ITP001 Axioms: ITP133_7.ax
%------------------------------------------------------------------------------
% File : ITP133_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : HolSmt.ax [Gau19]
% : HL4133_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 582 ( 193 unt; 134 typ; 0 def)
% Number of atoms : 907 ( 372 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 667 ( 208 ~; 118 |; 37 &)
% ( 216 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 36 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 108 ( 64 >; 44 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 128 ( 128 usr; 32 con; 0-6 aty)
% Number of variables : 1400 (1316 !; 1 ?;1400 :)
% ( 83 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(tyop_2Efcp_2Ebit0,type,
tyop_2Efcp_2Ebit0: $tType > $tType ).
tff(tyop_2Efcp_2Ebit1,type,
tyop_2Efcp_2Ebit1: $tType > $tType ).
tff(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: ( $tType * $tType ) > $tType ).
tff(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: $tType ).
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
tff(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Elist_2EALL__DISTINCT_2E0,type,
c_2Elist_2EALL__DISTINCT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Elist_2EALL__DISTINCT_2E1,type,
c_2Elist_2EALL__DISTINCT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ecombin_2EUPDATE_2E0,type,
c_2Ecombin_2EUPDATE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))) ).
tff(c_2Ecombin_2EUPDATE_2E3,type,
c_2Ecombin_2EUPDATE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Ecombin_2EUPDATE_2E4,type,
c_2Ecombin_2EUPDATE_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2EHolSmt_2Earray__ext_2E0,type,
c_2EHolSmt_2Earray__ext_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27a)) ).
tff(c_2EHolSmt_2Earray__ext_2E2,type,
c_2EHolSmt_2Earray__ext_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27a ) ).
tff(c_2Efcp_2Edimindex_2E0,type,
c_2Efcp_2Edimindex_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Efcp_2Edimindex_2E1,type,
c_2Efcp_2Edimindex_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Ewords_2Edimword_2E0,type,
c_2Ewords_2Edimword_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Ewords_2Edimword_2E1,type,
c_2Ewords_2Edimword_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Efcp_2Efcp__index_2E0,type,
c_2Efcp_2Efcp__index_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)) ).
tff(c_2Efcp_2Efcp__index_2E2,type,
c_2Efcp_2Efcp__index_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart(A_27a,A_27b) * tyop_2Enum_2Enum ) > A_27a ) ).
tff(c_2Einteger_2Eint__add_2E0,type,
c_2Einteger_2Eint__add_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__add_2E2,type,
c_2Einteger_2Eint__add_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__ge_2E0,type,
c_2Einteger_2Eint__ge_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__ge_2E2,type,
c_2Einteger_2Eint__ge_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__gt_2E0,type,
c_2Einteger_2Eint__gt_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__gt_2E2,type,
c_2Einteger_2Eint__gt_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__le_2E0,type,
c_2Einteger_2Eint__le_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__le_2E2,type,
c_2Einteger_2Eint__le_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__lt_2E0,type,
c_2Einteger_2Eint__lt_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__lt_2E2,type,
c_2Einteger_2Eint__lt_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__mul_2E0,type,
c_2Einteger_2Eint__mul_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__mul_2E2,type,
c_2Einteger_2Eint__mul_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__neg_2E0,type,
c_2Einteger_2Eint__neg_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint) ).
tff(c_2Einteger_2Eint__neg_2E1,type,
c_2Einteger_2Eint__neg_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__of__num_2E0,type,
c_2Einteger_2Eint__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint) ).
tff(c_2Einteger_2Eint__of__num_2E1,type,
c_2Einteger_2Eint__of__num_2E1: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__sub_2E0,type,
c_2Einteger_2Eint__sub_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__sub_2E2,type,
c_2Einteger_2Eint__sub_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Ewords_2En2w_2E0,type,
c_2Ewords_2En2w_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2En2w_2E1,type,
c_2Ewords_2En2w_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Erealax_2Ereal__add_2E0,type,
c_2Erealax_2Ereal__add_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__add_2E2,type,
c_2Erealax_2Ereal__add_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__ge_2E0,type,
c_2Ereal_2Ereal__ge_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__ge_2E2,type,
c_2Ereal_2Ereal__ge_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Ereal__gt_2E0,type,
c_2Ereal_2Ereal__gt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__gt_2E2,type,
c_2Ereal_2Ereal__gt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__lt_2E0,type,
c_2Erealax_2Ereal__lt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Erealax_2Ereal__lt_2E2,type,
c_2Erealax_2Ereal__lt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Ereal__lte_2E0,type,
c_2Ereal_2Ereal__lte_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__lte_2E2,type,
c_2Ereal_2Ereal__lte_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__mul_2E0,type,
c_2Erealax_2Ereal__mul_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__mul_2E2,type,
c_2Erealax_2Ereal__mul_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__neg_2E0,type,
c_2Erealax_2Ereal__neg_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Erealax_2Ereal__neg_2E1,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__of__num_2E0,type,
c_2Ereal_2Ereal__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Ereal__of__num_2E1,type,
c_2Ereal_2Ereal__of__num_2E1: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__sub_2E0,type,
c_2Ereal_2Ereal__sub_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2Ereal__sub_2E2,type,
c_2Ereal_2Ereal__sub_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ewords_2Esw2sw_2E0,type,
c_2Ewords_2Esw2sw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)) ).
tff(c_2Ewords_2Esw2sw_2E1,type,
c_2Ewords_2Esw2sw_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) ).
tff(c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0:
!>[A_27a: $tType] : tyop_2Ebool_2Eitself(A_27a) ).
