F_19: nat > arrow_1196572341e_indi,A_55: nat > $o,B_48: arrow_1196572341e_indi > $o] :
( ( member1113138010e_indi @ F_19
@ ( pi_nat986275508e_indi @ A_55
@ ^ [Uu: nat] : B_48 ) )
=> ( ( member_nat @ X_12 @ A_55 )
=> ( member1818997282e_indi @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_594_funcset__mem,axiom,
! [X_12: nat,F_19: nat > $o,A_55: nat > $o,B_48: $o > $o] :
( ( member_nat_o @ F_19
@ ( pi_nat_o @ A_55
@ ^ [Uu: nat] : B_48 ) )
=> ( ( member_nat @ X_12 @ A_55 )
=> ( member_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_595_funcset__mem,axiom,
! [X_12: nat,F_19: nat > product_unit,A_55: nat > $o,B_48: product_unit > $o] :
( ( member616671224t_unit @ F_19
@ ( pi_nat_Product_unit @ A_55
@ ^ [Uu: nat] : B_48 ) )
=> ( ( member_nat @ X_12 @ A_55 )
=> ( member_Product_unit @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_596_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > produc1572197287le_alt,A_55: arrow_1196572341e_indi > $o,B_48: produc1572197287le_alt > $o] :
( ( member232085823le_alt @ F_19
@ ( pi_Arr1762714837le_alt @ A_55
@ ^ [Uu: arrow_1196572341e_indi] : B_48 ) )
=> ( ( member1818997282e_indi @ X_12 @ A_55 )
=> ( member285112084le_alt @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_597_funcset__mem,axiom,
! [X_12: $o,F_19: $o > produc1572197287le_alt,A_55: $o > $o,B_48: produc1572197287le_alt > $o] :
( ( member1158049649le_alt @ F_19
@ ( pi_o_P728361163le_alt @ A_55
@ ^ [Uu: $o] : B_48 ) )
=> ( ( member_o @ X_12 @ A_55 )
=> ( member285112084le_alt @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_598_funcset__mem,axiom,
! [X_12: product_unit,F_19: product_unit > produc1572197287le_alt,A_55: product_unit > $o,B_48: produc1572197287le_alt > $o] :
( ( member1161214429le_alt @ F_19
@ ( pi_Pro772884595le_alt @ A_55
@ ^ [Uu: product_unit] : B_48 ) )
=> ( ( member_Product_unit @ X_12 @ A_55 )
=> ( member285112084le_alt @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_599_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_55: arrow_1196572341e_indi > $o,B_48: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2071265553_alt_o @ F_19
@ ( pi_Arr456308197_alt_o @ A_55
@ ^ [Uu: arrow_1196572341e_indi] : B_48 ) )
=> ( ( member1818997282e_indi @ X_12 @ A_55 )
=> ( member822980838_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_600_funcset__mem,axiom,
! [X_12: $o,F_19: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_55: $o > $o,B_48: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member984757343_alt_o @ F_19
@ ( pi_o_A1479825007_alt_o @ A_55
@ ^ [Uu: $o] : B_48 ) )
=> ( ( member_o @ X_12 @ A_55 )
=> ( member822980838_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_601_funcset__mem,axiom,
! [X_12: product_unit,F_19: product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o,A_55: product_unit > $o,B_48: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member2021528307_alt_o @ F_19
@ ( pi_Pro1959068871_alt_o @ A_55
@ ^ [Uu: product_unit] : B_48 ) )
=> ( ( member_Product_unit @ X_12 @ A_55 )
=> ( member822980838_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_602_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_55: arrow_1196572341e_indi > $o,B_48: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1521294075_alt_o @ F_19
@ ( pi_Arr583278353_alt_o @ A_55
@ ^ [Uu: arrow_1196572341e_indi] : B_48 ) )
=> ( ( member1818997282e_indi @ X_12 @ A_55 )
=> ( member1425217232_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_603_funcset__mem,axiom,
! [X_12: $o,F_19: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_55: $o > $o,B_48: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member161783341_alt_o @ F_19
@ ( pi_o_A1994447367_alt_o @ A_55
@ ^ [Uu: $o] : B_48 ) )
=> ( ( member_o @ X_12 @ A_55 )
=> ( member1425217232_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_604_funcset__mem,axiom,
! [X_12: product_unit,F_19: product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_55: product_unit > $o,B_48: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1888392857_alt_o @ F_19
@ ( pi_Pro443817391_alt_o @ A_55
@ ^ [Uu: product_unit] : B_48 ) )
=> ( ( member_Product_unit @ X_12 @ A_55 )
=> ( member1425217232_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_605_funcset__mem,axiom,
! [X_12: $o,F_19: $o > produc1572197287le_alt > $o,A_55: $o > $o,B_48: ( produc1572197287le_alt > $o ) > $o] :
( ( member1495989556_alt_o @ F_19
@ ( pi_o_P1417870404_alt_o @ A_55
@ ^ [Uu: $o] : B_48 ) )
=> ( ( member_o @ X_12 @ A_55 )
=> ( member1241905979_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_606_funcset__mem,axiom,
! [X_12: product_unit,F_19: product_unit > produc1572197287le_alt > $o,A_55: product_unit > $o,B_48: ( produc1572197287le_alt > $o ) > $o] :
( ( member1295651272_alt_o @ F_19
@ ( pi_Pro29851292_alt_o @ A_55
@ ^ [Uu: product_unit] : B_48 ) )
=> ( ( member_Product_unit @ X_12 @ A_55 )
=> ( member1241905979_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_607_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > nat,A_55: arrow_1196572341e_indi > $o,B_48: nat > $o] :
( ( member1842285448di_nat @ F_19
@ ( pi_Arr778514268di_nat @ A_55
@ ^ [Uu: arrow_1196572341e_indi] : B_48 ) )
=> ( ( member1818997282e_indi @ X_12 @ A_55 )
=> ( member_nat @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_608_funcset__mem,axiom,
! [X_12: $o,F_19: $o > nat,A_55: $o > $o,B_48: nat > $o] :
( ( member_o_nat @ F_19
@ ( pi_o_nat @ A_55
@ ^ [Uu: $o] : B_48 ) )
=> ( ( member_o @ X_12 @ A_55 )
=> ( member_nat @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_609_funcset__mem,axiom,
! [X_12: product_unit,F_19: product_unit > nat,A_55: product_unit > $o,B_48: nat > $o] :
( ( member1827227242it_nat @ F_19
@ ( pi_Product_unit_nat @ A_55
@ ^ [Uu: product_unit] : B_48 ) )
=> ( ( member_Product_unit @ X_12 @ A_55 )
=> ( member_nat @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_610_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi > produc1572197287le_alt > $o,F_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_55: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_48: ( produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ F_19
@ ( pi_Arr1196397536_alt_o @ A_55
@ ^ [Uu: arrow_1196572341e_indi > produc1572197287le_alt > $o] : B_48 ) )
=> ( ( member822980838_alt_o @ X_12 @ A_55 )
=> ( member1241905979_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_611_funcset__mem,axiom,
! [X_12: arrow_1196572341e_indi,F_19: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_55: arrow_1196572341e_indi > $o,B_48: ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ F_19
@ ( pi_Arr1309696186_alt_o @ A_55
@ ^ [Uu: arrow_1196572341e_indi] : B_48 ) )
=> ( ( member1818997282e_indi @ X_12 @ A_55 )
=> ( member1241905979_alt_o @ ( F_19 @ X_12 ) @ B_48 ) ) ) ).
thf(fact_612_inj__eq,axiom,
! [X_11: arrow_1196572341e_indi,Y_4: arrow_1196572341e_indi,F_18: arrow_1196572341e_indi > nat] :
( ( inj_on1505595958di_nat @ F_18 @ top_to54564308indi_o )
=> ( ( ( F_18 @ X_11 )
= ( F_18 @ Y_4 ) )
<=> ( X_11 = Y_4 ) ) ) ).
thf(fact_613_inj__eq,axiom,
! [X_11: nat,Y_4: nat,F_18: nat > nat] :
( ( inj_on_nat_nat @ F_18 @ top_top_nat_o )
=> ( ( ( F_18 @ X_11 )
= ( F_18 @ Y_4 ) )
<=> ( X_11 = Y_4 ) ) ) ).
thf(fact_614_injD,axiom,
! [X_10: arrow_1196572341e_indi,Y_3: arrow_1196572341e_indi,F_17: arrow_1196572341e_indi > nat] :
( ( inj_on1505595958di_nat @ F_17 @ top_to54564308indi_o )
=> ( ( ( F_17 @ X_10 )
= ( F_17 @ Y_3 ) )
=> ( X_10 = Y_3 ) ) ) ).
thf(fact_615_injD,axiom,
! [X_10: nat,Y_3: nat,F_17: nat > nat] :
( ( inj_on_nat_nat @ F_17 @ top_top_nat_o )
=> ( ( ( F_17 @ X_10 )
= ( F_17 @ Y_3 ) )
=> ( X_10 = Y_3 ) ) ) ).
thf(fact_616_inv__into__f__f,axiom,
! [X_9: arrow_1196572341e_indi,F_16: arrow_1196572341e_indi > nat,A_54: arrow_1196572341e_indi > $o] :
( ( inj_on1505595958di_nat @ F_16 @ A_54 )
=> ( ( member1818997282e_indi @ X_9 @ A_54 )
=> ( ( hilber1125280539di_nat @ A_54 @ F_16 @ ( F_16 @ X_9 ) )
= X_9 ) ) ) ).
thf(fact_617_inv__into__f__f,axiom,
! [X_9: nat,F_16: nat > nat,A_54: nat > $o] :
( ( inj_on_nat_nat @ F_16 @ A_54 )
=> ( ( member_nat @ X_9 @ A_54 )
=> ( ( hilber195283148at_nat @ A_54 @ F_16 @ ( F_16 @ X_9 ) )
= X_9 ) ) ) ).
thf(fact_618_inv__into__f__eq,axiom,
! [Y_2: nat,X_8: arrow_1196572341e_indi,F_15: arrow_1196572341e_indi > nat,A_53: arrow_1196572341e_indi > $o] :
( ( inj_on1505595958di_nat @ F_15 @ A_53 )
=> ( ( member1818997282e_indi @ X_8 @ A_53 )
=> ( ( ( F_15 @ X_8 )
= Y_2 )
=> ( ( hilber1125280539di_nat @ A_53 @ F_15 @ Y_2 )
= X_8 ) ) ) ) ).
thf(fact_619_inv__into__f__eq,axiom,
! [Y_2: nat,X_8: nat,F_15: nat > nat,A_53: nat > $o] :
( ( inj_on_nat_nat @ F_15 @ A_53 )
=> ( ( member_nat @ X_8 @ A_53 )
=> ( ( ( F_15 @ X_8 )
= Y_2 )
=> ( ( hilber195283148at_nat @ A_53 @ F_15 @ Y_2 )
= X_8 ) ) ) ) ).
thf(fact_620_Pi__I,axiom,
! [F_14: produc1572197287le_alt > arrow_1196572341e_indi,B_47: produc1572197287le_alt > arrow_1196572341e_indi > $o,A_52: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_52 )
=> ( member1818997282e_indi @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1074431551e_indi @ F_14 @ ( pi_Pro1246947541e_indi @ A_52 @ B_47 ) ) ) ).
thf(fact_621_Pi__I,axiom,
! [F_14: produc1572197287le_alt > product_unit,B_47: produc1572197287le_alt > product_unit > $o,A_52: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_52 )
=> ( member_Product_unit @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member44534621t_unit @ F_14 @ ( pi_Pro926528371t_unit @ A_52 @ B_47 ) ) ) ).
thf(fact_622_Pi__I,axiom,
! [F_14: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_47: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_52: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_52 )
=> ( member1818997282e_indi @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1186582243e_indi @ F_14 @ ( pi_Arr272777533e_indi @ A_52 @ B_47 ) ) ) ).
thf(fact_623_Pi__I,axiom,
! [F_14: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_47: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o,A_52: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_52 )
=> ( member_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1696373143lt_o_o @ F_14 @ ( pi_Arr1709554855lt_o_o @ A_52 @ B_47 ) ) ) ).
thf(fact_624_Pi__I,axiom,
! [F_14: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit,B_47: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit > $o,A_52: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_52 )
=> ( member_Product_unit @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1537523201t_unit @ F_14 @ ( pi_Arr509685723t_unit @ A_52 @ B_47 ) ) ) ).
thf(fact_625_Pi__I,axiom,
! [F_14: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_47: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_52: ( ( 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_52 )
=> ( member1818997282e_indi @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1539010427e_indi @ F_14 @ ( pi_Arr470535441e_indi @ A_52 @ B_47 ) ) ) ).
thf(fact_626_Pi__I,axiom,
! [F_14: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_47: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o,A_52: ( ( 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_52 )
=> ( member_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1346253567lt_o_o @ F_14 @ ( pi_Arr1865419731lt_o_o @ A_52 @ B_47 ) ) ) ).
thf(fact_627_Pi__I,axiom,
! [F_14: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit,B_47: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit > $o,A_52: ( ( 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_52 )
=> ( member_Product_unit @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1043380889t_unit @ F_14 @ ( pi_Arr2096782767t_unit @ A_52 @ B_47 ) ) ) ).
thf(fact_628_Pi__I,axiom,
! [F_14: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi,B_47: ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o,A_52: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_52 )
=> ( member1818997282e_indi @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1830244024e_indi @ F_14 @ ( pi_Pro2039443474e_indi @ A_52 @ B_47 ) ) ) ).
thf(fact_629_Pi__I,axiom,
! [F_14: ( produc1572197287le_alt > $o ) > $o,B_47: ( produc1572197287le_alt > $o ) > $o > $o,A_52: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_52 )
=> ( member_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1925470338lt_o_o @ F_14 @ ( pi_Pro386796690lt_o_o @ A_52 @ B_47 ) ) ) ).
thf(fact_630_Pi__I,axiom,
! [F_14: ( produc1572197287le_alt > $o ) > product_unit,B_47: ( produc1572197287le_alt > $o ) > product_unit > $o,A_52: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] :
( ( member1241905979_alt_o @ X_1 @ A_52 )
=> ( member_Product_unit @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1092867670t_unit @ F_14 @ ( pi_Pro30504752t_unit @ A_52 @ B_47 ) ) ) ).
thf(fact_631_Pi__I,axiom,
! [F_14: nat > arrow_1196572341e_indi,B_47: nat > arrow_1196572341e_indi > $o,A_52: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_52 )
=> ( member1818997282e_indi @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1113138010e_indi @ F_14 @ ( pi_nat986275508e_indi @ A_52 @ B_47 ) ) ) ).
thf(fact_632_Pi__I,axiom,
! [F_14: nat > $o,B_47: nat > $o > $o,A_52: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_52 )
=> ( member_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member_nat_o @ F_14 @ ( pi_nat_o @ A_52 @ B_47 ) ) ) ).
thf(fact_633_Pi__I,axiom,
! [F_14: nat > product_unit,B_47: nat > product_unit > $o,A_52: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ A_52 )
=> ( member_Product_unit @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member616671224t_unit @ F_14 @ ( pi_nat_Product_unit @ A_52 @ B_47 ) ) ) ).
thf(fact_634_Pi__I,axiom,
! [F_14: arrow_1196572341e_indi > produc1572197287le_alt,B_47: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_52: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_52 )
=> ( member285112084le_alt @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member232085823le_alt @ F_14 @ ( pi_Arr1762714837le_alt @ A_52 @ B_47 ) ) ) ).
thf(fact_635_Pi__I,axiom,
! [F_14: $o > produc1572197287le_alt,B_47: $o > produc1572197287le_alt > $o,A_52: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_52 )
=> ( member285112084le_alt @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1158049649le_alt @ F_14 @ ( pi_o_P728361163le_alt @ A_52 @ B_47 ) ) ) ).
thf(fact_636_Pi__I,axiom,
! [F_14: product_unit > produc1572197287le_alt,B_47: product_unit > produc1572197287le_alt > $o,A_52: product_unit > $o] :
( ! [X_1: product_unit] :
( ( member_Product_unit @ X_1 @ A_52 )
=> ( member285112084le_alt @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1161214429le_alt @ F_14 @ ( pi_Pro772884595le_alt @ A_52 @ B_47 ) ) ) ).
thf(fact_637_Pi__I,axiom,
! [F_14: arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_47: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_52: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_52 )
=> ( member822980838_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member2071265553_alt_o @ F_14 @ ( pi_Arr456308197_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_638_Pi__I,axiom,
! [F_14: $o > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_47: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_52: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_52 )
=> ( member822980838_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member984757343_alt_o @ F_14 @ ( pi_o_A1479825007_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_639_Pi__I,axiom,
! [F_14: product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o,B_47: product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_52: product_unit > $o] :
( ! [X_1: product_unit] :
( ( member_Product_unit @ X_1 @ A_52 )
=> ( member822980838_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member2021528307_alt_o @ F_14 @ ( pi_Pro1959068871_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_640_Pi__I,axiom,
! [F_14: arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_47: arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_52: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_52 )
=> ( member1425217232_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1521294075_alt_o @ F_14 @ ( pi_Arr583278353_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_641_Pi__I,axiom,
! [F_14: $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_47: $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_52: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_52 )
=> ( member1425217232_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member161783341_alt_o @ F_14 @ ( pi_o_A1994447367_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_642_Pi__I,axiom,
! [F_14: product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_47: product_unit > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_52: product_unit > $o] :
( ! [X_1: product_unit] :
( ( member_Product_unit @ X_1 @ A_52 )
=> ( member1425217232_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1888392857_alt_o @ F_14 @ ( pi_Pro443817391_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_643_Pi__I,axiom,
! [F_14: $o > produc1572197287le_alt > $o,B_47: $o > ( produc1572197287le_alt > $o ) > $o,A_52: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_52 )
=> ( member1241905979_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1495989556_alt_o @ F_14 @ ( pi_o_P1417870404_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_644_Pi__I,axiom,
! [F_14: product_unit > produc1572197287le_alt > $o,B_47: product_unit > ( produc1572197287le_alt > $o ) > $o,A_52: product_unit > $o] :
( ! [X_1: product_unit] :
( ( member_Product_unit @ X_1 @ A_52 )
=> ( member1241905979_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1295651272_alt_o @ F_14 @ ( pi_Pro29851292_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_645_Pi__I,axiom,
! [F_14: arrow_1196572341e_indi > nat,B_47: arrow_1196572341e_indi > nat > $o,A_52: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_52 )
=> ( member_nat @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1842285448di_nat @ F_14 @ ( pi_Arr778514268di_nat @ A_52 @ B_47 ) ) ) ).
thf(fact_646_Pi__I,axiom,
! [F_14: $o > nat,B_47: $o > nat > $o,A_52: $o > $o] :
( ! [X_1: $o] :
( ( member_o @ X_1 @ A_52 )
=> ( member_nat @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member_o_nat @ F_14 @ ( pi_o_nat @ A_52 @ B_47 ) ) ) ).