tff(c_2Ewords_2Ew2w_2E0,type,
c_2Ewords_2Ew2w_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)) ).
tff(c_2Ewords_2Ew2w_2E1,type,
c_2Ewords_2Ew2w_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) ).
tff(c_2Ewords_2Eword__1comp_2E0,type,
c_2Ewords_2Eword__1comp_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2Eword__1comp_2E1,type,
c_2Ewords_2Eword__1comp_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__add_2E0,type,
c_2Ewords_2Eword__add_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__add_2E2,type,
c_2Ewords_2Eword__add_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__and_2E0,type,
c_2Ewords_2Eword__and_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__and_2E2,type,
c_2Ewords_2Eword__and_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__concat_2E0,type,
c_2Ewords_2Eword__concat_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c))) ).
tff(c_2Ewords_2Eword__concat_2E2,type,
c_2Ewords_2Eword__concat_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c) ) ).
tff(c_2Ewords_2Eword__extract_2E0,type,
c_2Ewords_2Eword__extract_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)))) ).
tff(c_2Ewords_2Eword__extract_2E3,type,
c_2Ewords_2Eword__extract_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Enum_2Enum * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) ).
tff(c_2Ewords_2Eword__lo_2E0,type,
c_2Ewords_2Eword__lo_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ewords_2Eword__lo_2E2,type,
c_2Ewords_2Eword__lo_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewords_2Eword__ls_2E0,type,
c_2Ewords_2Eword__ls_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ewords_2Eword__ls_2E2,type,
c_2Ewords_2Eword__ls_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewords_2Eword__mul_2E0,type,
c_2Ewords_2Eword__mul_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__mul_2E2,type,
c_2Ewords_2Eword__mul_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__or_2E0,type,
c_2Ewords_2Eword__or_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__or_2E2,type,
c_2Ewords_2Eword__or_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2EHolSmt_2Exor_2E0,type,
c_2EHolSmt_2Exor_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2EHolSmt_2Exor_2E2,type,
c_2EHolSmt_2Exor_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Emin_2E_40_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ebool_2ECOND_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X2_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] : ( c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone))))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone))))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone))))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2EHolSmt_2Earray__ext_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2EHolSmt_2Earray__ext_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27a),c_2EHolSmt_2Earray__ext_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27b)] : ( c_2Efcp_2Edimindex_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27b),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27c)] : ( c_2Efcp_2Edimindex_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27c),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29,axiom,
! [X0_2E0: tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))))] : ( c_2Efcp_2Edimindex_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29,axiom,
! [X0_2E0: tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] : ( c_2Efcp_2Edimindex_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : ( c_2Ewords_2Edimword_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27b)] : ( c_2Ewords_2Edimword_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27b),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29,axiom,
! [X0_2E0: tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] : ( c_2Ewords_2Edimword_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Efcp_2Efcp__index_2E0(tyop_2Emin_2Ebool,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29,axiom,
! [X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),X1_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Efcp_2Efcp__index_2E0(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X1_2E0: tyop_2Enum_2Enum] : ( c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Efcp_2Efcp__index_2E0(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__add_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__ge_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__ge_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__gt_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__gt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__gt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__le_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__le_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__lt_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__mul_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Einteger_2Eint__neg_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__neg_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Einteger_2Eint__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__sub_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__sub_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2En2w_2E0(A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),c_2Ewords_2En2w_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),c_2Ewords_2En2w_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__ge_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__ge_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__ge_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__gt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__gt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__gt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Erealax_2Ereal__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__lte_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__neg_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Ereal__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__sub_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29,axiom,
! [X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] : ( c_2Ewords_2Esw2sw_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),c_2Ewords_2Esw2sw_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2Ew2w_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Ew2w_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Ew2w_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2Eword__1comp_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__1comp_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__1comp_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2Eword__1comp_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] : ( c_2Ewords_2Eword__1comp_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__1comp_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__add_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__add_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__and_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__and_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__and_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__and_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] : ( c_2Ewords_2Eword__and_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ewords_2Eword__and_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__concat_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : ( c_2Ewords_2Eword__concat_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),c_2Ewords_2Eword__concat_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ewords_2Eword__extract_2E3_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] : ( c_2Ewords_2Eword__extract_2E3(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),c_2Ewords_2Eword__extract_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ewords_2Eword__extract_2E3_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] : ( c_2Ewords_2Eword__extract_2E3(tyop_2Eone_2Eone,tyop_2Eone_2Eone,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone))),c_2Ewords_2Eword__extract_2E0(tyop_2Eone_2Eone,tyop_2Eone_2Eone),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__lo_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__lo_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Ewords_2Eword__lo_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__ls_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__ls_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Ewords_2Eword__ls_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__mul_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__mul_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__mul_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__mul_2E2_2Emono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29,axiom,
! [X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))))] : ( c_2Ewords_2Eword__mul_2E2(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))))),c_2Ewords_2Eword__mul_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__or_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__or_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__or_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewords_2Eword__or_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] : ( c_2Ewords_2Eword__or_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ewords_2Eword__or_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EHolSmt_2Exor_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] : ( c_2EHolSmt_2Exor_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2EHolSmt_2Exor_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2EHolSmt_2Exor__def,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Ebool] :
( p(c_2EHolSmt_2Exor_2E2(V0x_2E0,V1y_2E0))
<=> ( V0x_2E0 != V1y_2E0 ) ) ).
tff(thm_2EHolSmt_2Earray__ext__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1B_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2i_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1B_2E0),V2i_2E0))
<=> ( app_2E2(A_27a,A_27b,V0A_2E0,V2i_2E0) != app_2E2(A_27a,A_27b,V1B_2E0,V2i_2E0) ) )
=> ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1B_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2EHolSmt_2Earray__ext_2E2(A_27a,A_27b,V0A_2E0,V1B_2E0) = c_2Emin_2E_40_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1B_2E0)) ) ) ).
tff(thm_2EHolSmt_2EALL__DISTINCT__NIL,axiom,
! [A_27a: $tType] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2EHolSmt_2EALL__DISTINCT__CONS,axiom,
! [A_27a: $tType,V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)))
<=> ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0h_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1t_2E0)))
& p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1t_2E0)) ) ) ).
tff(thm_2EHolSmt_2ENOT__MEM__NIL,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a))))
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2ENOT__MEM__CONS,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a)] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2t_2E0))))
<=> ( ( V0x_2E0 != V1h_2E0 )
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2t_2E0))) ) ) ).
tff(thm_2EHolSmt_2EAND__T,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
& p(c_2Ebool_2ET_2E0) )
<=> p(V0t_2E0) ) ).
tff(thm_2EHolSmt_2ET__AND,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
& p(V0p_2E0) )
<=> ( p(c_2Ebool_2ET_2E0)
& p(V1q_2E0) ) )
=> ( V0p_2E0 = V1q_2E0 ) ) ).
tff(thm_2EHolSmt_2EF__OR,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2EF_2E0)
| p(V0p_2E0) )
<=> ( p(c_2Ebool_2EF_2E0)
| p(V1q_2E0) ) )
=> ( V0p_2E0 = V1q_2E0 ) ) ).
tff(thm_2EHolSmt_2ECONJ__CONG,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2r_2E0: tyop_2Emin_2Ebool,V3s_2E0: tyop_2Emin_2Ebool] :
( ( V0p_2E0 = V1q_2E0 )
=> ( ( V2r_2E0 = V3s_2E0 )
=> ( ( p(V0p_2E0)
& p(V2r_2E0) )
<=> ( p(V1q_2E0)
& p(V3s_2E0) ) ) ) ) ).
tff(thm_2EHolSmt_2ENOT__NOT__ELIM,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool] :
( ~ ~ p(V0p_2E0)
=> p(V0p_2E0) ) ).
tff(thm_2EHolSmt_2ENOT__FALSE,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool] :
( p(V0A_2E0)
=> ( ~ p(V0A_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2EHolSmt_2ENNF__CONJ,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2r_2E0: tyop_2Emin_2Ebool,V3s_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V0p_2E0)
<=> p(V2r_2E0) )
=> ( ( ~ p(V1q_2E0)
<=> p(V3s_2E0) )
=> ( ~ ( p(V0p_2E0)
& p(V1q_2E0) )
<=> ( p(V2r_2E0)
| p(V3s_2E0) ) ) ) ) ).
tff(thm_2EHolSmt_2ENNF__DISJ,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2r_2E0: tyop_2Emin_2Ebool,V3s_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V0p_2E0)
<=> p(V2r_2E0) )
=> ( ( ~ p(V1q_2E0)
<=> p(V3s_2E0) )
=> ( ~ ( p(V0p_2E0)
| p(V1q_2E0) )
<=> ( p(V2r_2E0)
& p(V3s_2E0) ) ) ) ) ).
tff(thm_2EHolSmt_2ENNF__NOT__NOT,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ( V0p_2E0 = V1q_2E0 )
=> ( ~ ~ p(V0p_2E0)
<=> p(V1q_2E0) ) ) ).
tff(thm_2EHolSmt_2ENEG__IFF__1__1,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ( V1q_2E0 = V0p_2E0 )
=> ~ ( p(V0p_2E0)
<=> ~ p(V1q_2E0) ) ) ).
tff(thm_2EHolSmt_2ENEG__IFF__1__2,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ~ ( p(V0p_2E0)
<=> ~ p(V1q_2E0) )
=> ( V1q_2E0 = V0p_2E0 ) ) ).
tff(thm_2EHolSmt_2ENEG__IFF__2__1,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ( p(V0p_2E0)
<=> ~ p(V1q_2E0) )
=> ( V0p_2E0 != V1q_2E0 ) ) ).
tff(thm_2EHolSmt_2ENEG__IFF__2__2,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ( V0p_2E0 != V1q_2E0 )
=> ( p(V0p_2E0)
<=> ~ p(V1q_2E0) ) ) ).
tff(thm_2EHolSmt_2EDISJ__ELIM__1,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2r_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V0p_2E0)
| p(V1q_2E0) )
=> p(V2r_2E0) )
=> ( p(V0p_2E0)
=> p(V2r_2E0) ) ) ).
tff(thm_2EHolSmt_2EDISJ__ELIM__2,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2r_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V0p_2E0)
| p(V1q_2E0) )
=> p(V2r_2E0) )
=> ( p(V1q_2E0)
=> p(V2r_2E0) ) ) ).
tff(thm_2EHolSmt_2EIMP__DISJ__1,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ( p(V0p_2E0)
=> p(V1q_2E0) )
=> ( ~ p(V0p_2E0)
| p(V1q_2E0) ) ) ).
tff(thm_2EHolSmt_2EIMP__DISJ__2,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V0p_2E0)
=> p(V1q_2E0) )
=> ( p(V0p_2E0)
| p(V1q_2E0) ) ) ).
tff(thm_2EHolSmt_2EIMP__FALSE,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V0p_2E0)
=> p(c_2Ebool_2EF_2E0) )
=> p(V0p_2E0) ) ).