thf(fact_647_Pi__I,axiom,
! [F_14: product_unit > nat,B_47: product_unit > nat > $o,A_52: product_unit > $o] :
( ! [X_1: product_unit] :
( ( member_Product_unit @ X_1 @ A_52 )
=> ( member_nat @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1827227242it_nat @ F_14 @ ( pi_Product_unit_nat @ A_52 @ B_47 ) ) ) ).
thf(fact_648_Pi__I,axiom,
! [F_14: produc1572197287le_alt > $o,B_47: produc1572197287le_alt > $o > $o,A_52: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] :
( ( member285112084le_alt @ X_1 @ A_52 )
=> ( member_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1241905979_alt_o @ F_14 @ ( pi_Pro418549519_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_649_Pi__I,axiom,
! [F_14: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,B_47: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o,A_52: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( ( member822980838_alt_o @ X_1 @ A_52 )
=> ( member1241905979_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member1425217232_alt_o @ F_14 @ ( pi_Arr1196397536_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_650_Pi__I,axiom,
! [F_14: arrow_1196572341e_indi > produc1572197287le_alt > $o,B_47: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,A_52: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] :
( ( member1818997282e_indi @ X_1 @ A_52 )
=> ( member1241905979_alt_o @ ( F_14 @ X_1 ) @ ( B_47 @ X_1 ) ) )
=> ( member822980838_alt_o @ F_14 @ ( pi_Arr1309696186_alt_o @ A_52 @ B_47 ) ) ) ).
thf(fact_651_inj__imp__inv__eq,axiom,
! [G_2: nat > arrow_1196572341e_indi,F_13: arrow_1196572341e_indi > nat] :
( ( inj_on1505595958di_nat @ F_13 @ top_to54564308indi_o )
=> ( ! [X_1: nat] :
( ( F_13 @ ( G_2 @ X_1 ) )
= X_1 )
=> ( ( hilber1125280539di_nat @ top_to54564308indi_o @ F_13 )
= G_2 ) ) ) ).
thf(fact_652_inj__imp__inv__eq,axiom,
! [G_2: nat > nat,F_13: nat > nat] :
( ( inj_on_nat_nat @ F_13 @ top_top_nat_o )
=> ( ! [X_1: nat] :
( ( F_13 @ ( G_2 @ X_1 ) )
= X_1 )
=> ( ( hilber195283148at_nat @ top_top_nat_o @ F_13 )
= G_2 ) ) ) ).
thf(fact_653_less__add__one,axiom,
! [A_51: nat] : ( ord_less_nat @ A_51 @ ( plus_plus_nat @ A_51 @ one_one_nat ) ) ).
thf(fact_654_add__less__le__mono,axiom,
! [C_33: nat,D_3: nat,A_50: nat,B_46: nat] :
( ( ord_less_nat @ A_50 @ B_46 )
=> ( ( ord_less_eq_nat @ C_33 @ D_3 )
=> ( ord_less_nat @ ( plus_plus_nat @ A_50 @ C_33 ) @ ( plus_plus_nat @ B_46 @ D_3 ) ) ) ) ).
thf(fact_655_add__le__less__mono,axiom,
! [C_32: nat,D_2: nat,A_49: nat,B_45: nat] :
( ( ord_less_eq_nat @ A_49 @ B_45 )
=> ( ( ord_less_nat @ C_32 @ D_2 )
=> ( ord_less_nat @ ( plus_plus_nat @ A_49 @ C_32 ) @ ( plus_plus_nat @ B_45 @ D_2 ) ) ) ) ).
thf(fact_656_injI,axiom,
! [F_12: arrow_1196572341e_indi > nat] :
( ! [X_1: arrow_1196572341e_indi,Y_1: arrow_1196572341e_indi] :
( ( ( F_12 @ X_1 )
= ( F_12 @ Y_1 ) )
=> ( X_1 = Y_1 ) )
=> ( inj_on1505595958di_nat @ F_12 @ top_to54564308indi_o ) ) ).
thf(fact_657_injI,axiom,
! [F_12: nat > nat] :
( ! [X_1: nat,Y_1: nat] :
( ( ( F_12 @ X_1 )
= ( F_12 @ Y_1 ) )
=> ( X_1 = Y_1 ) )
=> ( inj_on_nat_nat @ F_12 @ top_top_nat_o ) ) ).
thf(fact_658_xt5,axiom,
! [C_31: nat > $o,F_11: ( nat > $o ) > nat > $o,B_44: nat > $o,A_48: nat > $o] :
( ( ord_less_nat_o @ B_44 @ A_48 )
=> ( ( ord_less_eq_nat_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_nat_o @ Y_1 @ X_1 )
=> ( ord_less_nat_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_659_xt5,axiom,
! [C_31: nat > $o,F_11: ( product_unit > $o ) > nat > $o,B_44: product_unit > $o,A_48: product_unit > $o] :
( ( ord_le232288914unit_o @ B_44 @ A_48 )
=> ( ( ord_less_eq_nat_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le232288914unit_o @ Y_1 @ X_1 )
=> ( ord_less_nat_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_660_xt5,axiom,
! [C_31: nat > $o,F_11: ( arrow_1196572341e_indi > $o ) > nat > $o,B_44: arrow_1196572341e_indi > $o,A_48: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ B_44 @ A_48 )
=> ( ( ord_less_eq_nat_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ Y_1 @ X_1 )
=> ( ord_less_nat_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_661_xt5,axiom,
! [C_31: nat > $o,F_11: nat > nat > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_less_eq_nat_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_less_nat_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_662_xt5,axiom,
! [C_31: product_unit > $o,F_11: nat > product_unit > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_le1511552390unit_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le232288914unit_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_le232288914unit_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_663_xt5,axiom,
! [C_31: arrow_1196572341e_indi > $o,F_11: nat > arrow_1196572341e_indi > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_le865407012indi_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le1991507760indi_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_le1991507760indi_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_664_xt5,axiom,
! [C_31: ( produc1572197287le_alt > $o ) > $o,F_11: nat > ( produc1572197287le_alt > $o ) > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_le1027220427lt_o_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le874404799lt_o_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_le874404799lt_o_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_665_xt5,axiom,
! [C_31: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,F_11: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_le1805007862lt_o_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le1382328578lt_o_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_le1382328578lt_o_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_666_xt5,axiom,
! [C_31: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,F_11: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_le602483040lt_o_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le914873172lt_o_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_le914873172lt_o_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_667_xt5,axiom,
! [C_31: produc1572197287le_alt > $o,F_11: nat > produc1572197287le_alt > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_le962286258_alt_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le1852932542_alt_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_le1852932542_alt_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_668_xt5,axiom,
! [C_31: $o,F_11: nat > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_less_eq_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_less_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_less_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_669_xt5,axiom,
! [C_31: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_11: nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_44: nat,A_48: nat] :
( ( ord_less_nat @ B_44 @ A_48 )
=> ( ( ord_le1463467535_alt_o @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le1339521307_alt_o @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_le1339521307_alt_o @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_670_xt5,axiom,
! [C_31: nat,F_11: ( nat > $o ) > nat,B_44: nat > $o,A_48: nat > $o] :
( ( ord_less_nat_o @ B_44 @ A_48 )
=> ( ( ord_less_eq_nat @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_nat_o @ Y_1 @ X_1 )
=> ( ord_less_nat @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_less_nat @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_671_xt5,axiom,
! [C_31: nat,F_11: ( product_unit > $o ) > nat,B_44: product_unit > $o,A_48: product_unit > $o] :
( ( ord_le232288914unit_o @ B_44 @ A_48 )
=> ( ( ord_less_eq_nat @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le232288914unit_o @ Y_1 @ X_1 )
=> ( ord_less_nat @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_less_nat @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_672_xt5,axiom,
! [C_31: nat,F_11: ( arrow_1196572341e_indi > $o ) > nat,B_44: arrow_1196572341e_indi > $o,A_48: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ B_44 @ A_48 )
=> ( ( ord_less_eq_nat @ C_31 @ ( F_11 @ B_44 ) )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ Y_1 @ X_1 )
=> ( ord_less_nat @ ( F_11 @ Y_1 ) @ ( F_11 @ X_1 ) ) )
=> ( ord_less_nat @ C_31 @ ( F_11 @ A_48 ) ) ) ) ) ).
thf(fact_673_xt7,axiom,
! [C_30: nat > $o,F_10: nat > nat > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_674_xt7,axiom,
! [C_30: product_unit > $o,F_10: nat > product_unit > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_le232288914unit_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le1511552390unit_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le232288914unit_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_675_xt7,axiom,
! [C_30: arrow_1196572341e_indi > $o,F_10: nat > arrow_1196572341e_indi > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_le1991507760indi_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le865407012indi_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le1991507760indi_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_676_xt7,axiom,
! [C_30: ( produc1572197287le_alt > $o ) > $o,F_10: nat > ( produc1572197287le_alt > $o ) > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_le874404799lt_o_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le1027220427lt_o_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le874404799lt_o_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_677_xt7,axiom,
! [C_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,F_10: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_le1382328578lt_o_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le1805007862lt_o_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le1382328578lt_o_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_678_xt7,axiom,
! [C_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,F_10: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_le914873172lt_o_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le602483040lt_o_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le914873172lt_o_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_679_xt7,axiom,
! [C_30: produc1572197287le_alt > $o,F_10: nat > produc1572197287le_alt > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_le1852932542_alt_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le962286258_alt_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le1852932542_alt_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_680_xt7,axiom,
! [C_30: $o,F_10: nat > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_less_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_less_eq_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_681_xt7,axiom,
! [C_30: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_10: nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_43: nat,A_47: nat] :
( ( ord_less_eq_nat @ B_43 @ A_47 )
=> ( ( ord_le1339521307_alt_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le1463467535_alt_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le1339521307_alt_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_682_xt7,axiom,
! [C_30: nat > $o,F_10: ( nat > $o ) > nat > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_683_xt7,axiom,
! [C_30: product_unit > $o,F_10: ( nat > $o ) > product_unit > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_le232288914unit_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le1511552390unit_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le232288914unit_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_684_xt7,axiom,
! [C_30: arrow_1196572341e_indi > $o,F_10: ( nat > $o ) > arrow_1196572341e_indi > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_le1991507760indi_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le865407012indi_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le1991507760indi_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_685_xt7,axiom,
! [C_30: ( produc1572197287le_alt > $o ) > $o,F_10: ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_le874404799lt_o_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le1027220427lt_o_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le874404799lt_o_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_686_xt7,axiom,
! [C_30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,F_10: ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_le1382328578lt_o_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le1805007862lt_o_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le1382328578lt_o_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_687_xt7,axiom,
! [C_30: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,F_10: ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_le914873172lt_o_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le602483040lt_o_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le914873172lt_o_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_688_xt7,axiom,
! [C_30: produc1572197287le_alt > $o,F_10: ( nat > $o ) > produc1572197287le_alt > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_le1852932542_alt_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le962286258_alt_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le1852932542_alt_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_689_xt7,axiom,
! [C_30: $o,F_10: ( nat > $o ) > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_less_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_less_eq_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_690_xt7,axiom,
! [C_30: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_10: ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_43: nat > $o,A_47: nat > $o] :
( ( ord_less_eq_nat_o @ B_43 @ A_47 )
=> ( ( ord_le1339521307_alt_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le1463467535_alt_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_le1339521307_alt_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_691_xt7,axiom,
! [C_30: nat > $o,F_10: ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o,B_43: ( produc1572197287le_alt > $o ) > $o,A_47: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: ( produc1572197287le_alt > $o ) > $o,Y_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_692_xt7,axiom,
! [C_30: nat > $o,F_10: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o,B_43: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_47: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_693_xt7,axiom,
! [C_30: nat > $o,F_10: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o,B_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_47: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_694_xt7,axiom,
! [C_30: nat > $o,F_10: ( produc1572197287le_alt > $o ) > nat > $o,B_43: produc1572197287le_alt > $o,A_47: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: produc1572197287le_alt > $o,Y_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_695_xt7,axiom,
! [C_30: nat > $o,F_10: $o > nat > $o,B_43: $o,A_47: $o] :
( ( ord_less_eq_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: $o,Y_1: $o] :
( ( ord_less_eq_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_696_xt7,axiom,
! [C_30: nat > $o,F_10: ( arrow_1196572341e_indi > $o ) > nat > $o,B_43: arrow_1196572341e_indi > $o,A_47: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_697_xt7,axiom,
! [C_30: nat > $o,F_10: ( product_unit > $o ) > nat > $o,B_43: product_unit > $o,A_47: product_unit > $o] :
( ( ord_le1511552390unit_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le1511552390unit_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_698_xt7,axiom,
! [C_30: nat > $o,F_10: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o,B_43: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_47: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ B_43 @ A_47 )
=> ( ( ord_less_nat_o @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat_o @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_699_xt7,axiom,
! [C_30: nat,F_10: ( ( produc1572197287le_alt > $o ) > $o ) > nat,B_43: ( produc1572197287le_alt > $o ) > $o,A_47: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ B_43 @ A_47 )
=> ( ( ord_less_nat @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: ( produc1572197287le_alt > $o ) > $o,Y_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_700_xt7,axiom,
! [C_30: nat,F_10: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat,B_43: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_47: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ B_43 @ A_47 )
=> ( ( ord_less_nat @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_701_xt7,axiom,
! [C_30: nat,F_10: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat,B_43: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_47: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ B_43 @ A_47 )
=> ( ( ord_less_nat @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_702_xt7,axiom,
! [C_30: nat,F_10: ( produc1572197287le_alt > $o ) > nat,B_43: produc1572197287le_alt > $o,A_47: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ B_43 @ A_47 )
=> ( ( ord_less_nat @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: produc1572197287le_alt > $o,Y_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_703_xt7,axiom,
! [C_30: nat,F_10: $o > nat,B_43: $o,A_47: $o] :
( ( ord_less_eq_o @ B_43 @ A_47 )
=> ( ( ord_less_nat @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: $o,Y_1: $o] :
( ( ord_less_eq_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_704_xt7,axiom,
! [C_30: nat,F_10: ( arrow_1196572341e_indi > $o ) > nat,B_43: arrow_1196572341e_indi > $o,A_47: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ B_43 @ A_47 )
=> ( ( ord_less_nat @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_705_xt7,axiom,
! [C_30: nat,F_10: ( product_unit > $o ) > nat,B_43: product_unit > $o,A_47: product_unit > $o] :
( ( ord_le1511552390unit_o @ B_43 @ A_47 )
=> ( ( ord_less_nat @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le1511552390unit_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_706_xt7,axiom,
! [C_30: nat,F_10: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat,B_43: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_47: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ B_43 @ A_47 )
=> ( ( ord_less_nat @ C_30 @ ( F_10 @ B_43 ) )
=> ( ! [X_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_10 @ Y_1 ) @ ( F_10 @ X_1 ) ) )
=> ( ord_less_nat @ C_30 @ ( F_10 @ A_47 ) ) ) ) ) ).
thf(fact_707_less__fun__def,axiom,
! [F_9: product_unit > $o,G_1: product_unit > $o] :
( ( ord_le232288914unit_o @ F_9 @ G_1 )
<=> ( ( ord_le1511552390unit_o @ F_9 @ G_1 )
& ~ ( ord_le1511552390unit_o @ G_1 @ F_9 ) ) ) ).
thf(fact_708_less__fun__def,axiom,
! [F_9: arrow_1196572341e_indi > $o,G_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ F_9 @ G_1 )
<=> ( ( ord_le865407012indi_o @ F_9 @ G_1 )
& ~ ( ord_le865407012indi_o @ G_1 @ F_9 ) ) ) ).
thf(fact_709_less__fun__def,axiom,
! [F_9: ( produc1572197287le_alt > $o ) > $o,G_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ F_9 @ G_1 )
<=> ( ( ord_le1027220427lt_o_o @ F_9 @ G_1 )
& ~ ( ord_le1027220427lt_o_o @ G_1 @ F_9 ) ) ) ).
thf(fact_710_less__fun__def,axiom,
! [F_9: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,G_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ F_9 @ G_1 )
<=> ( ( ord_le1805007862lt_o_o @ F_9 @ G_1 )
& ~ ( ord_le1805007862lt_o_o @ G_1 @ F_9 ) ) ) ).
thf(fact_711_less__fun__def,axiom,
! [F_9: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,G_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ F_9 @ G_1 )
<=> ( ( ord_le602483040lt_o_o @ F_9 @ G_1 )
& ~ ( ord_le602483040lt_o_o @ G_1 @ F_9 ) ) ) ).
thf(fact_712_less__fun__def,axiom,
! [F_9: produc1572197287le_alt > $o,G_1: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ F_9 @ G_1 )
<=> ( ( ord_le962286258_alt_o @ F_9 @ G_1 )
& ~ ( ord_le962286258_alt_o @ G_1 @ F_9 ) ) ) ).
thf(fact_713_less__fun__def,axiom,
! [F_9: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,G_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1339521307_alt_o @ F_9 @ G_1 )
<=> ( ( ord_le1463467535_alt_o @ F_9 @ G_1 )
& ~ ( ord_le1463467535_alt_o @ G_1 @ F_9 ) ) ) ).
thf(fact_714_less__fun__def,axiom,
! [F_9: nat > $o,G_1: nat > $o] :
( ( ord_less_nat_o @ F_9 @ G_1 )
<=> ( ( ord_less_eq_nat_o @ F_9 @ G_1 )
& ~ ( ord_less_eq_nat_o @ G_1 @ F_9 ) ) ) ).
thf(fact_715_Pi__anti__mono,axiom,
! [B_42: produc1572197287le_alt > $o > $o,A_46: produc1572197287le_alt > $o,A_45: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_46 @ A_45 )
=> ( ord_le1027220427lt_o_o @ ( pi_Pro418549519_alt_o @ A_45 @ B_42 ) @ ( pi_Pro418549519_alt_o @ A_46 @ B_42 ) ) ) ).
thf(fact_716_Pi__anti__mono,axiom,
! [B_42: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o,A_46: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_45: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_46 @ A_45 )
=> ( ord_le1805007862lt_o_o @ ( pi_Arr1196397536_alt_o @ A_45 @ B_42 ) @ ( pi_Arr1196397536_alt_o @ A_46 @ B_42 ) ) ) ).
thf(fact_717_Pi__anti__mono,axiom,
! [B_42: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,A_46: arrow_1196572341e_indi > $o,A_45: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_46 @ A_45 )
=> ( ord_le602483040lt_o_o @ ( pi_Arr1309696186_alt_o @ A_45 @ B_42 ) @ ( pi_Arr1309696186_alt_o @ A_46 @ B_42 ) ) ) ).
thf(fact_718_pred__subset__eq2,axiom,
! [R_1: produc1572197287le_alt > $o,S_2: produc1572197287le_alt > $o] :
( ( ord_le1463467535_alt_o
@ ^ [X_1: arrow_1389031998le_alt,Y_1: arrow_1389031998le_alt] : ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Y_1 ) @ R_1 )
@ ^ [X_1: arrow_1389031998le_alt,Y_1: arrow_1389031998le_alt] : ( member285112084le_alt @ ( produc897867031le_alt @ X_1 @ Y_1 ) @ S_2 ) )
<=> ( ord_le962286258_alt_o @ R_1 @ S_2 ) ) ).