tff(thm_2EHolSmt_2EAND__IMP__INTRO__SYM,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool,V2C_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V0A_2E0)
& p(V1B_2E0) )
=> p(V2C_2E0) )
<=> ( p(V0A_2E0)
=> ( p(V1B_2E0)
=> p(V2C_2E0) ) ) ) ).
tff(thm_2EHolSmt_2EVALID__IFF__TRUE,axiom,
! [V0b_2E0: tyop_2Emin_2Ebool] :
( p(V0b_2E0)
=> ( V0b_2E0 = c_2Ebool_2ET_2E0 ) ) ).
tff(thm_2EHolSmt_2Ed001,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( V1p_2E0 != V0q_2E0 )
| ~ p(V1p_2E0)
| p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed002,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( V1p_2E0 != V0q_2E0 )
| p(V1p_2E0)
| ~ p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed003,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
<=> ~ p(V0q_2E0) )
| ~ p(V1p_2E0)
| p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed004,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
<=> p(V0q_2E0) )
| p(V1p_2E0)
| ~ p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed005,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( V1p_2E0 = V0q_2E0 )
| ~ p(V1p_2E0)
| ~ p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed006,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( V1p_2E0 = V0q_2E0 )
| p(V1p_2E0)
| p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed007,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ~ ( ~ p(V1p_2E0)
<=> p(V0q_2E0) )
| p(V1p_2E0)
| p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed008,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ~ ( p(V1p_2E0)
<=> ~ p(V0q_2E0) )
| p(V1p_2E0)
| p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed009,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ~ p(V1p_2E0)
| p(V0q_2E0)
| ( V1p_2E0 != V0q_2E0 ) ) ).
tff(thm_2EHolSmt_2Ed010,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(V1p_2E0)
| ~ p(V0q_2E0)
| ( V1p_2E0 != V0q_2E0 ) ) ).
tff(thm_2EHolSmt_2Ed011,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(V1p_2E0)
| p(V0q_2E0)
| ~ ( ~ p(V1p_2E0)
<=> p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Ed012,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(V1p_2E0)
| p(V0q_2E0)
| ~ ( p(V1p_2E0)
<=> ~ p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Ed013,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
& ~ p(V0q_2E0) )
| p(V1p_2E0)
| p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed014,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
& p(V0q_2E0) )
| p(V1p_2E0)
| ~ p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed015,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
& ~ p(V0q_2E0) )
| ~ p(V1p_2E0)
| p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed016,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
& p(V0q_2E0) )
| ~ p(V1p_2E0)
| ~ p(V0q_2E0) ) ).
tff(thm_2EHolSmt_2Ed017,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2p_2E0: tyop_2Emin_2Ebool] :
( p(V2p_2E0)
| ( V0y_2E0 = c_2Ebool_2ECOND_2E3(A_27a,V2p_2E0,V1x_2E0,V0y_2E0) ) ) ).
tff(thm_2EHolSmt_2Ed018,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2p_2E0: tyop_2Emin_2Ebool] :
( ~ p(V2p_2E0)
| ( V1x_2E0 = c_2Ebool_2ECOND_2E3(A_27a,V2p_2E0,V1x_2E0,V0y_2E0) ) ) ).
tff(thm_2EHolSmt_2Ed019,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2p_2E0: tyop_2Emin_2Ebool] :
( p(V2p_2E0)
| ( c_2Ebool_2ECOND_2E3(A_27a,V2p_2E0,V1x_2E0,V0y_2E0) = V0y_2E0 ) ) ).
tff(thm_2EHolSmt_2Ed020,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2p_2E0: tyop_2Emin_2Ebool] :
( ~ p(V2p_2E0)
| ( c_2Ebool_2ECOND_2E3(A_27a,V2p_2E0,V1x_2E0,V0y_2E0) = V1x_2E0 ) ) ).
tff(thm_2EHolSmt_2Ed021,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( p(V2p_2E0)
| p(V1q_2E0)
| ~ p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V2p_2E0,V0r_2E0,V1q_2E0)) ) ).
tff(thm_2EHolSmt_2Ed022,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ~ p(V2p_2E0)
| p(V1q_2E0)
| ~ p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V2p_2E0,V1q_2E0,V0r_2E0)) ) ).
tff(thm_2EHolSmt_2Ed023,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V2p_2E0,V1q_2E0,V0r_2E0))
| ~ p(V2p_2E0)
| ~ p(V1q_2E0) ) ).
tff(thm_2EHolSmt_2Ed024,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V2p_2E0,V1q_2E0,V0r_2E0))
| p(V2p_2E0)
| ~ p(V0r_2E0) ) ).
tff(thm_2EHolSmt_2Ed025,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V1q_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V1q_2E0))
<=> ~ p(V1q_2E0) )
=> ! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V2p_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V1q_2E0),V0r_2E0))
| ~ p(V2p_2E0)
| p(V1q_2E0) ) ) ).
tff(thm_2EHolSmt_2Ed026,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V0r_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0r_2E0))
<=> ~ p(V0r_2E0) )
=> ! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V2p_2E0,V1q_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0r_2E0)))
| p(V2p_2E0)
| p(V0r_2E0) ) ) ).
tff(thm_2EHolSmt_2Ed027,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V2p_2E0,V1q_2E0,V0r_2E0))
| ~ p(V2p_2E0)
| p(V1q_2E0) ) ).
tff(thm_2EHolSmt_2Ed028,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V2p_2E0,V1q_2E0,V0r_2E0))
| p(V2p_2E0)
| p(V0r_2E0) ) ).
tff(thm_2EHolSmt_2Er001,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a] :
( ( V1x_2E0 = V0y_2E0 )
<=> ( V0y_2E0 = V1x_2E0 ) ) ).
tff(thm_2EHolSmt_2Er002,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] :
( ( V0x_2E0 = V0x_2E0 )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er003,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool] :
( ( V0p_2E0 = c_2Ebool_2ET_2E0 )
<=> p(V0p_2E0) ) ).
tff(thm_2EHolSmt_2Er004,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = V0p_2E0 )
<=> p(V0p_2E0) ) ).
tff(thm_2EHolSmt_2Er005,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool] :
( ( V0p_2E0 = c_2Ebool_2EF_2E0 )
<=> ~ p(V0p_2E0) ) ).
tff(thm_2EHolSmt_2Er006,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = V0p_2E0 )
<=> ~ p(V0p_2E0) ) ).
tff(thm_2EHolSmt_2Er007,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
<=> ~ p(V0q_2E0) )
<=> ( V1p_2E0 = V0q_2E0 ) ) ).
tff(thm_2EHolSmt_2Er008,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ~ ( p(V1p_2E0)
<=> ~ p(V0q_2E0) )
<=> ( V1p_2E0 = V0q_2E0 ) ) ).
tff(thm_2EHolSmt_2Er009,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ~ ( ~ p(V1p_2E0)
<=> p(V0q_2E0) )
<=> ( V1p_2E0 = V0q_2E0 ) ) ).
tff(thm_2EHolSmt_2Er010,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2ET_2E0,V1x_2E0,V0y_2E0) = V1x_2E0 ) ).
tff(thm_2EHolSmt_2Er011,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2EF_2E0,V1x_2E0,V0y_2E0) = V0y_2E0 ) ).
tff(thm_2EHolSmt_2Er012,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V1p_2E0,V0q_2E0,c_2Ebool_2ET_2E0))
<=> ( ~ p(V1p_2E0)
| p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Er013,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V1p_2E0,V0q_2E0,c_2Ebool_2ET_2E0))
<=> ( p(V0q_2E0)
| ~ p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er014,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V0q_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0q_2E0))
<=> ~ p(V0q_2E0) )
=> ! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V1p_2E0,V0q_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0q_2E0)))
<=> ( V1p_2E0 = V0q_2E0 ) ) ) ).
tff(thm_2EHolSmt_2Er015,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V0q_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0q_2E0))
<=> ~ p(V0q_2E0) )
=> ! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V1p_2E0,V0q_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0q_2E0)))
<=> ( V0q_2E0 = V1p_2E0 ) ) ) ).
tff(thm_2EHolSmt_2Er016,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V0q_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0q_2E0))
<=> ~ p(V0q_2E0) )
=> ! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V1p_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0q_2E0),V0q_2E0))
<=> ( p(V1p_2E0)
<=> ~ p(V0q_2E0) ) ) ) ).
tff(thm_2EHolSmt_2Er017,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V0q_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0q_2E0))
<=> ~ p(V0q_2E0) )
=> ! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V1p_2E0,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V0q_2E0),V0q_2E0))
<=> ( ~ p(V0q_2E0)
<=> p(V1p_2E0) ) ) ) ).
tff(thm_2EHolSmt_2Er018,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V2p_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V2p_2E0))
<=> ~ p(V2p_2E0) )
=> ! [V0y_2E0: A_27a,V1x_2E0: A_27a,V2p_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V2p_2E0),V1x_2E0,V0y_2E0) = c_2Ebool_2ECOND_2E3(A_27a,V2p_2E0,V0y_2E0,V1x_2E0) ) ) ).
tff(thm_2EHolSmt_2Er019,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
( ! [V3p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V3p_2E0),V2q_2E0))
<=> ( p(V3p_2E0)
& ~ p(V2q_2E0) ) )
=> ! [V0y_2E0: A_27a,V1x_2E0: A_27a,V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,c_2Ebool_2ECOND_2E3(A_27a,V2q_2E0,V1x_2E0,V0y_2E0),V1x_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V3p_2E0),V2q_2E0),V0y_2E0,V1x_2E0) ) ) ).
tff(thm_2EHolSmt_2Er020,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
( ! [V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V2q_2E0),V3p_2E0))
<=> ( ~ p(V2q_2E0)
& p(V3p_2E0) ) )
=> ! [V0y_2E0: A_27a,V1x_2E0: A_27a,V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,c_2Ebool_2ECOND_2E3(A_27a,V2q_2E0,V1x_2E0,V0y_2E0),V1x_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V2q_2E0),V3p_2E0),V0y_2E0,V1x_2E0) ) ) ).
tff(thm_2EHolSmt_2Er021,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
( ! [V3p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V3p_2E0),V2q_2E0))
<=> ( p(V3p_2E0)
& p(V2q_2E0) ) )
=> ! [V0y_2E0: A_27a,V1x_2E0: A_27a,V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,c_2Ebool_2ECOND_2E3(A_27a,V2q_2E0,V1x_2E0,V0y_2E0),V0y_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V3p_2E0),V2q_2E0),V1x_2E0,V0y_2E0) ) ) ).
tff(thm_2EHolSmt_2Er022,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
( ! [V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V2q_2E0),V3p_2E0))
<=> ( p(V2q_2E0)
& p(V3p_2E0) ) )
=> ! [V0y_2E0: A_27a,V1x_2E0: A_27a,V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,c_2Ebool_2ECOND_2E3(A_27a,V2q_2E0,V1x_2E0,V0y_2E0),V0y_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V2q_2E0),V3p_2E0),V1x_2E0,V0y_2E0) ) ) ).