thf(fact_719_subset__UNIV,axiom,
! [A_44: ( produc1572197287le_alt > $o ) > $o] : ( ord_le1027220427lt_o_o @ A_44 @ top_to1806834203lt_o_o ) ).
thf(fact_720_subset__UNIV,axiom,
! [A_44: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] : ( ord_le602483040lt_o_o @ A_44 @ top_to732317616lt_o_o ) ).
thf(fact_721_subset__UNIV,axiom,
! [A_44: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] : ( ord_le1805007862lt_o_o @ A_44 @ top_to1492351398lt_o_o ) ).
thf(fact_722_subset__UNIV,axiom,
! [A_44: produc1572197287le_alt > $o] : ( ord_le962286258_alt_o @ A_44 @ top_to558618722_alt_o ) ).
thf(fact_723_subset__UNIV,axiom,
! [A_44: arrow_1196572341e_indi > $o] : ( ord_le865407012indi_o @ A_44 @ top_to54564308indi_o ) ).
thf(fact_724_subset__UNIV,axiom,
! [A_44: nat > $o] : ( ord_less_eq_nat_o @ A_44 @ top_top_nat_o ) ).
thf(fact_725_subset__UNIV,axiom,
! [A_44: product_unit > $o] : ( ord_le1511552390unit_o @ A_44 @ top_to1984820022unit_o ) ).
thf(fact_726_subset__inj__on,axiom,
! [A_43: arrow_1196572341e_indi > $o,F_8: arrow_1196572341e_indi > nat,B_41: arrow_1196572341e_indi > $o] :
( ( inj_on1505595958di_nat @ F_8 @ B_41 )
=> ( ( ord_le865407012indi_o @ A_43 @ B_41 )
=> ( inj_on1505595958di_nat @ F_8 @ A_43 ) ) ) ).
thf(fact_727_subset__inj__on,axiom,
! [A_43: nat > $o,F_8: nat > nat,B_41: nat > $o] :
( ( inj_on_nat_nat @ F_8 @ B_41 )
=> ( ( ord_less_eq_nat_o @ A_43 @ B_41 )
=> ( inj_on_nat_nat @ F_8 @ A_43 ) ) ) ).
thf(fact_728_add__right__imp__eq,axiom,
! [B_40: nat,A_42: nat,C_29: nat] :
( ( ( plus_plus_nat @ B_40 @ A_42 )
= ( plus_plus_nat @ C_29 @ A_42 ) )
=> ( B_40 = C_29 ) ) ).
thf(fact_729_add__imp__eq,axiom,
! [A_41: nat,B_39: nat,C_28: nat] :
( ( ( plus_plus_nat @ A_41 @ B_39 )
= ( plus_plus_nat @ A_41 @ C_28 ) )
=> ( B_39 = C_28 ) ) ).
thf(fact_730_add__left__imp__eq,axiom,
! [A_40: nat,B_38: nat,C_27: nat] :
( ( ( plus_plus_nat @ A_40 @ B_38 )
= ( plus_plus_nat @ A_40 @ C_27 ) )
=> ( B_38 = C_27 ) ) ).
thf(fact_731_add__right__cancel,axiom,
! [B_37: nat,A_39: nat,C_26: nat] :
( ( ( plus_plus_nat @ B_37 @ A_39 )
= ( plus_plus_nat @ C_26 @ A_39 ) )
<=> ( B_37 = C_26 ) ) ).
thf(fact_732_add__left__cancel,axiom,
! [A_38: nat,B_36: nat,C_25: nat] :
( ( ( plus_plus_nat @ A_38 @ B_36 )
= ( plus_plus_nat @ A_38 @ C_25 ) )
<=> ( B_36 = C_25 ) ) ).
thf(fact_733_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A_37: nat,B_35: nat,C_24: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_37 @ B_35 ) @ C_24 )
= ( plus_plus_nat @ A_37 @ ( plus_plus_nat @ B_35 @ C_24 ) ) ) ).
thf(fact_734_one__reorient,axiom,
! [X_7: nat] :
( ( one_one_nat = X_7 )
<=> ( X_7 = one_one_nat ) ) ).
thf(fact_735_add__le__imp__le__left,axiom,
! [C_23: nat,A_36: nat,B_34: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C_23 @ A_36 ) @ ( plus_plus_nat @ C_23 @ B_34 ) )
=> ( ord_less_eq_nat @ A_36 @ B_34 ) ) ).
thf(fact_736_add__le__imp__le__right,axiom,
! [A_35: nat,C_22: nat,B_33: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A_35 @ C_22 ) @ ( plus_plus_nat @ B_33 @ C_22 ) )
=> ( ord_less_eq_nat @ A_35 @ B_33 ) ) ).
thf(fact_737_add__mono,axiom,
! [C_21: nat,D_1: nat,A_34: nat,B_32: nat] :
( ( ord_less_eq_nat @ A_34 @ B_32 )
=> ( ( ord_less_eq_nat @ C_21 @ D_1 )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A_34 @ C_21 ) @ ( plus_plus_nat @ B_32 @ D_1 ) ) ) ) ).
thf(fact_738_add__left__mono,axiom,
! [C_20: nat,A_33: nat,B_31: nat] :
( ( ord_less_eq_nat @ A_33 @ B_31 )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C_20 @ A_33 ) @ ( plus_plus_nat @ C_20 @ B_31 ) ) ) ).
thf(fact_739_add__right__mono,axiom,
! [C_19: nat,A_32: nat,B_30: nat] :
( ( ord_less_eq_nat @ A_32 @ B_30 )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A_32 @ C_19 ) @ ( plus_plus_nat @ B_30 @ C_19 ) ) ) ).
thf(fact_740_add__le__cancel__left,axiom,
! [C_18: nat,A_31: nat,B_29: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C_18 @ A_31 ) @ ( plus_plus_nat @ C_18 @ B_29 ) )
<=> ( ord_less_eq_nat @ A_31 @ B_29 ) ) ).
thf(fact_741_add__le__cancel__right,axiom,
! [A_30: nat,C_17: nat,B_28: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A_30 @ C_17 ) @ ( plus_plus_nat @ B_28 @ C_17 ) )
<=> ( ord_less_eq_nat @ A_30 @ B_28 ) ) ).
thf(fact_742_add__less__imp__less__left,axiom,
! [C_16: nat,A_29: nat,B_27: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C_16 @ A_29 ) @ ( plus_plus_nat @ C_16 @ B_27 ) )
=> ( ord_less_nat @ A_29 @ B_27 ) ) ).
thf(fact_743_add__less__imp__less__right,axiom,
! [A_28: nat,C_15: nat,B_26: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A_28 @ C_15 ) @ ( plus_plus_nat @ B_26 @ C_15 ) )
=> ( ord_less_nat @ A_28 @ B_26 ) ) ).
thf(fact_744_add__strict__mono,axiom,
! [C_14: nat,D: nat,A_27: nat,B_25: nat] :
( ( ord_less_nat @ A_27 @ B_25 )
=> ( ( ord_less_nat @ C_14 @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A_27 @ C_14 ) @ ( plus_plus_nat @ B_25 @ D ) ) ) ) ).
thf(fact_745_add__strict__left__mono,axiom,
! [C_13: nat,A_26: nat,B_24: nat] :
( ( ord_less_nat @ A_26 @ B_24 )
=> ( ord_less_nat @ ( plus_plus_nat @ C_13 @ A_26 ) @ ( plus_plus_nat @ C_13 @ B_24 ) ) ) ).
thf(fact_746_add__strict__right__mono,axiom,
! [C_12: nat,A_25: nat,B_23: nat] :
( ( ord_less_nat @ A_25 @ B_23 )
=> ( ord_less_nat @ ( plus_plus_nat @ A_25 @ C_12 ) @ ( plus_plus_nat @ B_23 @ C_12 ) ) ) ).
thf(fact_747_add__less__cancel__left,axiom,
! [C_11: nat,A_24: nat,B_22: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C_11 @ A_24 ) @ ( plus_plus_nat @ C_11 @ B_22 ) )
<=> ( ord_less_nat @ A_24 @ B_22 ) ) ).
thf(fact_748_add__less__cancel__right,axiom,
! [A_23: nat,C_10: nat,B_21: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A_23 @ C_10 ) @ ( plus_plus_nat @ B_21 @ C_10 ) )
<=> ( ord_less_nat @ A_23 @ B_21 ) ) ).
thf(fact_749_le__funI,axiom,
! [F_7: ( produc1572197287le_alt > $o ) > $o,G: ( produc1572197287le_alt > $o ) > $o] :
( ! [X_1: produc1572197287le_alt > $o] : ( ord_less_eq_o @ ( F_7 @ X_1 ) @ ( G @ X_1 ) )
=> ( ord_le1027220427lt_o_o @ F_7 @ G ) ) ).
thf(fact_750_le__funI,axiom,
! [F_7: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,G: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o] : ( ord_less_eq_o @ ( F_7 @ X_1 ) @ ( G @ X_1 ) )
=> ( ord_le1805007862lt_o_o @ F_7 @ G ) ) ).
thf(fact_751_le__funI,axiom,
! [F_7: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,G: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ! [X_1: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( ord_less_eq_o @ ( F_7 @ X_1 ) @ ( G @ X_1 ) )
=> ( ord_le602483040lt_o_o @ F_7 @ G ) ) ).
thf(fact_752_le__funI,axiom,
! [F_7: produc1572197287le_alt > $o,G: produc1572197287le_alt > $o] :
( ! [X_1: produc1572197287le_alt] : ( ord_less_eq_o @ ( F_7 @ X_1 ) @ ( G @ X_1 ) )
=> ( ord_le962286258_alt_o @ F_7 @ G ) ) ).
thf(fact_753_le__funI,axiom,
! [F_7: arrow_1196572341e_indi > $o,G: arrow_1196572341e_indi > $o] :
( ! [X_1: arrow_1196572341e_indi] : ( ord_less_eq_o @ ( F_7 @ X_1 ) @ ( G @ X_1 ) )
=> ( ord_le865407012indi_o @ F_7 @ G ) ) ).
thf(fact_754_le__funI,axiom,
! [F_7: product_unit > $o,G: product_unit > $o] :
( ! [X_1: product_unit] : ( ord_less_eq_o @ ( F_7 @ X_1 ) @ ( G @ X_1 ) )
=> ( ord_le1511552390unit_o @ F_7 @ G ) ) ).
thf(fact_755_le__funI,axiom,
! [F_7: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,G: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ! [X_1: arrow_1389031998le_alt] : ( ord_le1423491573_alt_o @ ( F_7 @ X_1 ) @ ( G @ X_1 ) )
=> ( ord_le1463467535_alt_o @ F_7 @ G ) ) ).
thf(fact_756_le__funI,axiom,
! [F_7: nat > $o,G: nat > $o] :
( ! [X_1: nat] : ( ord_less_eq_o @ ( F_7 @ X_1 ) @ ( G @ X_1 ) )
=> ( ord_less_eq_nat_o @ F_7 @ G ) ) ).
thf(fact_757_xt6,axiom,
! [C_9: nat > $o,F_6: ( nat > $o ) > nat > $o,B_20: nat > $o,A_22: nat > $o] :
( ( ord_less_eq_nat_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat_o @ C_9 @ B_20 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_nat_o @ Y_1 @ X_1 )
=> ( ord_less_nat_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_758_xt6,axiom,
! [C_9: product_unit > $o,F_6: ( product_unit > $o ) > nat > $o,B_20: product_unit > $o,A_22: nat > $o] :
( ( ord_less_eq_nat_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_le232288914unit_o @ C_9 @ B_20 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le232288914unit_o @ Y_1 @ X_1 )
=> ( ord_less_nat_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_759_xt6,axiom,
! [C_9: arrow_1196572341e_indi > $o,F_6: ( arrow_1196572341e_indi > $o ) > nat > $o,B_20: arrow_1196572341e_indi > $o,A_22: nat > $o] :
( ( ord_less_eq_nat_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_le1991507760indi_o @ C_9 @ B_20 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ Y_1 @ X_1 )
=> ( ord_less_nat_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_760_xt6,axiom,
! [C_9: nat,F_6: nat > nat > $o,B_20: nat,A_22: nat > $o] :
( ( ord_less_eq_nat_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_less_nat_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_761_xt6,axiom,
! [C_9: nat,F_6: nat > product_unit > $o,B_20: nat,A_22: product_unit > $o] :
( ( ord_le1511552390unit_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le232288914unit_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_le232288914unit_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_762_xt6,axiom,
! [C_9: nat,F_6: nat > arrow_1196572341e_indi > $o,B_20: nat,A_22: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le1991507760indi_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_le1991507760indi_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_763_xt6,axiom,
! [C_9: nat,F_6: nat > ( produc1572197287le_alt > $o ) > $o,B_20: nat,A_22: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le874404799lt_o_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_le874404799lt_o_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_764_xt6,axiom,
! [C_9: nat,F_6: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_20: nat,A_22: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le1382328578lt_o_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_le1382328578lt_o_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_765_xt6,axiom,
! [C_9: nat,F_6: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_20: nat,A_22: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le914873172lt_o_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_le914873172lt_o_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_766_xt6,axiom,
! [C_9: nat,F_6: nat > produc1572197287le_alt > $o,B_20: nat,A_22: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le1852932542_alt_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_le1852932542_alt_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_767_xt6,axiom,
! [C_9: nat,F_6: nat > $o,B_20: nat,A_22: $o] :
( ( ord_less_eq_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_less_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_less_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_768_xt6,axiom,
! [C_9: nat,F_6: nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_20: nat,A_22: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat @ C_9 @ B_20 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ Y_1 @ X_1 )
=> ( ord_le1339521307_alt_o @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_le1339521307_alt_o @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_769_xt6,axiom,
! [C_9: nat > $o,F_6: ( nat > $o ) > nat,B_20: nat > $o,A_22: nat] :
( ( ord_less_eq_nat @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_less_nat_o @ C_9 @ B_20 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_nat_o @ Y_1 @ X_1 )
=> ( ord_less_nat @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_770_xt6,axiom,
! [C_9: product_unit > $o,F_6: ( product_unit > $o ) > nat,B_20: product_unit > $o,A_22: nat] :
( ( ord_less_eq_nat @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_le232288914unit_o @ C_9 @ B_20 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le232288914unit_o @ Y_1 @ X_1 )
=> ( ord_less_nat @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_771_xt6,axiom,
! [C_9: arrow_1196572341e_indi > $o,F_6: ( arrow_1196572341e_indi > $o ) > nat,B_20: arrow_1196572341e_indi > $o,A_22: nat] :
( ( ord_less_eq_nat @ ( F_6 @ B_20 ) @ A_22 )
=> ( ( ord_le1991507760indi_o @ C_9 @ B_20 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ Y_1 @ X_1 )
=> ( ord_less_nat @ ( F_6 @ Y_1 ) @ ( F_6 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_6 @ C_9 ) @ A_22 ) ) ) ) ).
thf(fact_772_xt4,axiom,
! [C_8: nat,F_5: nat > nat > $o,B_19: nat,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_773_xt4,axiom,
! [C_8: nat,F_5: nat > product_unit > $o,B_19: nat,A_21: product_unit > $o] :
( ( ord_le232288914unit_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le1511552390unit_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le232288914unit_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_774_xt4,axiom,
! [C_8: nat,F_5: nat > arrow_1196572341e_indi > $o,B_19: nat,A_21: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le865407012indi_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le1991507760indi_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_775_xt4,axiom,
! [C_8: nat,F_5: nat > ( produc1572197287le_alt > $o ) > $o,B_19: nat,A_21: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le1027220427lt_o_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le874404799lt_o_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_776_xt4,axiom,
! [C_8: nat,F_5: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_19: nat,A_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le1805007862lt_o_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le1382328578lt_o_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_777_xt4,axiom,
! [C_8: nat,F_5: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_19: nat,A_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le602483040lt_o_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le914873172lt_o_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_778_xt4,axiom,
! [C_8: nat,F_5: nat > produc1572197287le_alt > $o,B_19: nat,A_21: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le962286258_alt_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le1852932542_alt_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_779_xt4,axiom,
! [C_8: nat,F_5: nat > $o,B_19: nat,A_21: $o] :
( ( ord_less_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_less_eq_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_780_xt4,axiom,
! [C_8: nat,F_5: nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_19: nat,A_21: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1339521307_alt_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat @ C_8 @ B_19 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ Y_1 @ X_1 )
=> ( ord_le1463467535_alt_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le1339521307_alt_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_781_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > nat > $o,B_19: nat > $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_782_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > product_unit > $o,B_19: nat > $o,A_21: product_unit > $o] :
( ( ord_le232288914unit_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le1511552390unit_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le232288914unit_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_783_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > arrow_1196572341e_indi > $o,B_19: nat > $o,A_21: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le865407012indi_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le1991507760indi_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_784_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o,B_19: nat > $o,A_21: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le1027220427lt_o_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le874404799lt_o_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_785_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_19: nat > $o,A_21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le1805007862lt_o_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le1382328578lt_o_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_786_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_19: nat > $o,A_21: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le602483040lt_o_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le914873172lt_o_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_787_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > produc1572197287le_alt > $o,B_19: nat > $o,A_21: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le962286258_alt_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le1852932542_alt_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_788_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > $o,B_19: nat > $o,A_21: $o] :
( ( ord_less_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_less_eq_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_789_xt4,axiom,
! [C_8: nat > $o,F_5: ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_19: nat > $o,A_21: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1339521307_alt_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_nat_o @ C_8 @ B_19 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ Y_1 @ X_1 )
=> ( ord_le1463467535_alt_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_le1339521307_alt_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_790_xt4,axiom,
! [C_8: ( produc1572197287le_alt > $o ) > $o,F_5: ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o,B_19: ( produc1572197287le_alt > $o ) > $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le1027220427lt_o_o @ C_8 @ B_19 )
=> ( ! [X_1: ( produc1572197287le_alt > $o ) > $o,Y_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_791_xt4,axiom,
! [C_8: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,F_5: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o,B_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le1805007862lt_o_o @ C_8 @ B_19 )
=> ( ! [X_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_792_xt4,axiom,
! [C_8: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,F_5: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o,B_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le602483040lt_o_o @ C_8 @ B_19 )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_793_xt4,axiom,
! [C_8: produc1572197287le_alt > $o,F_5: ( produc1572197287le_alt > $o ) > nat > $o,B_19: produc1572197287le_alt > $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le962286258_alt_o @ C_8 @ B_19 )
=> ( ! [X_1: produc1572197287le_alt > $o,Y_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_794_xt4,axiom,
! [C_8: $o,F_5: $o > nat > $o,B_19: $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_o @ C_8 @ B_19 )
=> ( ! [X_1: $o,Y_1: $o] :
( ( ord_less_eq_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_795_xt4,axiom,
! [C_8: arrow_1196572341e_indi > $o,F_5: ( arrow_1196572341e_indi > $o ) > nat > $o,B_19: arrow_1196572341e_indi > $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le865407012indi_o @ C_8 @ B_19 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_796_xt4,axiom,
! [C_8: product_unit > $o,F_5: ( product_unit > $o ) > nat > $o,B_19: product_unit > $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le1511552390unit_o @ C_8 @ B_19 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le1511552390unit_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_797_xt4,axiom,
! [C_8: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_5: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o,B_19: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_21: nat > $o] :
( ( ord_less_nat_o @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le1463467535_alt_o @ C_8 @ B_19 )
=> ( ! [X_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat_o @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat_o @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_798_xt4,axiom,
! [C_8: ( produc1572197287le_alt > $o ) > $o,F_5: ( ( produc1572197287le_alt > $o ) > $o ) > nat,B_19: ( produc1572197287le_alt > $o ) > $o,A_21: nat] :
( ( ord_less_nat @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le1027220427lt_o_o @ C_8 @ B_19 )
=> ( ! [X_1: ( produc1572197287le_alt > $o ) > $o,Y_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_799_xt4,axiom,
! [C_8: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,F_5: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat,B_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_21: nat] :
( ( ord_less_nat @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le1805007862lt_o_o @ C_8 @ B_19 )
=> ( ! [X_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_800_xt4,axiom,
! [C_8: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,F_5: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat,B_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_21: nat] :
( ( ord_less_nat @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le602483040lt_o_o @ C_8 @ B_19 )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_801_xt4,axiom,
! [C_8: produc1572197287le_alt > $o,F_5: ( produc1572197287le_alt > $o ) > nat,B_19: produc1572197287le_alt > $o,A_21: nat] :
( ( ord_less_nat @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le962286258_alt_o @ C_8 @ B_19 )
=> ( ! [X_1: produc1572197287le_alt > $o,Y_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_802_xt4,axiom,
! [C_8: $o,F_5: $o > nat,B_19: $o,A_21: nat] :
( ( ord_less_nat @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_less_eq_o @ C_8 @ B_19 )
=> ( ! [X_1: $o,Y_1: $o] :
( ( ord_less_eq_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_803_xt4,axiom,
! [C_8: arrow_1196572341e_indi > $o,F_5: ( arrow_1196572341e_indi > $o ) > nat,B_19: arrow_1196572341e_indi > $o,A_21: nat] :
( ( ord_less_nat @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le865407012indi_o @ C_8 @ B_19 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_804_xt4,axiom,
! [C_8: product_unit > $o,F_5: ( product_unit > $o ) > nat,B_19: product_unit > $o,A_21: nat] :
( ( ord_less_nat @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le1511552390unit_o @ C_8 @ B_19 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le1511552390unit_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_805_xt4,axiom,
! [C_8: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_5: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat,B_19: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_21: nat] :
( ( ord_less_nat @ ( F_5 @ B_19 ) @ A_21 )
=> ( ( ord_le1463467535_alt_o @ C_8 @ B_19 )
=> ( ! [X_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ Y_1 @ X_1 )
=> ( ord_less_eq_nat @ ( F_5 @ Y_1 ) @ ( F_5 @ X_1 ) ) )
=> ( ord_less_nat @ ( F_5 @ C_8 ) @ A_21 ) ) ) ) ).
thf(fact_806_order__le__less__subst1,axiom,
! [C_7: nat > $o,A_20: nat > $o,F_4: ( nat > $o ) > nat > $o,B_18: nat > $o] :
( ( ord_less_eq_nat_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat_o @ B_18 @ C_7 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_nat_o @ X_1 @ Y_1 )
=> ( ord_less_nat_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_807_order__le__less__subst1,axiom,
! [C_7: product_unit > $o,A_20: nat > $o,F_4: ( product_unit > $o ) > nat > $o,B_18: product_unit > $o] :
( ( ord_less_eq_nat_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_le232288914unit_o @ B_18 @ C_7 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le232288914unit_o @ X_1 @ Y_1 )
=> ( ord_less_nat_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_808_order__le__less__subst1,axiom,
! [C_7: arrow_1196572341e_indi > $o,A_20: nat > $o,F_4: ( arrow_1196572341e_indi > $o ) > nat > $o,B_18: arrow_1196572341e_indi > $o] :
( ( ord_less_eq_nat_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_le1991507760indi_o @ B_18 @ C_7 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_1 @ Y_1 )
=> ( ord_less_nat_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_809_order__le__less__subst1,axiom,
! [C_7: nat,A_20: nat > $o,F_4: nat > nat > $o,B_18: nat] :
( ( ord_less_eq_nat_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_less_nat_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_810_order__le__less__subst1,axiom,
! [C_7: nat,A_20: product_unit > $o,F_4: nat > product_unit > $o,B_18: nat] :
( ( ord_le1511552390unit_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le232288914unit_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_le232288914unit_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_811_order__le__less__subst1,axiom,
! [C_7: nat,A_20: arrow_1196572341e_indi > $o,F_4: nat > arrow_1196572341e_indi > $o,B_18: nat] :
( ( ord_le865407012indi_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le1991507760indi_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_le1991507760indi_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_812_order__le__less__subst1,axiom,
! [C_7: nat,A_20: ( produc1572197287le_alt > $o ) > $o,F_4: nat > ( produc1572197287le_alt > $o ) > $o,B_18: nat] :
( ( ord_le1027220427lt_o_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le874404799lt_o_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_le874404799lt_o_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_813_order__le__less__subst1,axiom,
! [C_7: nat,A_20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,F_4: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_18: nat] :
( ( ord_le1805007862lt_o_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le1382328578lt_o_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_le1382328578lt_o_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_814_order__le__less__subst1,axiom,
! [C_7: nat,A_20: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,F_4: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_18: nat] :
( ( ord_le602483040lt_o_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le914873172lt_o_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_le914873172lt_o_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_815_order__le__less__subst1,axiom,
! [C_7: nat,A_20: produc1572197287le_alt > $o,F_4: nat > produc1572197287le_alt > $o,B_18: nat] :
( ( ord_le962286258_alt_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le1852932542_alt_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_le1852932542_alt_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_816_order__le__less__subst1,axiom,
! [C_7: nat,A_20: $o,F_4: nat > $o,B_18: nat] :
( ( ord_less_eq_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_less_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_less_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_817_order__le__less__subst1,axiom,
! [C_7: nat,A_20: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_4: nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_18: nat] :
( ( ord_le1463467535_alt_o @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat @ B_18 @ C_7 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le1339521307_alt_o @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_le1339521307_alt_o @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_818_order__le__less__subst1,axiom,
! [C_7: nat > $o,A_20: nat,F_4: ( nat > $o ) > nat,B_18: nat > $o] :
( ( ord_less_eq_nat @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_less_nat_o @ B_18 @ C_7 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_nat_o @ X_1 @ Y_1 )
=> ( ord_less_nat @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_less_nat @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_819_order__le__less__subst1,axiom,
! [C_7: product_unit > $o,A_20: nat,F_4: ( product_unit > $o ) > nat,B_18: product_unit > $o] :
( ( ord_less_eq_nat @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_le232288914unit_o @ B_18 @ C_7 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le232288914unit_o @ X_1 @ Y_1 )
=> ( ord_less_nat @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_less_nat @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_820_order__le__less__subst1,axiom,
! [C_7: arrow_1196572341e_indi > $o,A_20: nat,F_4: ( arrow_1196572341e_indi > $o ) > nat,B_18: arrow_1196572341e_indi > $o] :
( ( ord_less_eq_nat @ A_20 @ ( F_4 @ B_18 ) )
=> ( ( ord_le1991507760indi_o @ B_18 @ C_7 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_1 @ Y_1 )
=> ( ord_less_nat @ ( F_4 @ X_1 ) @ ( F_4 @ Y_1 ) ) )
=> ( ord_less_nat @ A_20 @ ( F_4 @ C_7 ) ) ) ) ) ).
thf(fact_821_order__less__le__subst1,axiom,
! [C_6: nat,A_19: nat > $o,F_3: nat > nat > $o,B_17: nat] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_822_order__less__le__subst1,axiom,
! [C_6: nat,A_19: product_unit > $o,F_3: nat > product_unit > $o,B_17: nat] :
( ( ord_le232288914unit_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le1511552390unit_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le232288914unit_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_823_order__less__le__subst1,axiom,
! [C_6: nat,A_19: arrow_1196572341e_indi > $o,F_3: nat > arrow_1196572341e_indi > $o,B_17: nat] :
( ( ord_le1991507760indi_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le865407012indi_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le1991507760indi_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_824_order__less__le__subst1,axiom,
! [C_6: nat,A_19: ( produc1572197287le_alt > $o ) > $o,F_3: nat > ( produc1572197287le_alt > $o ) > $o,B_17: nat] :
( ( ord_le874404799lt_o_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le1027220427lt_o_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le874404799lt_o_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_825_order__less__le__subst1,axiom,
! [C_6: nat,A_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,F_3: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_17: nat] :
( ( ord_le1382328578lt_o_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le1805007862lt_o_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le1382328578lt_o_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_826_order__less__le__subst1,axiom,
! [C_6: nat,A_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,F_3: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_17: nat] :
( ( ord_le914873172lt_o_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le602483040lt_o_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le914873172lt_o_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_827_order__less__le__subst1,axiom,
! [C_6: nat,A_19: produc1572197287le_alt > $o,F_3: nat > produc1572197287le_alt > $o,B_17: nat] :
( ( ord_le1852932542_alt_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le962286258_alt_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le1852932542_alt_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_828_order__less__le__subst1,axiom,
! [C_6: nat,A_19: $o,F_3: nat > $o,B_17: nat] :
( ( ord_less_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_less_eq_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_829_order__less__le__subst1,axiom,
! [C_6: nat,A_19: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_3: nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_17: nat] :
( ( ord_le1339521307_alt_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat @ B_17 @ C_6 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le1463467535_alt_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le1339521307_alt_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_830_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: nat > $o,F_3: ( nat > $o ) > nat > $o,B_17: nat > $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_831_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: product_unit > $o,F_3: ( nat > $o ) > product_unit > $o,B_17: nat > $o] :
( ( ord_le232288914unit_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le1511552390unit_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le232288914unit_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_832_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: arrow_1196572341e_indi > $o,F_3: ( nat > $o ) > arrow_1196572341e_indi > $o,B_17: nat > $o] :
( ( ord_le1991507760indi_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le865407012indi_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le1991507760indi_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_833_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: ( produc1572197287le_alt > $o ) > $o,F_3: ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o,B_17: nat > $o] :
( ( ord_le874404799lt_o_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le1027220427lt_o_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le874404799lt_o_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_834_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,F_3: ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_17: nat > $o] :
( ( ord_le1382328578lt_o_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le1805007862lt_o_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le1382328578lt_o_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_835_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,F_3: ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_17: nat > $o] :
( ( ord_le914873172lt_o_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le602483040lt_o_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le914873172lt_o_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_836_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: produc1572197287le_alt > $o,F_3: ( nat > $o ) > produc1572197287le_alt > $o,B_17: nat > $o] :
( ( ord_le1852932542_alt_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le962286258_alt_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le1852932542_alt_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_837_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: $o,F_3: ( nat > $o ) > $o,B_17: nat > $o] :
( ( ord_less_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_less_eq_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_838_order__less__le__subst1,axiom,
! [C_6: nat > $o,A_19: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,F_3: ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_17: nat > $o] :
( ( ord_le1339521307_alt_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_nat_o @ B_17 @ C_6 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le1463467535_alt_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_le1339521307_alt_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_839_order__less__le__subst1,axiom,
! [C_6: ( produc1572197287le_alt > $o ) > $o,A_19: nat > $o,F_3: ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o,B_17: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le1027220427lt_o_o @ B_17 @ C_6 )
=> ( ! [X_1: ( produc1572197287le_alt > $o ) > $o,Y_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_840_order__less__le__subst1,axiom,
! [C_6: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_19: nat > $o,F_3: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o,B_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le1805007862lt_o_o @ B_17 @ C_6 )
=> ( ! [X_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_841_order__less__le__subst1,axiom,
! [C_6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_19: nat > $o,F_3: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o,B_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le602483040lt_o_o @ B_17 @ C_6 )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_842_order__less__le__subst1,axiom,
! [C_6: produc1572197287le_alt > $o,A_19: nat > $o,F_3: ( produc1572197287le_alt > $o ) > nat > $o,B_17: produc1572197287le_alt > $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le962286258_alt_o @ B_17 @ C_6 )
=> ( ! [X_1: produc1572197287le_alt > $o,Y_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_843_order__less__le__subst1,axiom,
! [C_6: $o,A_19: nat > $o,F_3: $o > nat > $o,B_17: $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_o @ B_17 @ C_6 )
=> ( ! [X_1: $o,Y_1: $o] :
( ( ord_less_eq_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_844_order__less__le__subst1,axiom,
! [C_6: arrow_1196572341e_indi > $o,A_19: nat > $o,F_3: ( arrow_1196572341e_indi > $o ) > nat > $o,B_17: arrow_1196572341e_indi > $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le865407012indi_o @ B_17 @ C_6 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_845_order__less__le__subst1,axiom,
! [C_6: product_unit > $o,A_19: nat > $o,F_3: ( product_unit > $o ) > nat > $o,B_17: product_unit > $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le1511552390unit_o @ B_17 @ C_6 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_846_order__less__le__subst1,axiom,
! [C_6: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_19: nat > $o,F_3: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o,B_17: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_less_nat_o @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le1463467535_alt_o @ B_17 @ C_6 )
=> ( ! [X_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat_o @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_847_order__less__le__subst1,axiom,
! [C_6: ( produc1572197287le_alt > $o ) > $o,A_19: nat,F_3: ( ( produc1572197287le_alt > $o ) > $o ) > nat,B_17: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_less_nat @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le1027220427lt_o_o @ B_17 @ C_6 )
=> ( ! [X_1: ( produc1572197287le_alt > $o ) > $o,Y_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_848_order__less__le__subst1,axiom,
! [C_6: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_19: nat,F_3: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat,B_17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_less_nat @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le1805007862lt_o_o @ B_17 @ C_6 )
=> ( ! [X_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_849_order__less__le__subst1,axiom,
! [C_6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_19: nat,F_3: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat,B_17: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_less_nat @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le602483040lt_o_o @ B_17 @ C_6 )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_850_order__less__le__subst1,axiom,
! [C_6: produc1572197287le_alt > $o,A_19: nat,F_3: ( produc1572197287le_alt > $o ) > nat,B_17: produc1572197287le_alt > $o] :
( ( ord_less_nat @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le962286258_alt_o @ B_17 @ C_6 )
=> ( ! [X_1: produc1572197287le_alt > $o,Y_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_851_order__less__le__subst1,axiom,
! [C_6: $o,A_19: nat,F_3: $o > nat,B_17: $o] :
( ( ord_less_nat @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_less_eq_o @ B_17 @ C_6 )
=> ( ! [X_1: $o,Y_1: $o] :
( ( ord_less_eq_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_852_order__less__le__subst1,axiom,
! [C_6: arrow_1196572341e_indi > $o,A_19: nat,F_3: ( arrow_1196572341e_indi > $o ) > nat,B_17: arrow_1196572341e_indi > $o] :
( ( ord_less_nat @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le865407012indi_o @ B_17 @ C_6 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_853_order__less__le__subst1,axiom,
! [C_6: product_unit > $o,A_19: nat,F_3: ( product_unit > $o ) > nat,B_17: product_unit > $o] :
( ( ord_less_nat @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le1511552390unit_o @ B_17 @ C_6 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_854_order__less__le__subst1,axiom,
! [C_6: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_19: nat,F_3: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat,B_17: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_less_nat @ A_19 @ ( F_3 @ B_17 ) )
=> ( ( ord_le1463467535_alt_o @ B_17 @ C_6 )
=> ( ! [X_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_3 @ X_1 ) @ ( F_3 @ Y_1 ) ) )
=> ( ord_less_nat @ A_19 @ ( F_3 @ C_6 ) ) ) ) ) ).