tff(thm_2EHolSmt_2Er023,axiom,
! [A_27a: $tType,V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3p_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,V2x_2E0,c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,V1y_2E0,V0z_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,V2x_2E0,V0z_2E0) ) ).
tff(thm_2EHolSmt_2Er024,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
( ! [V3p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V3p_2E0),V2q_2E0))
<=> ( p(V3p_2E0)
| p(V2q_2E0) ) )
=> ! [V0y_2E0: A_27a,V1x_2E0: A_27a,V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,V1x_2E0,c_2Ebool_2ECOND_2E3(A_27a,V2q_2E0,V1x_2E0,V0y_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V3p_2E0),V2q_2E0),V1x_2E0,V0y_2E0) ) ) ).
tff(thm_2EHolSmt_2Er025,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
( ! [V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V2q_2E0),V3p_2E0))
<=> ( p(V2q_2E0)
| p(V3p_2E0) ) )
=> ! [V0y_2E0: A_27a,V1x_2E0: A_27a,V2q_2E0: tyop_2Emin_2Ebool,V3p_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,V1x_2E0,c_2Ebool_2ECOND_2E3(A_27a,V2q_2E0,V1x_2E0,V0y_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V2q_2E0),V3p_2E0),V1x_2E0,V0y_2E0) ) ) ).
tff(thm_2EHolSmt_2Er026,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V1y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V2x_2E0),V1y_2E0))
<=> ( V2x_2E0 = V1y_2E0 ) )
=> ! [V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V3p_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V2x_2E0),V1y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V2x_2E0),V0z_2E0)))
<=> ( V2x_2E0 = c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,V1y_2E0,V0z_2E0) ) ) ) ).
tff(thm_2EHolSmt_2Er027,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V1y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V2x_2E0),V1y_2E0))
<=> ( V2x_2E0 = V1y_2E0 ) )
=> ! [V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V3p_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V2x_2E0),V1y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1y_2E0),V0z_2E0)))
<=> ( V1y_2E0 = c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,V2x_2E0,V0z_2E0) ) ) ) ).
tff(thm_2EHolSmt_2Er028,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a,V1y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V2x_2E0),V1y_2E0))
<=> ( V2x_2E0 = V1y_2E0 ) )
=> ! [V0z_2E0: A_27a,V1y_2E0: A_27a,V2x_2E0: A_27a,V3p_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V3p_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V2x_2E0),V1y_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0z_2E0),V1y_2E0)))
<=> ( V1y_2E0 = c_2Ebool_2ECOND_2E3(A_27a,V3p_2E0,V2x_2E0,V0z_2E0) ) ) ) ).
tff(thm_2EHolSmt_2Er029,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
=> p(V0q_2E0) )
<=> ( p(V1p_2E0)
| p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Er030,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
=> p(V0q_2E0) )
<=> ( p(V0q_2E0)
| p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er031,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
=> p(V0q_2E0) )
<=> ( ~ p(V1p_2E0)
| p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Er032,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
=> p(V0q_2E0) )
<=> ( p(V0q_2E0)
| ~ p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er033,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2ET_2E0)
=> p(V0t_2E0) )
<=> p(V0t_2E0) ) ).
tff(thm_2EHolSmt_2Er034,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
=> p(c_2Ebool_2ET_2E0) )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er035,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2EF_2E0)
=> p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er036,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
=> p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er037,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ( ( V2p_2E0 = V1q_2E0 )
=> p(V0r_2E0) )
<=> ( p(V0r_2E0)
| ( p(V1q_2E0)
<=> ~ p(V2p_2E0) ) ) ) ).
tff(thm_2EHolSmt_2Er038,axiom,
( ~ p(c_2Ebool_2ET_2E0)
<=> p(c_2Ebool_2EF_2E0) ) ).
tff(thm_2EHolSmt_2Er039,axiom,
( ~ p(c_2Ebool_2EF_2E0)
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er040,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ~ ~ p(V0t_2E0)
<=> p(V0t_2E0) ) ).
tff(thm_2EHolSmt_2Er041,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
| p(V0q_2E0) )
<=> ( p(V0q_2E0)
| p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er042,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
| p(c_2Ebool_2ET_2E0) )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er043,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool] :
( ( p(V0p_2E0)
| ~ p(V0p_2E0) )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er044,axiom,
! [V0p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V0p_2E0)
| p(V0p_2E0) )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er045,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2ET_2E0)
| p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2EHolSmt_2Er046,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
| p(c_2Ebool_2EF_2E0) )
<=> p(V0t_2E0) ) ).
tff(thm_2EHolSmt_2Er047,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2EF_2E0)
| p(V0t_2E0) )
<=> p(V0t_2E0) ) ).
tff(thm_2EHolSmt_2Er048,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
& p(V0q_2E0) )
<=> ( p(V0q_2E0)
& p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er049,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
& p(c_2Ebool_2ET_2E0) )
<=> p(V0t_2E0) ) ).
tff(thm_2EHolSmt_2Er050,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2ET_2E0)
& p(V0t_2E0) )
<=> p(V0t_2E0) ) ).
tff(thm_2EHolSmt_2Er051,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
& p(c_2Ebool_2EF_2E0) )
<=> p(c_2Ebool_2EF_2E0) ) ).
tff(thm_2EHolSmt_2Er052,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2EF_2E0)
& p(V0t_2E0) )
<=> p(c_2Ebool_2EF_2E0) ) ).