thf(fact_855_order__le__less__subst2,axiom,
! [F_2: nat > nat > $o,C_5: nat > $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_856_order__le__less__subst2,axiom,
! [F_2: nat > product_unit > $o,C_5: product_unit > $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_le232288914unit_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le1511552390unit_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le232288914unit_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_857_order__le__less__subst2,axiom,
! [F_2: nat > arrow_1196572341e_indi > $o,C_5: arrow_1196572341e_indi > $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_le1991507760indi_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le865407012indi_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le1991507760indi_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_858_order__le__less__subst2,axiom,
! [F_2: nat > ( produc1572197287le_alt > $o ) > $o,C_5: ( produc1572197287le_alt > $o ) > $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_le874404799lt_o_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le1027220427lt_o_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le874404799lt_o_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_859_order__le__less__subst2,axiom,
! [F_2: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,C_5: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_le1382328578lt_o_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le1805007862lt_o_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le1382328578lt_o_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_860_order__le__less__subst2,axiom,
! [F_2: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,C_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_le914873172lt_o_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le602483040lt_o_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le914873172lt_o_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_861_order__le__less__subst2,axiom,
! [F_2: nat > produc1572197287le_alt > $o,C_5: produc1572197287le_alt > $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_le1852932542_alt_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le962286258_alt_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le1852932542_alt_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_862_order__le__less__subst2,axiom,
! [F_2: nat > $o,C_5: $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_less_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_less_eq_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_863_order__le__less__subst2,axiom,
! [F_2: nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,C_5: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_18: nat,B_16: nat] :
( ( ord_less_eq_nat @ A_18 @ B_16 )
=> ( ( ord_le1339521307_alt_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_eq_nat @ X_1 @ Y_1 )
=> ( ord_le1463467535_alt_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le1339521307_alt_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_864_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > nat > $o,C_5: nat > $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_865_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > product_unit > $o,C_5: product_unit > $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_le232288914unit_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le1511552390unit_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le232288914unit_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_866_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > arrow_1196572341e_indi > $o,C_5: arrow_1196572341e_indi > $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_le1991507760indi_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le865407012indi_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le1991507760indi_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_867_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o,C_5: ( produc1572197287le_alt > $o ) > $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_le874404799lt_o_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le1027220427lt_o_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le874404799lt_o_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_868_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,C_5: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_le1382328578lt_o_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le1805007862lt_o_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le1382328578lt_o_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_869_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,C_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_le914873172lt_o_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le602483040lt_o_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le914873172lt_o_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_870_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > produc1572197287le_alt > $o,C_5: produc1572197287le_alt > $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_le1852932542_alt_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le962286258_alt_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le1852932542_alt_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_871_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > $o,C_5: $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_less_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_less_eq_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_872_order__le__less__subst2,axiom,
! [F_2: ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,C_5: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_18: nat > $o,B_16: nat > $o] :
( ( ord_less_eq_nat_o @ A_18 @ B_16 )
=> ( ( ord_le1339521307_alt_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_eq_nat_o @ X_1 @ Y_1 )
=> ( ord_le1463467535_alt_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_le1339521307_alt_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_873_order__le__less__subst2,axiom,
! [F_2: ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o,C_5: nat > $o,A_18: ( produc1572197287le_alt > $o ) > $o,B_16: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: ( produc1572197287le_alt > $o ) > $o,Y_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_874_order__le__less__subst2,axiom,
! [F_2: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o,C_5: nat > $o,A_18: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_875_order__le__less__subst2,axiom,
! [F_2: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o,C_5: nat > $o,A_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_876_order__le__less__subst2,axiom,
! [F_2: ( produc1572197287le_alt > $o ) > nat > $o,C_5: nat > $o,A_18: produc1572197287le_alt > $o,B_16: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: produc1572197287le_alt > $o,Y_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_877_order__le__less__subst2,axiom,
! [F_2: $o > nat > $o,C_5: nat > $o,A_18: $o,B_16: $o] :
( ( ord_less_eq_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: $o,Y_1: $o] :
( ( ord_less_eq_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_878_order__le__less__subst2,axiom,
! [F_2: ( arrow_1196572341e_indi > $o ) > nat > $o,C_5: nat > $o,A_18: arrow_1196572341e_indi > $o,B_16: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_879_order__le__less__subst2,axiom,
! [F_2: ( product_unit > $o ) > nat > $o,C_5: nat > $o,A_18: product_unit > $o,B_16: product_unit > $o] :
( ( ord_le1511552390unit_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_880_order__le__less__subst2,axiom,
! [F_2: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o,C_5: nat > $o,A_18: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_16: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ A_18 @ B_16 )
=> ( ( ord_less_nat_o @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat_o @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_881_order__le__less__subst2,axiom,
! [F_2: ( ( produc1572197287le_alt > $o ) > $o ) > nat,C_5: nat,A_18: ( produc1572197287le_alt > $o ) > $o,B_16: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_18 @ B_16 )
=> ( ( ord_less_nat @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: ( produc1572197287le_alt > $o ) > $o,Y_1: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_882_order__le__less__subst2,axiom,
! [F_2: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat,C_5: nat,A_18: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_18 @ B_16 )
=> ( ( ord_less_nat @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,Y_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_883_order__le__less__subst2,axiom,
! [F_2: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat,C_5: nat,A_18: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_18 @ B_16 )
=> ( ( ord_less_nat @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,Y_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_884_order__le__less__subst2,axiom,
! [F_2: ( produc1572197287le_alt > $o ) > nat,C_5: nat,A_18: produc1572197287le_alt > $o,B_16: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_18 @ B_16 )
=> ( ( ord_less_nat @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: produc1572197287le_alt > $o,Y_1: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_885_order__le__less__subst2,axiom,
! [F_2: $o > nat,C_5: nat,A_18: $o,B_16: $o] :
( ( ord_less_eq_o @ A_18 @ B_16 )
=> ( ( ord_less_nat @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: $o,Y_1: $o] :
( ( ord_less_eq_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_886_order__le__less__subst2,axiom,
! [F_2: ( arrow_1196572341e_indi > $o ) > nat,C_5: nat,A_18: arrow_1196572341e_indi > $o,B_16: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_18 @ B_16 )
=> ( ( ord_less_nat @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_887_order__le__less__subst2,axiom,
! [F_2: ( product_unit > $o ) > nat,C_5: nat,A_18: product_unit > $o,B_16: product_unit > $o] :
( ( ord_le1511552390unit_o @ A_18 @ B_16 )
=> ( ( ord_less_nat @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le1511552390unit_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_888_order__le__less__subst2,axiom,
! [F_2: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat,C_5: nat,A_18: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,B_16: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ A_18 @ B_16 )
=> ( ( ord_less_nat @ ( F_2 @ B_16 ) @ C_5 )
=> ( ! [X_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,Y_1: arrow_1389031998le_alt > arrow_1389031998le_alt > $o] :
( ( ord_le1463467535_alt_o @ X_1 @ Y_1 )
=> ( ord_less_eq_nat @ ( F_2 @ X_1 ) @ ( F_2 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_2 @ A_18 ) @ C_5 ) ) ) ) ).
thf(fact_889_order__less__le__subst2,axiom,
! [F_1: ( nat > $o ) > nat > $o,C_4: nat > $o,A_17: nat > $o,B_15: nat > $o] :
( ( ord_less_nat_o @ A_17 @ B_15 )
=> ( ( ord_less_eq_nat_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_nat_o @ X_1 @ Y_1 )
=> ( ord_less_nat_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_890_order__less__le__subst2,axiom,
! [F_1: ( product_unit > $o ) > nat > $o,C_4: nat > $o,A_17: product_unit > $o,B_15: product_unit > $o] :
( ( ord_le232288914unit_o @ A_17 @ B_15 )
=> ( ( ord_less_eq_nat_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le232288914unit_o @ X_1 @ Y_1 )
=> ( ord_less_nat_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_891_order__less__le__subst2,axiom,
! [F_1: ( arrow_1196572341e_indi > $o ) > nat > $o,C_4: nat > $o,A_17: arrow_1196572341e_indi > $o,B_15: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ A_17 @ B_15 )
=> ( ( ord_less_eq_nat_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_1 @ Y_1 )
=> ( ord_less_nat_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_892_order__less__le__subst2,axiom,
! [F_1: nat > nat > $o,C_4: nat > $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_less_eq_nat_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_less_nat_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_less_nat_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_893_order__less__le__subst2,axiom,
! [F_1: nat > product_unit > $o,C_4: product_unit > $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_le1511552390unit_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le232288914unit_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_le232288914unit_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_894_order__less__le__subst2,axiom,
! [F_1: nat > arrow_1196572341e_indi > $o,C_4: arrow_1196572341e_indi > $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_le865407012indi_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le1991507760indi_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_le1991507760indi_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_895_order__less__le__subst2,axiom,
! [F_1: nat > ( produc1572197287le_alt > $o ) > $o,C_4: ( produc1572197287le_alt > $o ) > $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_le1027220427lt_o_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le874404799lt_o_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_le874404799lt_o_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_896_order__less__le__subst2,axiom,
! [F_1: nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,C_4: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_le1805007862lt_o_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le1382328578lt_o_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_le1382328578lt_o_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_897_order__less__le__subst2,axiom,
! [F_1: nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,C_4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_le602483040lt_o_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le914873172lt_o_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_le914873172lt_o_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_898_order__less__le__subst2,axiom,
! [F_1: nat > produc1572197287le_alt > $o,C_4: produc1572197287le_alt > $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_le962286258_alt_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le1852932542_alt_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_le1852932542_alt_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_899_order__less__le__subst2,axiom,
! [F_1: nat > $o,C_4: $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_less_eq_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_less_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_less_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_900_order__less__le__subst2,axiom,
! [F_1: nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o,C_4: arrow_1389031998le_alt > arrow_1389031998le_alt > $o,A_17: nat,B_15: nat] :
( ( ord_less_nat @ A_17 @ B_15 )
=> ( ( ord_le1463467535_alt_o @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat,Y_1: nat] :
( ( ord_less_nat @ X_1 @ Y_1 )
=> ( ord_le1339521307_alt_o @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_le1339521307_alt_o @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_901_order__less__le__subst2,axiom,
! [F_1: ( nat > $o ) > nat,C_4: nat,A_17: nat > $o,B_15: nat > $o] :
( ( ord_less_nat_o @ A_17 @ B_15 )
=> ( ( ord_less_eq_nat @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: nat > $o,Y_1: nat > $o] :
( ( ord_less_nat_o @ X_1 @ Y_1 )
=> ( ord_less_nat @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_902_order__less__le__subst2,axiom,
! [F_1: ( product_unit > $o ) > nat,C_4: nat,A_17: product_unit > $o,B_15: product_unit > $o] :
( ( ord_le232288914unit_o @ A_17 @ B_15 )
=> ( ( ord_less_eq_nat @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: product_unit > $o,Y_1: product_unit > $o] :
( ( ord_le232288914unit_o @ X_1 @ Y_1 )
=> ( ord_less_nat @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_903_order__less__le__subst2,axiom,
! [F_1: ( arrow_1196572341e_indi > $o ) > nat,C_4: nat,A_17: arrow_1196572341e_indi > $o,B_15: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ A_17 @ B_15 )
=> ( ( ord_less_eq_nat @ ( F_1 @ B_15 ) @ C_4 )
=> ( ! [X_1: arrow_1196572341e_indi > $o,Y_1: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ X_1 @ Y_1 )
=> ( ord_less_nat @ ( F_1 @ X_1 ) @ ( F_1 @ Y_1 ) ) )
=> ( ord_less_nat @ ( F_1 @ A_17 ) @ C_4 ) ) ) ) ).
thf(fact_904_add__leE,axiom,
! [M_1: nat,K: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M_1 @ K ) @ N_1 )
=> ~ ( ( ord_less_eq_nat @ M_1 @ N_1 )
=> ~ ( ord_less_eq_nat @ K @ N_1 ) ) ) ).
thf(fact_905_equalityI,axiom,
! [A_16: ( produc1572197287le_alt > $o ) > $o,B_14: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_16 @ B_14 )
=> ( ( ord_le1027220427lt_o_o @ B_14 @ A_16 )
=> ( A_16 = B_14 ) ) ) ).
thf(fact_906_equalityI,axiom,
! [A_16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_14: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_16 @ B_14 )
=> ( ( ord_le1805007862lt_o_o @ B_14 @ A_16 )
=> ( A_16 = B_14 ) ) ) ).
thf(fact_907_equalityI,axiom,
! [A_16: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_14: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_16 @ B_14 )
=> ( ( ord_le602483040lt_o_o @ B_14 @ A_16 )
=> ( A_16 = B_14 ) ) ) ).
thf(fact_908_equalityI,axiom,
! [A_16: produc1572197287le_alt > $o,B_14: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_16 @ B_14 )
=> ( ( ord_le962286258_alt_o @ B_14 @ A_16 )
=> ( A_16 = B_14 ) ) ) ).
thf(fact_909_equalityI,axiom,
! [A_16: arrow_1196572341e_indi > $o,B_14: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_16 @ B_14 )
=> ( ( ord_le865407012indi_o @ B_14 @ A_16 )
=> ( A_16 = B_14 ) ) ) ).
thf(fact_910_equalityI,axiom,
! [A_16: product_unit > $o,B_14: product_unit > $o] :
( ( ord_le1511552390unit_o @ A_16 @ B_14 )
=> ( ( ord_le1511552390unit_o @ B_14 @ A_16 )
=> ( A_16 = B_14 ) ) ) ).
thf(fact_911_equalityI,axiom,
! [A_16: nat > $o,B_14: nat > $o] :
( ( ord_less_eq_nat_o @ A_16 @ B_14 )
=> ( ( ord_less_eq_nat_o @ B_14 @ A_16 )
=> ( A_16 = B_14 ) ) ) ).
thf(fact_912_subsetD,axiom,
! [C_3: arrow_1196572341e_indi,A_15: arrow_1196572341e_indi > $o,B_13: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_15 @ B_13 )
=> ( ( member1818997282e_indi @ C_3 @ A_15 )
=> ( member1818997282e_indi @ C_3 @ B_13 ) ) ) ).
thf(fact_913_subsetD,axiom,
! [C_3: $o,A_15: $o > $o,B_13: $o > $o] :
( ( ord_less_eq_o_o @ A_15 @ B_13 )
=> ( ( member_o @ C_3 @ A_15 )
=> ( member_o @ C_3 @ B_13 ) ) ) ).
thf(fact_914_subsetD,axiom,
! [C_3: product_unit,A_15: product_unit > $o,B_13: product_unit > $o] :
( ( ord_le1511552390unit_o @ A_15 @ B_13 )
=> ( ( member_Product_unit @ C_3 @ A_15 )
=> ( member_Product_unit @ C_3 @ B_13 ) ) ) ).
thf(fact_915_subsetD,axiom,
! [C_3: produc1572197287le_alt,A_15: produc1572197287le_alt > $o,B_13: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_15 @ B_13 )
=> ( ( member285112084le_alt @ C_3 @ A_15 )
=> ( member285112084le_alt @ C_3 @ B_13 ) ) ) ).
thf(fact_916_subsetD,axiom,
! [C_3: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_15: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_13: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_15 @ B_13 )
=> ( ( member822980838_alt_o @ C_3 @ A_15 )
=> ( member822980838_alt_o @ C_3 @ B_13 ) ) ) ).
thf(fact_917_subsetD,axiom,
! [C_3: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_15: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_13: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_15 @ B_13 )
=> ( ( member1425217232_alt_o @ C_3 @ A_15 )
=> ( member1425217232_alt_o @ C_3 @ B_13 ) ) ) ).
thf(fact_918_subsetD,axiom,
! [C_3: produc1572197287le_alt > $o,A_15: ( produc1572197287le_alt > $o ) > $o,B_13: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_15 @ B_13 )
=> ( ( member1241905979_alt_o @ C_3 @ A_15 )
=> ( member1241905979_alt_o @ C_3 @ B_13 ) ) ) ).
thf(fact_919_subsetD,axiom,
! [C_3: nat,A_15: nat > $o,B_13: nat > $o] :
( ( ord_less_eq_nat_o @ A_15 @ B_13 )
=> ( ( member_nat @ C_3 @ A_15 )
=> ( member_nat @ C_3 @ B_13 ) ) ) ).
thf(fact_920_psubset__eq,axiom,
! [A_14: product_unit > $o,B_12: product_unit > $o] :
( ( ord_le232288914unit_o @ A_14 @ B_12 )
<=> ( ( ord_le1511552390unit_o @ A_14 @ B_12 )
& ( A_14 != B_12 ) ) ) ).
thf(fact_921_psubset__eq,axiom,
! [A_14: arrow_1196572341e_indi > $o,B_12: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ A_14 @ B_12 )
<=> ( ( ord_le865407012indi_o @ A_14 @ B_12 )
& ( A_14 != B_12 ) ) ) ).
thf(fact_922_psubset__eq,axiom,
! [A_14: ( produc1572197287le_alt > $o ) > $o,B_12: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ A_14 @ B_12 )
<=> ( ( ord_le1027220427lt_o_o @ A_14 @ B_12 )
& ( A_14 != B_12 ) ) ) ).
thf(fact_923_psubset__eq,axiom,
! [A_14: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_12: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ A_14 @ B_12 )
<=> ( ( ord_le1805007862lt_o_o @ A_14 @ B_12 )
& ( A_14 != B_12 ) ) ) ).
thf(fact_924_psubset__eq,axiom,
! [A_14: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_12: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ A_14 @ B_12 )
<=> ( ( ord_le602483040lt_o_o @ A_14 @ B_12 )
& ( A_14 != B_12 ) ) ) ).
thf(fact_925_psubset__eq,axiom,
! [A_14: produc1572197287le_alt > $o,B_12: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ A_14 @ B_12 )
<=> ( ( ord_le962286258_alt_o @ A_14 @ B_12 )
& ( A_14 != B_12 ) ) ) ).
thf(fact_926_psubset__eq,axiom,
! [A_14: nat > $o,B_12: nat > $o] :
( ( ord_less_nat_o @ A_14 @ B_12 )
<=> ( ( ord_less_eq_nat_o @ A_14 @ B_12 )
& ( A_14 != B_12 ) ) ) ).
thf(fact_927_subset__iff__psubset__eq,axiom,
! [A_13: product_unit > $o,B_11: product_unit > $o] :
( ( ord_le1511552390unit_o @ A_13 @ B_11 )
<=> ( ( ord_le232288914unit_o @ A_13 @ B_11 )
| ( A_13 = B_11 ) ) ) ).
thf(fact_928_subset__iff__psubset__eq,axiom,
! [A_13: arrow_1196572341e_indi > $o,B_11: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_13 @ B_11 )
<=> ( ( ord_le1991507760indi_o @ A_13 @ B_11 )
| ( A_13 = B_11 ) ) ) ).
thf(fact_929_subset__iff__psubset__eq,axiom,
! [A_13: ( produc1572197287le_alt > $o ) > $o,B_11: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_13 @ B_11 )
<=> ( ( ord_le874404799lt_o_o @ A_13 @ B_11 )
| ( A_13 = B_11 ) ) ) ).
thf(fact_930_subset__iff__psubset__eq,axiom,
! [A_13: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_11: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_13 @ B_11 )
<=> ( ( ord_le1382328578lt_o_o @ A_13 @ B_11 )
| ( A_13 = B_11 ) ) ) ).
thf(fact_931_subset__iff__psubset__eq,axiom,
! [A_13: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_11: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_13 @ B_11 )
<=> ( ( ord_le914873172lt_o_o @ A_13 @ B_11 )
| ( A_13 = B_11 ) ) ) ).
thf(fact_932_subset__iff__psubset__eq,axiom,
! [A_13: produc1572197287le_alt > $o,B_11: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_13 @ B_11 )
<=> ( ( ord_le1852932542_alt_o @ A_13 @ B_11 )
| ( A_13 = B_11 ) ) ) ).
thf(fact_933_subset__iff__psubset__eq,axiom,
! [A_13: nat > $o,B_11: nat > $o] :
( ( ord_less_eq_nat_o @ A_13 @ B_11 )
<=> ( ( ord_less_nat_o @ A_13 @ B_11 )
| ( A_13 = B_11 ) ) ) ).
thf(fact_934_psubset__imp__subset,axiom,
! [A_12: product_unit > $o,B_10: product_unit > $o] :
( ( ord_le232288914unit_o @ A_12 @ B_10 )
=> ( ord_le1511552390unit_o @ A_12 @ B_10 ) ) ).
thf(fact_935_psubset__imp__subset,axiom,
! [A_12: arrow_1196572341e_indi > $o,B_10: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ A_12 @ B_10 )
=> ( ord_le865407012indi_o @ A_12 @ B_10 ) ) ).
thf(fact_936_psubset__imp__subset,axiom,
! [A_12: ( produc1572197287le_alt > $o ) > $o,B_10: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ A_12 @ B_10 )
=> ( ord_le1027220427lt_o_o @ A_12 @ B_10 ) ) ).
thf(fact_937_psubset__imp__subset,axiom,
! [A_12: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_10: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ A_12 @ B_10 )
=> ( ord_le1805007862lt_o_o @ A_12 @ B_10 ) ) ).
thf(fact_938_psubset__imp__subset,axiom,
! [A_12: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_10: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ A_12 @ B_10 )
=> ( ord_le602483040lt_o_o @ A_12 @ B_10 ) ) ).
thf(fact_939_psubset__imp__subset,axiom,
! [A_12: produc1572197287le_alt > $o,B_10: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ A_12 @ B_10 )
=> ( ord_le962286258_alt_o @ A_12 @ B_10 ) ) ).
thf(fact_940_psubset__imp__subset,axiom,
! [A_12: nat > $o,B_10: nat > $o] :
( ( ord_less_nat_o @ A_12 @ B_10 )
=> ( ord_less_eq_nat_o @ A_12 @ B_10 ) ) ).
thf(fact_941_psubset__subset__trans,axiom,
! [C_2: product_unit > $o,A_11: product_unit > $o,B_9: product_unit > $o] :
( ( ord_le232288914unit_o @ A_11 @ B_9 )
=> ( ( ord_le1511552390unit_o @ B_9 @ C_2 )
=> ( ord_le232288914unit_o @ A_11 @ C_2 ) ) ) ).
thf(fact_942_psubset__subset__trans,axiom,
! [C_2: arrow_1196572341e_indi > $o,A_11: arrow_1196572341e_indi > $o,B_9: arrow_1196572341e_indi > $o] :
( ( ord_le1991507760indi_o @ A_11 @ B_9 )
=> ( ( ord_le865407012indi_o @ B_9 @ C_2 )
=> ( ord_le1991507760indi_o @ A_11 @ C_2 ) ) ) ).
thf(fact_943_psubset__subset__trans,axiom,
! [C_2: ( produc1572197287le_alt > $o ) > $o,A_11: ( produc1572197287le_alt > $o ) > $o,B_9: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le874404799lt_o_o @ A_11 @ B_9 )
=> ( ( ord_le1027220427lt_o_o @ B_9 @ C_2 )
=> ( ord_le874404799lt_o_o @ A_11 @ C_2 ) ) ) ).
thf(fact_944_psubset__subset__trans,axiom,
! [C_2: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_11: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_9: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1382328578lt_o_o @ A_11 @ B_9 )
=> ( ( ord_le1805007862lt_o_o @ B_9 @ C_2 )
=> ( ord_le1382328578lt_o_o @ A_11 @ C_2 ) ) ) ).
thf(fact_945_psubset__subset__trans,axiom,
! [C_2: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_11: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_9: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le914873172lt_o_o @ A_11 @ B_9 )
=> ( ( ord_le602483040lt_o_o @ B_9 @ C_2 )
=> ( ord_le914873172lt_o_o @ A_11 @ C_2 ) ) ) ).
thf(fact_946_psubset__subset__trans,axiom,
! [C_2: produc1572197287le_alt > $o,A_11: produc1572197287le_alt > $o,B_9: produc1572197287le_alt > $o] :
( ( ord_le1852932542_alt_o @ A_11 @ B_9 )
=> ( ( ord_le962286258_alt_o @ B_9 @ C_2 )
=> ( ord_le1852932542_alt_o @ A_11 @ C_2 ) ) ) ).
thf(fact_947_psubset__subset__trans,axiom,
! [C_2: nat > $o,A_11: nat > $o,B_9: nat > $o] :
( ( ord_less_nat_o @ A_11 @ B_9 )
=> ( ( ord_less_eq_nat_o @ B_9 @ C_2 )
=> ( ord_less_nat_o @ A_11 @ C_2 ) ) ) ).
thf(fact_948_subset__psubset__trans,axiom,
! [C_1: ( produc1572197287le_alt > $o ) > $o,A_10: ( produc1572197287le_alt > $o ) > $o,B_8: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_10 @ B_8 )
=> ( ( ord_le874404799lt_o_o @ B_8 @ C_1 )
=> ( ord_le874404799lt_o_o @ A_10 @ C_1 ) ) ) ).
thf(fact_949_subset__psubset__trans,axiom,
! [C_1: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,A_10: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_8: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_10 @ B_8 )
=> ( ( ord_le1382328578lt_o_o @ B_8 @ C_1 )
=> ( ord_le1382328578lt_o_o @ A_10 @ C_1 ) ) ) ).
thf(fact_950_subset__psubset__trans,axiom,
! [C_1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,A_10: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_8: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_10 @ B_8 )
=> ( ( ord_le914873172lt_o_o @ B_8 @ C_1 )
=> ( ord_le914873172lt_o_o @ A_10 @ C_1 ) ) ) ).
thf(fact_951_subset__psubset__trans,axiom,
! [C_1: produc1572197287le_alt > $o,A_10: produc1572197287le_alt > $o,B_8: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_10 @ B_8 )
=> ( ( ord_le1852932542_alt_o @ B_8 @ C_1 )
=> ( ord_le1852932542_alt_o @ A_10 @ C_1 ) ) ) ).
thf(fact_952_subset__psubset__trans,axiom,
! [C_1: nat > $o,A_10: nat > $o,B_8: nat > $o] :
( ( ord_less_eq_nat_o @ A_10 @ B_8 )
=> ( ( ord_less_nat_o @ B_8 @ C_1 )
=> ( ord_less_nat_o @ A_10 @ C_1 ) ) ) ).
thf(fact_953_equalityE,axiom,
! [A_9: nat > $o,B_7: nat > $o] :
( ( A_9 = B_7 )
=> ~ ( ( ord_less_eq_nat_o @ A_9 @ B_7 )
=> ~ ( ord_less_eq_nat_o @ B_7 @ A_9 ) ) ) ).
thf(fact_954_subset__trans,axiom,
! [C: nat > $o,A_8: nat > $o,B_6: nat > $o] :
( ( ord_less_eq_nat_o @ A_8 @ B_6 )
=> ( ( ord_less_eq_nat_o @ B_6 @ C )
=> ( ord_less_eq_nat_o @ A_8 @ C ) ) ) ).
thf(fact_955_set__mp,axiom,
! [X_6: nat,A_7: nat > $o,B_5: nat > $o] :
( ( ord_less_eq_nat_o @ A_7 @ B_5 )
=> ( ( member_nat @ X_6 @ A_7 )
=> ( member_nat @ X_6 @ B_5 ) ) ) ).
thf(fact_956_set__mp,axiom,
! [X_6: produc1572197287le_alt > $o,A_7: ( produc1572197287le_alt > $o ) > $o,B_5: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_7 @ B_5 )
=> ( ( member1241905979_alt_o @ X_6 @ A_7 )
=> ( member1241905979_alt_o @ X_6 @ B_5 ) ) ) ).
thf(fact_957_set__mp,axiom,
! [X_6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_7: ( ( 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_7 @ B_5 )
=> ( ( member1425217232_alt_o @ X_6 @ A_7 )
=> ( member1425217232_alt_o @ X_6 @ B_5 ) ) ) ).
thf(fact_958_set__mp,axiom,
! [X_6: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_7: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_7 @ B_5 )
=> ( ( member822980838_alt_o @ X_6 @ A_7 )
=> ( member822980838_alt_o @ X_6 @ B_5 ) ) ) ).
thf(fact_959_set__mp,axiom,
! [X_6: produc1572197287le_alt,A_7: produc1572197287le_alt > $o,B_5: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_7 @ B_5 )
=> ( ( member285112084le_alt @ X_6 @ A_7 )
=> ( member285112084le_alt @ X_6 @ B_5 ) ) ) ).
thf(fact_960_set__rev__mp,axiom,
! [B_4: nat > $o,X_5: nat,A_6: nat > $o] :
( ( member_nat @ X_5 @ A_6 )
=> ( ( ord_less_eq_nat_o @ A_6 @ B_4 )
=> ( member_nat @ X_5 @ B_4 ) ) ) ).
thf(fact_961_set__rev__mp,axiom,
! [B_4: ( produc1572197287le_alt > $o ) > $o,X_5: produc1572197287le_alt > $o,A_6: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ X_5 @ A_6 )
=> ( ( ord_le1027220427lt_o_o @ A_6 @ B_4 )
=> ( member1241905979_alt_o @ X_5 @ B_4 ) ) ) ).
thf(fact_962_set__rev__mp,axiom,
! [B_4: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,X_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_6: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( member1425217232_alt_o @ X_5 @ A_6 )
=> ( ( ord_le1805007862lt_o_o @ A_6 @ B_4 )
=> ( member1425217232_alt_o @ X_5 @ B_4 ) ) ) ).
thf(fact_963_set__rev__mp,axiom,
! [B_4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X_5: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X_5 @ A_6 )
=> ( ( ord_le602483040lt_o_o @ A_6 @ B_4 )
=> ( member822980838_alt_o @ X_5 @ B_4 ) ) ) ).
thf(fact_964_set__rev__mp,axiom,
! [B_4: produc1572197287le_alt > $o,X_5: produc1572197287le_alt,A_6: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X_5 @ A_6 )
=> ( ( ord_le962286258_alt_o @ A_6 @ B_4 )
=> ( member285112084le_alt @ X_5 @ B_4 ) ) ) ).
thf(fact_965_predicate1D,axiom,
! [X_4: nat,P_2: nat > $o,Q_1: nat > $o] :
( ( ord_less_eq_nat_o @ P_2 @ Q_1 )
=> ( ( P_2 @ X_4 )
=> ( Q_1 @ X_4 ) ) ) ).
thf(fact_966_in__mono,axiom,
! [X_3: nat,A_5: nat > $o,B_3: nat > $o] :
( ( ord_less_eq_nat_o @ A_5 @ B_3 )
=> ( ( member_nat @ X_3 @ A_5 )
=> ( member_nat @ X_3 @ B_3 ) ) ) ).
thf(fact_967_in__mono,axiom,
! [X_3: produc1572197287le_alt > $o,A_5: ( produc1572197287le_alt > $o ) > $o,B_3: ( produc1572197287le_alt > $o ) > $o] :
( ( ord_le1027220427lt_o_o @ A_5 @ B_3 )
=> ( ( member1241905979_alt_o @ X_3 @ A_5 )
=> ( member1241905979_alt_o @ X_3 @ B_3 ) ) ) ).
thf(fact_968_in__mono,axiom,
! [X_3: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o,A_5: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o,B_3: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o] :
( ( ord_le1805007862lt_o_o @ A_5 @ B_3 )
=> ( ( member1425217232_alt_o @ X_3 @ A_5 )
=> ( member1425217232_alt_o @ X_3 @ B_3 ) ) ) ).
thf(fact_969_in__mono,axiom,
! [X_3: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_5: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_3: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_5 @ B_3 )
=> ( ( member822980838_alt_o @ X_3 @ A_5 )
=> ( member822980838_alt_o @ X_3 @ B_3 ) ) ) ).
thf(fact_970_in__mono,axiom,
! [X_3: produc1572197287le_alt,A_5: produc1572197287le_alt > $o,B_3: produc1572197287le_alt > $o] :
( ( ord_le962286258_alt_o @ A_5 @ B_3 )
=> ( ( member285112084le_alt @ X_3 @ A_5 )
=> ( member285112084le_alt @ X_3 @ B_3 ) ) ) ).
thf(fact_971_equalityD2,axiom,
! [A_4: nat > $o,B_2: nat > $o] :
( ( A_4 = B_2 )
=> ( ord_less_eq_nat_o @ B_2 @ A_4 ) ) ).
thf(fact_972_equalityD1,axiom,
! [A_3: nat > $o,B_1: nat > $o] :
( ( A_3 = B_1 )
=> ( ord_less_eq_nat_o @ A_3 @ B_1 ) ) ).
thf(fact_973_rev__predicate1D,axiom,
! [Q: nat > $o,P_1: nat > $o,X_2: nat] :
( ( P_1 @ X_2 )
=> ( ( ord_less_eq_nat_o @ P_1 @ Q )
=> ( Q @ X_2 ) ) ) ).
thf(fact_974_set__eq__subset,axiom,
! [A_2: nat > $o,B: nat > $o] :
( ( A_2 = B )
<=> ( ( ord_less_eq_nat_o @ A_2 @ B )
& ( ord_less_eq_nat_o @ B @ A_2 ) ) ) ).
thf(fact_975_subset__refl,axiom,
! [A_1: nat > $o] : ( ord_less_eq_nat_o @ A_1 @ A_1 ) ).
thf(fact_976_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_977_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_978_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_979_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_980_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_981_less__not__refl,axiom,
! [N_1: nat] :
~ ( ord_less_nat @ N_1 @ N_1 ) ).
thf(fact_982_nat__neq__iff,axiom,
! [M_1: nat,N_1: nat] :
( ( M_1 != N_1 )
<=> ( ( ord_less_nat @ M_1 @ N_1 )
| ( ord_less_nat @ N_1 @ M_1 ) ) ) ).
thf(fact_983_linorder__neqE__nat,axiom,
! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ) ).
thf(fact_984_less__irrefl__nat,axiom,
! [N_1: nat] :
~ ( ord_less_nat @ N_1 @ N_1 ) ).
thf(fact_985_less__not__refl2,axiom,
! [N_1: nat,M_1: nat] :
( ( ord_less_nat @ N_1 @ M_1 )
=> ( M_1 != N_1 ) ) ).
thf(fact_986_less__not__refl3,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) ).
thf(fact_987_nat__less__cases,axiom,
! [P: nat > nat > $o,M_1: nat,N_1: nat] :
( ( ( ord_less_nat @ M_1 @ N_1 )
=> ( P @ N_1 @ M_1 ) )
=> ( ( ( M_1 = N_1 )
=> ( P @ N_1 @ M_1 ) )
=> ( ( ( ord_less_nat @ N_1 @ M_1 )
=> ( P @ N_1 @ M_1 ) )
=> ( P @ N_1 @ M_1 ) ) ) ) ).
thf(fact_988_nat__add__commute,axiom,
! [M_1: nat,N_1: nat] :
( ( plus_plus_nat @ M_1 @ N_1 )
= ( plus_plus_nat @ N_1 @ M_1 ) ) ).
thf(fact_989_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_990_nat__add__assoc,axiom,
! [M_1: nat,N_1: nat,K: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ M_1 @ N_1 ) @ K )
= ( plus_plus_nat @ M_1 @ ( plus_plus_nat @ N_1 @ K ) ) ) ).
thf(fact_991_nat__add__left__cancel,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ( plus_plus_nat @ K @ M_1 )
= ( plus_plus_nat @ K @ N_1 ) )
<=> ( M_1 = N_1 ) ) ).
thf(fact_992_nat__add__right__cancel,axiom,
! [M_1: nat,K: nat,N_1: nat] :
( ( ( plus_plus_nat @ M_1 @ K )
= ( plus_plus_nat @ N_1 @ K ) )
<=> ( M_1 = N_1 ) ) ).
thf(fact_993_le__refl,axiom,
! [N_1: nat] : ( ord_less_eq_nat @ N_1 @ N_1 ) ).
thf(fact_994_nat__le__linear,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ N_1 )
| ( ord_less_eq_nat @ N_1 @ M_1 ) ) ).
thf(fact_995_eq__imp__le,axiom,
! [M_1: nat,N_1: nat] :
( ( M_1 = N_1 )
=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ).
thf(fact_996_le__trans,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I @ K ) ) ) ).
thf(fact_997_le__antisym,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ N_1 )
=> ( ( ord_less_eq_nat @ N_1 @ M_1 )
=> ( M_1 = N_1 ) ) ) ).
thf(fact_998_inj__on__add__nat,axiom,
! [K: nat,N_2: nat > $o] :
( inj_on_nat_nat
@ ^ [N: nat] : ( plus_plus_nat @ N @ K )
@ N_2 ) ).
thf(fact_999_not__add__less1,axiom,
! [I: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
thf(fact_1000_not__add__less2,axiom,
! [J: nat,I: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
thf(fact_1001_nat__add__left__cancel__less,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M_1 ) @ ( plus_plus_nat @ K @ N_1 ) )
<=> ( ord_less_nat @ M_1 @ N_1 ) ) ).
thf(fact_1002_trans__less__add1,axiom,
! [M_1: nat,I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M_1 ) ) ) ).
thf(fact_1003_trans__less__add2,axiom,
! [M_1: nat,I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ M_1 @ J ) ) ) ).
thf(fact_1004_add__less__mono1,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
thf(fact_1005_add__less__mono,axiom,
! [K: nat,L: nat,I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
thf(fact_1006_less__add__eq__less,axiom,
! [M_1: nat,N_1: nat,K: nat,L: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M_1 @ L )
= ( plus_plus_nat @ K @ N_1 ) )
=> ( ord_less_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1007_add__lessD1,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
=> ( ord_less_nat @ I @ K ) ) ).
thf(fact_1008_nat__less__le,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
<=> ( ( ord_less_eq_nat @ M_1 @ N_1 )
& ( M_1 != N_1 ) ) ) ).
thf(fact_1009_le__eq__less__or__eq,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ N_1 )
<=> ( ( ord_less_nat @ M_1 @ N_1 )
| ( M_1 = N_1 ) ) ) ).
thf(fact_1010_less__imp__le__nat,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ).
thf(fact_1011_le__neq__implies__less,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ N_1 )
=> ( ( M_1 != N_1 )
=> ( ord_less_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1012_less__or__eq__imp__le,axiom,
! [M_1: nat,N_1: nat] :
( ( ( ord_less_nat @ M_1 @ N_1 )
| ( M_1 = N_1 ) )
=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ).
thf(fact_1013_le__add2,axiom,
! [N_1: nat,M_1: nat] : ( ord_less_eq_nat @ N_1 @ ( plus_plus_nat @ M_1 @ N_1 ) ) ).
thf(fact_1014_le__add1,axiom,
! [N_1: nat,M_1: nat] : ( ord_less_eq_nat @ N_1 @ ( plus_plus_nat @ N_1 @ M_1 ) ) ).
thf(fact_1015_le__iff__add,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ N_1 )
<=> ? [K_1: nat] :
( N_1
= ( plus_plus_nat @ M_1 @ K_1 ) ) ) ).
thf(fact_1016_nat__add__left__cancel__le,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M_1 ) @ ( plus_plus_nat @ K @ N_1 ) )
<=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ).
thf(fact_1017_trans__le__add1,axiom,
! [M_1: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M_1 ) ) ) ).
thf(fact_1018_trans__le__add2,axiom,
! [M_1: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M_1 @ J ) ) ) ).
thf(fact_1019_add__le__mono1,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
thf(fact_1020_add__le__mono,axiom,
! [K: nat,L: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
thf(fact_1021_add__leD2,axiom,
! [M_1: nat,K: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M_1 @ K ) @ N_1 )
=> ( ord_less_eq_nat @ K @ N_1 ) ) ).
thf(fact_1022_add__leD1,axiom,
! [M_1: nat,K: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M_1 @ K ) @ N_1 )
=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ).
thf(fact_1023_mono__nat__linear__lb,axiom,
! [M_1: nat,K: nat,F: nat > nat] :
( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( F @ M ) @ ( F @ N ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M_1 ) @ K ) @ ( F @ ( plus_plus_nat @ M_1 @ K ) ) ) ) ).
thf(fact_1024_less__mono__imp__le__mono,axiom,
! [I: nat,J: nat,F: nat > nat] :
( ! [I_1: nat,J_1: nat] :
( ( ord_less_nat @ I_1 @ J_1 )
=> ( ord_less_nat @ ( F @ I_1 ) @ ( F @ J_1 ) ) )
=> ( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
thf(fact_1025_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_1026_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_1027_termination__basic__simps_I5_J,axiom,
! [X: nat,Y: nat] :
( ( ord_less_nat @ X @ Y )
=> ( ord_less_eq_nat @ X @ Y ) ) ).