tff(thm_2EHolSmt_2Er053,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
& p(V0q_2E0) )
<=> ~ ( ~ p(V1p_2E0)
| ~ p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Er054,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
& p(V0q_2E0) )
<=> ~ ( p(V1p_2E0)
| ~ p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Er055,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
& ~ p(V0q_2E0) )
<=> ~ ( ~ p(V1p_2E0)
| p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Er056,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
& ~ p(V0q_2E0) )
<=> ~ ( p(V1p_2E0)
| p(V0q_2E0) ) ) ).
tff(thm_2EHolSmt_2Er057,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
& p(V0q_2E0) )
<=> ~ ( ~ p(V0q_2E0)
| ~ p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er058,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
& p(V0q_2E0) )
<=> ~ ( ~ p(V0q_2E0)
| p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er059,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
& ~ p(V0q_2E0) )
<=> ~ ( p(V0q_2E0)
| ~ p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er060,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V1p_2E0)
& ~ p(V0q_2E0) )
<=> ~ ( p(V0q_2E0)
| p(V1p_2E0) ) ) ).
tff(thm_2EHolSmt_2Er061,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V0x_2E0,app_2E2(A_27a,A_27b,V1f_2E0,V0x_2E0),V1f_2E0) = V1f_2E0 ) ).
tff(thm_2EHolSmt_2Er062,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)))) = c_2Ebool_2EF_2E0 ) ).
tff(thm_2EHolSmt_2Er063,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a] :
( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ECONS_2E2(A_27a,V0y_2E0,c_2Elist_2ENIL_2E0(A_27a)))))
<=> ( V1x_2E0 != V0y_2E0 ) ) ).
tff(thm_2EHolSmt_2Er064,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a] :
( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ECONS_2E2(A_27a,V0y_2E0,c_2Elist_2ENIL_2E0(A_27a)))))
<=> ( V0y_2E0 != V1x_2E0 ) ) ).
tff(thm_2EHolSmt_2Er065,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( ( V1x_2E0 = V0y_2E0 )
<=> ( c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er066,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( V2x_2E0 = c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0) )
<=> ( c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0)) = V1y_2E0 ) ) ).
tff(thm_2EHolSmt_2Er067,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( V2x_2E0 = c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0)) )
<=> ( c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),V0z_2E0)) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er068,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( V2x_2E0 = c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),V0z_2E0) )
<=> ( c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0),V2x_2E0)) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er069,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( V2x_2E0 = c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0) )
<=> ( c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0))) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er070,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( V2x_2E0 = c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0) )
<=> ( c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0))) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er071,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( V2x_2E0 = c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0) )
<=> ( c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),V0z_2E0)) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er072,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( V2x_2E0 = c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0) )
<=> ( c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0)) = c_2Einteger_2Eint__neg_2E1(V1y_2E0) ) ) ).
tff(thm_2EHolSmt_2Er073,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( V2x_2E0 = c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V1y_2E0),V0z_2E0) )
<=> ( c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0)) = V1y_2E0 ) ) ).
tff(thm_2EHolSmt_2Er074,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1x_2E0) = c_2Einteger_2Eint__neg_2E1(V0y_2E0) )
<=> ( V1x_2E0 = V0y_2E0 ) ) ).
tff(thm_2EHolSmt_2Er075,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),V1y_2E0) = V0z_2E0 )
<=> ( c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0)) = c_2Einteger_2Eint__neg_2E1(V0z_2E0) ) ) ).
tff(thm_2EHolSmt_2Er076,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ( V0y_2E0 = c_2Einteger_2Eint__neg_2E1(V1x_2E0) ) ) ).
tff(thm_2EHolSmt_2Er077,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2(V2x_2E0,V1y_2E0) = V0z_2E0 )
<=> ( c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0)) = c_2Einteger_2Eint__neg_2E1(V2x_2E0) ) ) ).
tff(thm_2EHolSmt_2Er078,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint,V3w_2E0: tyop_2Einteger_2Eint,V4v_2E0: tyop_2Einteger_2Eint,V5a_2E0: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2(V5a_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(V4v_2E0,V1y_2E0),c_2Einteger_2Eint__mul_2E2(V3w_2E0,V0z_2E0)))) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ( c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(V4v_2E0),V1y_2E0),c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(V3w_2E0),V0z_2E0))) = V5a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er079,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er080,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er081,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__add_2E2(V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er082,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(V0x_2E0,V0x_2E0) = c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V0x_2E0) ) ).
tff(thm_2EHolSmt_2Er083,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0) = c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0)) ) ).
tff(thm_2EHolSmt_2Er084,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0) = c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V0z_2E0,V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er085,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0)) = c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__add_2E2(V0z_2E0,V2x_2E0)) ) ).
tff(thm_2EHolSmt_2Er086,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0)) = c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__add_2E2(V2x_2E0,V0z_2E0)) ) ).
tff(thm_2EHolSmt_2Er087,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint,V3u_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__add_2E2(V0z_2E0,V3u_2E0))) = c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__add_2E2(V3u_2E0,V2x_2E0))) ) ).
tff(thm_2EHolSmt_2Er088,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(V0x_2E0,V0x_2E0) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2EHolSmt_2Er089,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er090,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V0y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1x_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er091,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0)) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0))),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er092,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0x_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Einteger_2Eint__le_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er093,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1x_2E0),c_2Einteger_2Eint__neg_2E1(V0y_2E0)) = c_2Einteger_2Eint__le_2E2(V1x_2E0,V0y_2E0) ) ).
tff(thm_2EHolSmt_2Er094,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1x_2E0),V0y_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er095,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Einteger_2Eint__le_2E2(V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er096,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__gt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Einteger_2Eint__ge_2E2(V0y_2E0,V1x_2E0)) ) ).