thf(fact_1028_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_1029_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_1030_linear__alt,axiom,
? [L_1: produc1572197287le_alt > $o] : ( member1241905979_alt_o @ L_1 @ arrow_1982173296le_Lin ) ).
thf(fact_1031_finite__indi,axiom,
finite431949602e_indi @ top_to54564308indi_o ).
thf(fact_1032_finite__Collect__le__nat,axiom,
! [K: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
thf(fact_1033_finite__Collect__less__nat,axiom,
! [K: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
thf(fact_1034_infinite__UNIV__nat,axiom,
~ ( finite_finite_nat @ top_top_nat_o ) ).
thf(fact_1035_card__UNIV__unit,axiom,
( ( finite1949902593t_unit @ top_to1984820022unit_o )
= one_one_nat ) ).
thf(fact_1036_card__Collect__less__nat,axiom,
! [N_1: nat] :
( ( finite_card_nat
@ ( collect_nat
@ ^ [I_1: nat] : ( ord_less_nat @ I_1 @ N_1 ) ) )
= N_1 ) ).
thf(fact_1037_finite__M__bounded__by__nat,axiom,
! [P: nat > $o,I: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [K_1: nat] : ( (&) @ ( P @ K_1 ) @ ( ord_less_nat @ K_1 @ I ) ) ) ) ).
thf(fact_1038_finite__nat__set__iff__bounded__le,axiom,
! [N_2: nat > $o] :
( ( finite_finite_nat @ N_2 )
<=> ? [M: nat] :
! [X_1: nat] :
( ( member_nat @ X_1 @ N_2 )
=> ( ord_less_eq_nat @ X_1 @ M ) ) ) ).
thf(fact_1039_finite__nat__set__iff__bounded,axiom,
! [N_2: nat > $o] :
( ( finite_finite_nat @ N_2 )
<=> ? [M: nat] :
! [X_1: nat] :
( ( member_nat @ X_1 @ N_2 )
=> ( ord_less_nat @ X_1 @ M ) ) ) ).
thf(fact_1040_finite__less__ub,axiom,
! [U: nat,F: nat > nat] :
( ! [N: nat] : ( ord_less_eq_nat @ N @ ( F @ N ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
thf(fact_1041_bounded__nat__set__is__finite,axiom,
! [N_1: nat,N_2: nat > $o] :
( ! [X_1: nat] :
( ( member_nat @ X_1 @ N_2 )
=> ( ord_less_nat @ X_1 @ N_1 ) )
=> ( finite_finite_nat @ N_2 ) ) ).
thf(fact_1042_less__zeroE,axiom,
! [N_1: nat] :
~ ( ord_less_nat @ N_1 @ zero_zero_nat ) ).
thf(fact_1043_le0,axiom,
! [N_1: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N_1 ) ).
thf(fact_1044_not__less0,axiom,
! [N_1: nat] :
~ ( ord_less_nat @ N_1 @ zero_zero_nat ) ).
thf(fact_1045_neq0__conv,axiom,
! [N_1: nat] :
( ( N_1 != zero_zero_nat )
<=> ( ord_less_nat @ zero_zero_nat @ N_1 ) ) ).
thf(fact_1046_less__nat__zero__code,axiom,
! [N_1: nat] :
~ ( ord_less_nat @ N_1 @ zero_zero_nat ) ).
thf(fact_1047_gr__implies__not0,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
=> ( N_1 != zero_zero_nat ) ) ).
thf(fact_1048_gr0I,axiom,
! [N_1: nat] :
( ( N_1 != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N_1 ) ) ).
thf(fact_1049_plus__nat_Oadd__0,axiom,
! [N_1: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N_1 )
= N_1 ) ).
thf(fact_1050_Nat_Oadd__0__right,axiom,
! [M_1: nat] :
( ( plus_plus_nat @ M_1 @ zero_zero_nat )
= M_1 ) ).
thf(fact_1051_add__is__0,axiom,
! [M_1: nat,N_1: nat] :
( ( ( plus_plus_nat @ M_1 @ N_1 )
= zero_zero_nat )
<=> ( ( M_1 = zero_zero_nat )
& ( N_1 = zero_zero_nat ) ) ) ).
thf(fact_1052_add__eq__self__zero,axiom,
! [M_1: nat,N_1: nat] :
( ( ( plus_plus_nat @ M_1 @ N_1 )
= M_1 )
=> ( N_1 = zero_zero_nat ) ) ).
thf(fact_1053_le__0__eq,axiom,
! [N_1: nat] :
( ( ord_less_eq_nat @ N_1 @ zero_zero_nat )
<=> ( N_1 = zero_zero_nat ) ) ).
thf(fact_1054_less__eq__nat_Osimps_I1_J,axiom,
! [N_1: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N_1 ) ).
thf(fact_1055_add__gr__0,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M_1 @ N_1 ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ M_1 )
| ( ord_less_nat @ zero_zero_nat @ N_1 ) ) ) ).
thf(fact_1056_ex__least__nat__less,axiom,
! [N_1: nat,P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ( P @ N_1 )
=> ? [K_1: nat] :
( ( ord_less_nat @ K_1 @ N_1 )
& ! [I_1: nat] :
( ( ord_less_eq_nat @ I_1 @ K_1 )
=> ~ ( P @ I_1 ) )
& ( P @ ( plus_plus_nat @ K_1 @ one_one_nat ) ) ) ) ) ).
thf(fact_1057_ex__least__nat__le,axiom,
! [N_1: nat,P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ( P @ N_1 )
=> ? [K_1: nat] :
( ( ord_less_eq_nat @ K_1 @ N_1 )
& ! [I_1: nat] :
( ( ord_less_nat @ I_1 @ K_1 )
=> ~ ( P @ I_1 ) )
& ( P @ K_1 ) ) ) ) ).
thf(fact_1058_less__imp__add__positive,axiom,
! [I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ? [K_1: nat] :
( ( ord_less_nat @ zero_zero_nat @ K_1 )
& ( ( plus_plus_nat @ I @ K_1 )
= J ) ) ) ).
thf(fact_1059_lessI,axiom,
! [N_1: nat] : ( ord_less_nat @ N_1 @ ( suc @ N_1 ) ) ).
thf(fact_1060_Suc__mono,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
=> ( ord_less_nat @ ( suc @ M_1 ) @ ( suc @ N_1 ) ) ) ).
thf(fact_1061_zero__less__Suc,axiom,
! [N_1: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N_1 ) ) ).
thf(fact_1062_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
thf(fact_1063_nat_Oinject,axiom,
! [Nat: nat,Nat_2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat_2 ) )
<=> ( Nat = Nat_2 ) ) ).
thf(fact_1064_Suc__n__not__n,axiom,
! [N_1: nat] :
( ( suc @ N_1 )
!= N_1 ) ).
thf(fact_1065_n__not__Suc__n,axiom,
! [N_1: nat] :
( N_1
!= ( suc @ N_1 ) ) ).
thf(fact_1066_Suc__neq__Zero,axiom,
! [M_1: nat] :
( ( suc @ M_1 )
!= zero_zero_nat ) ).
thf(fact_1067_Zero__neq__Suc,axiom,
! [M_1: nat] :
( zero_zero_nat
!= ( suc @ M_1 ) ) ).
thf(fact_1068_nat_Osimps_I3_J,axiom,
! [Nat_3: nat] :
( ( suc @ Nat_3 )
!= zero_zero_nat ) ).
thf(fact_1069_Suc__not__Zero,axiom,
! [M_1: nat] :
( ( suc @ M_1 )
!= zero_zero_nat ) ).
thf(fact_1070_nat_Osimps_I2_J,axiom,
! [Nat_2: nat] :
( zero_zero_nat
!= ( suc @ Nat_2 ) ) ).
thf(fact_1071_Zero__not__Suc,axiom,
! [M_1: nat] :
( zero_zero_nat
!= ( suc @ M_1 ) ) ).
thf(fact_1072_Suc__less__SucD,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( suc @ M_1 ) @ ( suc @ N_1 ) )
=> ( ord_less_nat @ M_1 @ N_1 ) ) ).
thf(fact_1073_Suc__lessD,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( suc @ M_1 ) @ N_1 )
=> ( ord_less_nat @ M_1 @ N_1 ) ) ).
thf(fact_1074_less__SucE,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ ( suc @ N_1 ) )
=> ( ~ ( ord_less_nat @ M_1 @ N_1 )
=> ( M_1 = N_1 ) ) ) ).
thf(fact_1075_less__trans__Suc,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
thf(fact_1076_Suc__lessI,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
=> ( ( ( suc @ M_1 )
!= N_1 )
=> ( ord_less_nat @ ( suc @ M_1 ) @ N_1 ) ) ) ).
thf(fact_1077_less__SucI,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
=> ( ord_less_nat @ M_1 @ ( suc @ N_1 ) ) ) ).
thf(fact_1078_less__antisym,axiom,
! [N_1: nat,M_1: nat] :
( ~ ( ord_less_nat @ N_1 @ M_1 )
=> ( ( ord_less_nat @ N_1 @ ( suc @ M_1 ) )
=> ( M_1 = N_1 ) ) ) ).
thf(fact_1079_not__less__less__Suc__eq,axiom,
! [N_1: nat,M_1: nat] :
( ~ ( ord_less_nat @ N_1 @ M_1 )
=> ( ( ord_less_nat @ N_1 @ ( suc @ M_1 ) )
<=> ( N_1 = M_1 ) ) ) ).
thf(fact_1080_Suc__less__eq,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( suc @ M_1 ) @ ( suc @ N_1 ) )
<=> ( ord_less_nat @ M_1 @ N_1 ) ) ).
thf(fact_1081_less__Suc__eq,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ ( suc @ N_1 ) )
<=> ( ( ord_less_nat @ M_1 @ N_1 )
| ( M_1 = N_1 ) ) ) ).
thf(fact_1082_not__less__eq,axiom,
! [M_1: nat,N_1: nat] :
( ~ ( ord_less_nat @ M_1 @ N_1 )
<=> ( ord_less_nat @ N_1 @ ( suc @ M_1 ) ) ) ).
thf(fact_1083_add__Suc__shift,axiom,
! [M_1: nat,N_1: nat] :
( ( plus_plus_nat @ ( suc @ M_1 ) @ N_1 )
= ( plus_plus_nat @ M_1 @ ( suc @ N_1 ) ) ) ).
thf(fact_1084_add__Suc,axiom,
! [M_1: nat,N_1: nat] :
( ( plus_plus_nat @ ( suc @ M_1 ) @ N_1 )
= ( suc @ ( plus_plus_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1085_add__Suc__right,axiom,
! [M_1: nat,N_1: nat] :
( ( plus_plus_nat @ M_1 @ ( suc @ N_1 ) )
= ( suc @ ( plus_plus_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1086_Suc__leD,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( suc @ M_1 ) @ N_1 )
=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ).
thf(fact_1087_le__SucE,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ ( suc @ N_1 ) )
=> ( ~ ( ord_less_eq_nat @ M_1 @ N_1 )
=> ( M_1
= ( suc @ N_1 ) ) ) ) ).
thf(fact_1088_le__SucI,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ N_1 )
=> ( ord_less_eq_nat @ M_1 @ ( suc @ N_1 ) ) ) ).
thf(fact_1089_Suc__le__mono,axiom,
! [N_1: nat,M_1: nat] :
( ( ord_less_eq_nat @ ( suc @ N_1 ) @ ( suc @ M_1 ) )
<=> ( ord_less_eq_nat @ N_1 @ M_1 ) ) ).
thf(fact_1090_le__Suc__eq,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ ( suc @ N_1 ) )
<=> ( ( ord_less_eq_nat @ M_1 @ N_1 )
| ( M_1
= ( suc @ N_1 ) ) ) ) ).
thf(fact_1091_not__less__eq__eq,axiom,
! [M_1: nat,N_1: nat] :
( ~ ( ord_less_eq_nat @ M_1 @ N_1 )
<=> ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_1 ) ) ).
thf(fact_1092_Suc__n__not__le__n,axiom,
! [N_1: nat] :
~ ( ord_less_eq_nat @ ( suc @ N_1 ) @ N_1 ) ).
thf(fact_1093_inj__Suc,axiom,
! [N_2: nat > $o] : ( inj_on_nat_nat @ suc @ N_2 ) ).
thf(fact_1094_gr0__conv__Suc,axiom,
! [N_1: nat] :
( ( ord_less_nat @ zero_zero_nat @ N_1 )
<=> ? [M: nat] :
( N_1
= ( suc @ M ) ) ) ).
thf(fact_1095_less__Suc0,axiom,
! [N_1: nat] :
( ( ord_less_nat @ N_1 @ ( suc @ zero_zero_nat ) )
<=> ( N_1 = zero_zero_nat ) ) ).
thf(fact_1096_less__Suc__eq__0__disj,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ ( suc @ N_1 ) )
<=> ( ( M_1 = zero_zero_nat )
| ? [J_1: nat] :
( ( M_1
= ( suc @ J_1 ) )
& ( ord_less_nat @ J_1 @ N_1 ) ) ) ) ).
thf(fact_1097_add__is__1,axiom,
! [M_1: nat,N_1: nat] :
( ( ( plus_plus_nat @ M_1 @ N_1 )
= ( suc @ zero_zero_nat ) )
<=> ( ( ( M_1
= ( suc @ zero_zero_nat ) )
& ( N_1 = zero_zero_nat ) )
| ( ( M_1 = zero_zero_nat )
& ( N_1
= ( suc @ zero_zero_nat ) ) ) ) ) ).
thf(fact_1098_one__is__add,axiom,
! [M_1: nat,N_1: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ M_1 @ N_1 ) )
<=> ( ( ( M_1
= ( suc @ zero_zero_nat ) )
& ( N_1 = zero_zero_nat ) )
| ( ( M_1 = zero_zero_nat )
& ( N_1
= ( suc @ zero_zero_nat ) ) ) ) ) ).
thf(fact_1099_less__add__Suc1,axiom,
! [I: nat,M_1: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M_1 ) ) ) ).
thf(fact_1100_less__add__Suc2,axiom,
! [I: nat,M_1: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M_1 @ I ) ) ) ).
thf(fact_1101_less__iff__Suc__add,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
<=> ? [K_1: nat] :
( N_1
= ( suc @ ( plus_plus_nat @ M_1 @ K_1 ) ) ) ) ).
thf(fact_1102_less__eq__Suc__le,axiom,
! [N_1: nat,M_1: nat] :
( ( ord_less_nat @ N_1 @ M_1 )
<=> ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_1 ) ) ).
thf(fact_1103_less__Suc__eq__le,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ ( suc @ N_1 ) )
<=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ).
thf(fact_1104_Suc__le__eq,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( suc @ M_1 ) @ N_1 )
<=> ( ord_less_nat @ M_1 @ N_1 ) ) ).
thf(fact_1105_le__imp__less__Suc,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ N_1 )
=> ( ord_less_nat @ M_1 @ ( suc @ N_1 ) ) ) ).
thf(fact_1106_Suc__leI,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
=> ( ord_less_eq_nat @ ( suc @ M_1 ) @ N_1 ) ) ).
thf(fact_1107_le__less__Suc__eq,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ M_1 @ N_1 )
=> ( ( ord_less_nat @ N_1 @ ( suc @ M_1 ) )
<=> ( N_1 = M_1 ) ) ) ).
thf(fact_1108_Suc__le__lessD,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( suc @ M_1 ) @ N_1 )
=> ( ord_less_nat @ M_1 @ N_1 ) ) ).
thf(fact_1109_One__nat__def,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ) ).
thf(fact_1110_less__eq__Suc__le__raw,axiom,
! [X_1: nat] :
( ( ord_less_nat @ X_1 )
= ( ord_less_eq_nat @ ( suc @ X_1 ) ) ) ).
thf(fact_1111_card__Collect__le__nat,axiom,
! [N_1: nat] :
( ( finite_card_nat
@ ( collect_nat
@ ^ [I_1: nat] : ( ord_less_eq_nat @ I_1 @ N_1 ) ) )
= ( suc @ N_1 ) ) ).
thf(fact_1112_card__less__Suc,axiom,
! [I: nat,M_3: nat > $o] :
( ( member_nat @ zero_zero_nat @ M_3 )
=> ( ( suc
@ ( finite_card_nat
@ ( collect_nat
@ ^ [K_1: nat] : ( (&) @ ( member_nat @ ( suc @ K_1 ) @ M_3 ) @ ( ord_less_nat @ K_1 @ I ) ) ) ) )
= ( finite_card_nat
@ ( collect_nat
@ ^ [K_1: nat] : ( (&) @ ( member_nat @ K_1 @ M_3 ) @ ( ord_less_nat @ K_1 @ ( suc @ I ) ) ) ) ) ) ) ).
thf(fact_1113_card__less,axiom,
! [I: nat,M_3: nat > $o] :
( ( member_nat @ zero_zero_nat @ M_3 )
=> ( ( finite_card_nat
@ ( collect_nat
@ ^ [K_1: nat] : ( (&) @ ( member_nat @ K_1 @ M_3 ) @ ( ord_less_nat @ K_1 @ ( suc @ I ) ) ) ) )
!= zero_zero_nat ) ) ).
thf(fact_1114_card__less__Suc2,axiom,
! [I: nat,M_3: nat > $o] :
( ~ ( member_nat @ zero_zero_nat @ M_3 )
=> ( ( finite_card_nat
@ ( collect_nat
@ ^ [K_1: nat] : ( (&) @ ( member_nat @ ( suc @ K_1 ) @ M_3 ) @ ( ord_less_nat @ K_1 @ I ) ) ) )
= ( finite_card_nat
@ ( collect_nat
@ ^ [K_1: nat] : ( (&) @ ( member_nat @ K_1 @ M_3 ) @ ( ord_less_nat @ K_1 @ ( suc @ I ) ) ) ) ) ) ) ).
thf(fact_1115_inc__induct,axiom,
! [P: nat > $o,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ J )
=> ( ! [I_1: nat] :
( ( ord_less_nat @ I_1 @ J )
=> ( ( P @ ( suc @ I_1 ) )
=> ( P @ I_1 ) ) )
=> ( P @ I ) ) ) ) ).
thf(fact_1116_less__imp__Suc__add,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ M_1 @ N_1 )
=> ? [K_1: nat] :
( N_1
= ( suc @ ( plus_plus_nat @ M_1 @ K_1 ) ) ) ) ).
thf(fact_1117_gr0__implies__Suc,axiom,
! [N_1: nat] :
( ( ord_less_nat @ zero_zero_nat @ N_1 )
=> ? [M: nat] :
( N_1
= ( suc @ M ) ) ) ).
thf(fact_1118_Suc__eq__plus1,axiom,
! [N_1: nat] :
( ( suc @ N_1 )
= ( plus_plus_nat @ N_1 @ one_one_nat ) ) ).
thf(fact_1119_Suc__eq__plus1__left,axiom,
! [N_1: nat] :
( ( suc @ N_1 )
= ( plus_plus_nat @ one_one_nat @ N_1 ) ) ).
thf(fact_1120_Suc__le__D,axiom,
! [N_1: nat,M_2: nat] :
( ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_2 )
=> ? [M: nat] :
( M_2
= ( suc @ M ) ) ) ).
thf(fact_1121_lessE,axiom,
! [I: nat,K: nat] :
( ( ord_less_nat @ I @ K )
=> ( ( K
!= ( suc @ I ) )
=> ~ ! [J_1: nat] :
( ( ord_less_nat @ I @ J_1 )
=> ( K
!= ( suc @ J_1 ) ) ) ) ) ).
thf(fact_1122_Suc__lessE,axiom,
! [I: nat,K: nat] :
( ( ord_less_nat @ ( suc @ I ) @ K )
=> ~ ! [J_1: nat] :
( ( ord_less_nat @ I @ J_1 )
=> ( K
!= ( suc @ J_1 ) ) ) ) ).
thf(fact_1123_not0__implies__Suc,axiom,
! [N_1: nat] :
( ( N_1 != zero_zero_nat )
=> ? [M: nat] :
( N_1
= ( suc @ M ) ) ) ).
thf(fact_1124_nat_Oexhaust,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat_1: nat] :
( Y
!= ( suc @ Nat_1 ) ) ) ).
thf(fact_1125_zero__induct,axiom,
! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N: nat] :
( ( P @ ( suc @ N ) )
=> ( P @ N ) )
=> ( P @ zero_zero_nat ) ) ) ).
thf(fact_1126_nat__induct,axiom,
! [N_1: nat,P: nat > $o] :
( ( P @ zero_zero_nat )
=> ( ! [N: nat] :
( ( P @ N )
=> ( P @ ( suc @ N ) ) )
=> ( P @ N_1 ) ) ) ).
thf(fact_1127_surjh,axiom,
( ( image_1011045538di_nat @ h @ top_to54564308indi_o )
= ( ord_at4362885an_nat @ zero_zero_nat @ ( finite2011930979e_indi @ top_to54564308indi_o ) ) ) ).
thf(fact_1128_finite__atLeastLessThan,axiom,
! [L: nat,U: nat] : ( finite_finite_nat @ ( ord_at4362885an_nat @ L @ U ) ) ).
thf(fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12,axiom,
~ ! [H: arrow_1196572341e_indi > nat] :
( ( inj_on1505595958di_nat @ H @ top_to54564308indi_o )
=> ( ( image_1011045538di_nat @ H @ top_to54564308indi_o )
!= ( ord_at4362885an_nat @ zero_zero_nat @ ( finite2011930979e_indi @ top_to54564308indi_o ) ) ) ) ).
thf(fact_1130_subset__card__intvl__is__intvl,axiom,
! [A: nat > $o,K: nat] :
( ( ord_less_eq_nat_o @ A @ ( ord_at4362885an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A ) ) ) )
=> ( A
= ( ord_at4362885an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A ) ) ) ) ) ).
thf(fact_1131_image__Suc__atLeastLessThan,axiom,
! [I: nat,J: nat] :
( ( image_nat_nat @ suc @ ( ord_at4362885an_nat @ I @ J ) )
= ( ord_at4362885an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
thf(fact_1132_image__add__atLeastLessThan,axiom,
! [K: nat,I: nat,J: nat] :
( ( image_nat_nat
@ ^ [N: nat] : ( plus_plus_nat @ N @ K )
@ ( ord_at4362885an_nat @ I @ J ) )
= ( ord_at4362885an_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
thf(fact_1133_all__nat__less__eq,axiom,
! [P: nat > $o,N_1: nat] :
( ! [M: nat] :
( ( ord_less_nat @ M @ N_1 )
=> ( P @ M ) )
<=> ! [X_1: nat] :
( ( member_nat @ X_1 @ ( ord_at4362885an_nat @ zero_zero_nat @ N_1 ) )
=> ( P @ X_1 ) ) ) ).
thf(fact_1134_ex__nat__less__eq,axiom,
! [P: nat > $o,N_1: nat] :
( ? [M: nat] :
( ( ord_less_nat @ M @ N_1 )
& ( P @ M ) )
<=> ? [X_1: nat] :
( ( member_nat @ X_1 @ ( ord_at4362885an_nat @ zero_zero_nat @ N_1 ) )
& ( P @ X_1 ) ) ) ).
thf(fact_1135_greaterThan__0,axiom,
( ( ord_greaterThan_nat @ zero_zero_nat )
= ( image_nat_nat @ suc @ top_top_nat_o ) ) ).
thf(fact_1136_less__eq__nat_Osimps_I2_J,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( suc @ M_1 ) @ N_1 )
<=> ( nat_case_o @ $false @ ( ord_less_eq_nat @ M_1 ) @ N_1 ) ) ).
thf(fact_1137_finite__greaterThanAtMost,axiom,
! [L: nat,U: nat] : ( finite_finite_nat @ ( ord_gr375877188st_nat @ L @ U ) ) ).
thf(fact_1138_finite__greaterThanLessThan,axiom,
! [L: nat,U: nat] : ( finite_finite_nat @ ( ord_gr660468384an_nat @ L @ U ) ) ).
thf(fact_1139_atLeastSucLessThan__greaterThanLessThan,axiom,
! [L: nat,U: nat] :
( ( ord_at4362885an_nat @ ( suc @ L ) @ U )
= ( ord_gr660468384an_nat @ L @ U ) ) ).
thf(fact_1140_le__square,axiom,
! [M_1: nat] : ( ord_less_eq_nat @ M_1 @ ( times_times_nat @ M_1 @ M_1 ) ) ).
thf(fact_1141_le__cube,axiom,
! [M_1: nat] : ( ord_less_eq_nat @ M_1 @ ( times_times_nat @ M_1 @ ( times_times_nat @ M_1 @ M_1 ) ) ) ).
thf(fact_1142_mult__le__mono1,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
thf(fact_1143_mult__le__mono2,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
thf(fact_1144_mult__le__mono,axiom,
! [K: nat,L: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
thf(fact_1145_nat__mult__eq__1__iff,axiom,
! [M_1: nat,N_1: nat] :
( ( ( times_times_nat @ M_1 @ N_1 )
= one_one_nat )
<=> ( ( M_1 = one_one_nat )
& ( N_1 = one_one_nat ) ) ) ).
thf(fact_1146_nat__mult__1__right,axiom,
! [N_1: nat] :
( ( times_times_nat @ N_1 @ one_one_nat )
= N_1 ) ).
thf(fact_1147_nat__1__eq__mult__iff,axiom,
! [M_1: nat,N_1: nat] :
( ( one_one_nat
= ( times_times_nat @ M_1 @ N_1 ) )
<=> ( ( M_1 = one_one_nat )
& ( N_1 = one_one_nat ) ) ) ).
thf(fact_1148_nat__mult__1,axiom,
! [N_1: nat] :
( ( times_times_nat @ one_one_nat @ N_1 )
= N_1 ) ).
thf(fact_1149_add__mult__distrib,axiom,
! [M_1: nat,N_1: nat,K: nat] :
( ( times_times_nat @ ( plus_plus_nat @ M_1 @ N_1 ) @ K )
= ( plus_plus_nat @ ( times_times_nat @ M_1 @ K ) @ ( times_times_nat @ N_1 @ K ) ) ) ).
thf(fact_1150_add__mult__distrib2,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( times_times_nat @ K @ ( plus_plus_nat @ M_1 @ N_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ K @ M_1 ) @ ( times_times_nat @ K @ N_1 ) ) ) ).
thf(fact_1151_Suc__mult__cancel1,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ( times_times_nat @ ( suc @ K ) @ M_1 )
= ( times_times_nat @ ( suc @ K ) @ N_1 ) )
<=> ( M_1 = N_1 ) ) ).
thf(fact_1152_mult__cancel2,axiom,
! [M_1: nat,K: nat,N_1: nat] :
( ( ( times_times_nat @ M_1 @ K )
= ( times_times_nat @ N_1 @ K ) )
<=> ( ( M_1 = N_1 )
| ( K = zero_zero_nat ) ) ) ).
thf(fact_1153_mult__cancel1,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ( times_times_nat @ K @ M_1 )
= ( times_times_nat @ K @ N_1 ) )
<=> ( ( M_1 = N_1 )
| ( K = zero_zero_nat ) ) ) ).
thf(fact_1154_mult__is__0,axiom,
! [M_1: nat,N_1: nat] :
( ( ( times_times_nat @ M_1 @ N_1 )
= zero_zero_nat )
<=> ( ( M_1 = zero_zero_nat )
| ( N_1 = zero_zero_nat ) ) ) ).
thf(fact_1155_mult__0__right,axiom,
! [M_1: nat] :
( ( times_times_nat @ M_1 @ zero_zero_nat )
= zero_zero_nat ) ).
thf(fact_1156_mult__0,axiom,
! [N_1: nat] :
( ( times_times_nat @ zero_zero_nat @ N_1 )
= zero_zero_nat ) ).
thf(fact_1157_mult__eq__1__iff,axiom,
! [M_1: nat,N_1: nat] :
( ( ( times_times_nat @ M_1 @ N_1 )
= ( suc @ zero_zero_nat ) )
<=> ( ( M_1
= ( suc @ zero_zero_nat ) )
& ( N_1
= ( suc @ zero_zero_nat ) ) ) ) ).
thf(fact_1158_mult__less__mono2,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
thf(fact_1159_mult__less__mono1,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
thf(fact_1160_mult__less__cancel2,axiom,
! [M_1: nat,K: nat,N_1: nat] :
( ( ord_less_nat @ ( times_times_nat @ M_1 @ K ) @ ( times_times_nat @ N_1 @ K ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ K )
& ( ord_less_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1161_mult__less__cancel1,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( times_times_nat @ K @ M_1 ) @ ( times_times_nat @ K @ N_1 ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ K )
& ( ord_less_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1162_nat__0__less__mult__iff,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M_1 @ N_1 ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ M_1 )
& ( ord_less_nat @ zero_zero_nat @ N_1 ) ) ) ).
thf(fact_1163_Suc__mult__less__cancel1,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M_1 ) @ ( times_times_nat @ ( suc @ K ) @ N_1 ) )
<=> ( ord_less_nat @ M_1 @ N_1 ) ) ).
thf(fact_1164_mult__Suc__right,axiom,
! [M_1: nat,N_1: nat] :
( ( times_times_nat @ M_1 @ ( suc @ N_1 ) )
= ( plus_plus_nat @ M_1 @ ( times_times_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1165_mult__Suc,axiom,
! [M_1: nat,N_1: nat] :
( ( times_times_nat @ ( suc @ M_1 ) @ N_1 )
= ( plus_plus_nat @ N_1 @ ( times_times_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1166_Suc__mult__le__cancel1,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M_1 ) @ ( times_times_nat @ ( suc @ K ) @ N_1 ) )
<=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ).
thf(fact_1167_mult__eq__self__implies__10,axiom,
! [M_1: nat,N_1: nat] :
( ( M_1
= ( times_times_nat @ M_1 @ N_1 ) )
=> ( ( N_1 = one_one_nat )
| ( M_1 = zero_zero_nat ) ) ) ).
thf(fact_1168_n__less__m__mult__n,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N_1 )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M_1 )
=> ( ord_less_nat @ N_1 @ ( times_times_nat @ M_1 @ N_1 ) ) ) ) ).
thf(fact_1169_n__less__n__mult__m,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N_1 )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M_1 )
=> ( ord_less_nat @ N_1 @ ( times_times_nat @ N_1 @ M_1 ) ) ) ) ).
thf(fact_1170_one__less__mult,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N_1 )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M_1 )
=> ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M_1 @ N_1 ) ) ) ) ).
thf(fact_1171_one__le__mult__iff,axiom,
! [M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M_1 @ N_1 ) )
<=> ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M_1 )
& ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N_1 ) ) ) ).
thf(fact_1172_mult__le__cancel2,axiom,
! [M_1: nat,K: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ M_1 @ K ) @ ( times_times_nat @ N_1 @ K ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1173_mult__le__cancel1,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ K @ M_1 ) @ ( times_times_nat @ K @ N_1 ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1174_nat__mult__commute,axiom,
! [M_1: nat,N_1: nat] :
( ( times_times_nat @ M_1 @ N_1 )
= ( times_times_nat @ N_1 @ M_1 ) ) ).
thf(fact_1175_nat__mult__assoc,axiom,
! [M_1: nat,N_1: nat,K: nat] :
( ( times_times_nat @ ( times_times_nat @ M_1 @ N_1 ) @ K )
= ( times_times_nat @ M_1 @ ( times_times_nat @ N_1 @ K ) ) ) ).
thf(fact_1176_nat__mult__le__cancel1,axiom,
! [M_1: nat,N_1: nat,K: nat] :
( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M_1 ) @ ( times_times_nat @ K @ N_1 ) )
<=> ( ord_less_eq_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1177_nat__mult__less__cancel1,axiom,
! [M_1: nat,N_1: nat,K: nat] :
( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ( ord_less_nat @ ( times_times_nat @ K @ M_1 ) @ ( times_times_nat @ K @ N_1 ) )
<=> ( ord_less_nat @ M_1 @ N_1 ) ) ) ).
thf(fact_1178_nat__mult__eq__cancel1,axiom,
! [M_1: nat,N_1: nat,K: nat] :
( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ( ( times_times_nat @ K @ M_1 )
= ( times_times_nat @ K @ N_1 ) )
<=> ( M_1 = N_1 ) ) ) ).
thf(fact_1179_nat__mult__eq__cancel__disj,axiom,
! [K: nat,M_1: nat,N_1: nat] :
( ( ( times_times_nat @ K @ M_1 )
= ( times_times_nat @ K @ N_1 ) )
<=> ( ( K = zero_zero_nat )
| ( M_1 = N_1 ) ) ) ).
thf(fact_1180_left__add__mult__distrib,axiom,
! [I: nat,U: nat,J: nat,K: nat] :
( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
thf(fact_1181_nat_Osize_I2_J,axiom,
! [Nat: nat] :
( ( nat_size @ ( suc @ Nat ) )
= ( plus_plus_nat @ ( nat_size @ Nat ) @ ( suc @ zero_zero_nat ) ) ) ).
thf(fact_1182_nat_Osize_I1_J,axiom,
( ( nat_size @ zero_zero_nat )
= zero_zero_nat ) ).
thf(fact_1183_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_1184_nat__size,axiom,
! [N_1: nat] :
( ( size_size_nat @ N_1 )
= N_1 ) ).
thf(fact_1185_nat_Osize_I3_J,axiom,
( ( size_size_nat @ zero_zero_nat )
= zero_zero_nat ) ).
thf(fact_1186_weak__decr__stable,axiom,
! [F: nat > nat] :
( ! [I_1: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ I_1 ) ) @ ( F @ I_1 ) )
=> ? [I_1: nat] :
! [K_1: nat] :
( ( F @ ( plus_plus_nat @ I_1 @ K_1 ) )
= ( F @ I_1 ) ) ) ).
thf(fact_1187_bool_Osize_I1_J,axiom,
( ( bool_size @ $true )
= zero_zero_nat ) ).
thf(fact_1188_bool_Osize_I2_J,axiom,
( ( bool_size @ $false )
= zero_zero_nat ) ).
thf(fact_1189_finite__atLeastAtMost,axiom,
! [L: nat,U: nat] : ( finite_finite_nat @ ( ord_at238088361st_nat @ L @ U ) ) ).
thf(fact_1190_atLeastLessThanSuc__atLeastAtMost,axiom,
! [L: nat,U: nat] :
( ( ord_at4362885an_nat @ L @ ( suc @ U ) )
= ( ord_at238088361st_nat @ L @ U ) ) ).
thf(fact_1191_ex__nat__less,axiom,
! [P: nat > $o,N_1: nat] :
( ? [M: nat] :
( ( ord_less_eq_nat @ M @ N_1 )
& ( P @ M ) )
<=> ? [X_1: nat] :
( ( member_nat @ X_1 @ ( ord_at238088361st_nat @ zero_zero_nat @ N_1 ) )
& ( P @ X_1 ) ) ) ).
thf(fact_1192_all__nat__less,axiom,
! [P: nat > $o,N_1: nat] :
( ! [M: nat] :
( ( ord_less_eq_nat @ M @ N_1 )
=> ( P @ M ) )
<=> ! [X_1: nat] :
( ( member_nat @ X_1 @ ( ord_at238088361st_nat @ zero_zero_nat @ N_1 ) )
=> ( P @ X_1 ) ) ) ).
thf(fact_1193_image__Suc__atLeastAtMost,axiom,
! [I: nat,J: nat] :
( ( image_nat_nat @ suc @ ( ord_at238088361st_nat @ I @ J ) )
= ( ord_at238088361st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
thf(fact_1194_atLeastSucAtMost__greaterThanAtMost,axiom,
! [L: nat,U: nat] :
( ( ord_at238088361st_nat @ ( suc @ L ) @ U )
= ( ord_gr375877188st_nat @ L @ U ) ) ).
thf(fact_1195_image__add__atLeastAtMost,axiom,
! [K: nat,I: nat,J: nat] :
( ( image_nat_nat
@ ^ [N: nat] : ( plus_plus_nat @ N @ K )
@ ( ord_at238088361st_nat @ I @ J ) )
= ( ord_at238088361st_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
thf(fact_1196_atLeastLessThan__add__Un,axiom,
! [K: nat,I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_at4362885an_nat @ I @ ( plus_plus_nat @ J @ K ) )
= ( semila848761471_nat_o @ ( ord_at4362885an_nat @ I @ J ) @ ( ord_at4362885an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
thf(fact_1197_atLeast__0,axiom,
( ( ord_atLeast_nat @ zero_zero_nat )
= top_top_nat_o ) ).
thf(fact_1198_atLeast__Suc__greaterThan,axiom,
! [K: nat] :
( ( ord_atLeast_nat @ ( suc @ K ) )
= ( ord_greaterThan_nat @ K ) ) ).
thf(fact_1199_setsum__shift__lb__Suc0__0,axiom,
! [K: nat,F: nat > nat] :
( ( ( F @ zero_zero_nat )
= zero_zero_nat )
=> ( ( big_co387207925at_nat @ F @ ( ord_at238088361st_nat @ ( suc @ zero_zero_nat ) @ K ) )
= ( big_co387207925at_nat @ F @ ( ord_at238088361st_nat @ zero_zero_nat @ K ) ) ) ) ).
%----Helper facts (3)
thf(help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_,axiom,
! [X: produc1572197287le_alt > $o,Y: produc1572197287le_alt > $o] :
( ( if_Pro278423000_alt_o @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_,axiom,
! [X: produc1572197287le_alt > $o,Y: produc1572197287le_alt > $o] :
( ( if_Pro278423000_alt_o @ $false @ X @ Y )
= Y ) ).
thf(help_If_3_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) ).
%------------------------------------------------------------------------------