tff(thm_2EHolSmt_2Er097,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__gt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Einteger_2Eint__le_2E2(V1x_2E0,V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Er098,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__gt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er099,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__gt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V0y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1x_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er100,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__gt_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0)))
<=> ~ p(c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0)),c_2Einteger_2Eint__neg_2E1(V1y_2E0))) ) ).
tff(thm_2EHolSmt_2Er101,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(V0x_2E0,V0x_2E0) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2EHolSmt_2Er102,axiom,
c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Ebool_2ET_2E0 ).
tff(thm_2EHolSmt_2Er103,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__ge_2E2(V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er104,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V1x_2E0),V0y_2E0)) = c_2Einteger_2Eint__ge_2E2(V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er105,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0x_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Einteger_2Eint__ge_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er106,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er107,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V0y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1x_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er108,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1x_2E0),V0y_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er109,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),V1y_2E0),c_2Einteger_2Eint__neg_2E1(V0z_2E0)) = c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0)),V0z_2E0) ) ).
tff(thm_2EHolSmt_2Er110,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V2x_2E0),V1y_2E0),V0z_2E0) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0)),V2x_2E0) ) ).
tff(thm_2EHolSmt_2Er111,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0)),V0z_2E0) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0))),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er112,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0)) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0)),V1y_2E0) ) ).
tff(thm_2EHolSmt_2Er113,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0)) = c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0)),c_2Einteger_2Eint__neg_2E1(V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er114,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,V0z_2E0)) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0))),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er115,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Einteger_2Eint__le_2E2(V0y_2E0,V1x_2E0)) ) ).
tff(thm_2EHolSmt_2Er116,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Einteger_2Eint__ge_2E2(V1x_2E0,V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Er117,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V0y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1x_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er118,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er119,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0))))
<=> ~ p(c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0)),V0z_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er120,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0))))
<=> ~ p(c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),V0z_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er121,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V1y_2E0),V0z_2E0)))
<=> ~ p(c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0)),V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er122,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint,V3u_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V1y_2E0),c_2Einteger_2Eint__add_2E2(V0z_2E0,V3u_2E0))))
<=> ~ p(c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__add_2E2(V3u_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0))),V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er123,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint,V3v_2E0: tyop_2Einteger_2Eint,V4u_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V1y_2E0),c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__add_2E2(V4u_2E0,V3v_2E0)))))
<=> ~ p(c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__add_2E2(V4u_2E0,c_2Einteger_2Eint__add_2E2(V3v_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0)))),V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er124,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V2x_2E0),V1y_2E0),V0z_2E0))
<=> ~ p(c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0)),V2x_2E0)) ) ).
tff(thm_2EHolSmt_2Er125,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0))
<=> ~ p(c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V0z_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0)),V2x_2E0)) ) ).
tff(thm_2EHolSmt_2Er126,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V1x_2E0),V0y_2E0)))
<=> ~ p(c_2Einteger_2Eint__le_2E2(V0y_2E0,V1x_2E0)) ) ).
tff(thm_2EHolSmt_2Er127,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er128,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V0x_2E0) = c_2Einteger_2Eint__neg_2E1(V0x_2E0) ) ).
tff(thm_2EHolSmt_2Er129,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V0x_2E0) = c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0x_2E0) ) ).
tff(thm_2EHolSmt_2Er130,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(V0y_2E0),V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er131,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Er132,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(V1x_2E0,V0y_2E0) = c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0),V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er133,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0x_2E0) ) ).
tff(thm_2EHolSmt_2Er134,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0) = c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(V1y_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0))) ) ).
tff(thm_2EHolSmt_2Er135,axiom,
! [V0z_2E0: tyop_2Einteger_2Eint,V1y_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0) = c_2Einteger_2Eint__add_2E2(V2x_2E0,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0),V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er136,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1u_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) = c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V1u_2E0),V0x_2E0) )
<=> ( c_2Erealax_2Ereal__mul_2E2(V1u_2E0,V0x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er137,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1u_2E0: tyop_2Erealax_2Ereal,V2a_2E0: tyop_2Erealax_2Ereal] :
( ( V2a_2E0 = c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V1u_2E0),V0x_2E0) )
<=> ( c_2Erealax_2Ereal__mul_2E2(V1u_2E0,V0x_2E0) = c_2Erealax_2Ereal__neg_2E1(V2a_2E0) ) ) ).
tff(thm_2EHolSmt_2Er138,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3a_2E0: tyop_2Erealax_2Ereal] :
( ( V3a_2E0 = c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,V0z_2E0)) )
<=> ( c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V3a_2E0),V0z_2E0))) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er139,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3a_2E0: tyop_2Erealax_2Ereal] :
( ( V3a_2E0 = c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,V0z_2E0)) )
<=> ( c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__add_2E2(V0z_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V3a_2E0)))) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er140,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] :
( ( V4a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0z_2E0)) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1y_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0z_2E0),V4a_2E0)) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er141,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] :
( ( V4a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0z_2E0)) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1y_2E0),c_2Erealax_2Ereal__add_2E2(V4a_2E0,c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0z_2E0))) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er142,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__neg_2E1(V4a_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)) = V4a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er143,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( V6a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0),V6a_2E0))) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2EHolSmt_2Er144,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( V6a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V6a_2E0) ) ) ).
tff(thm_2EHolSmt_2Er145,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( V6a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V6a_2E0) ) ) ).
tff(thm_2EHolSmt_2Er146,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( V6a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V6a_2E0) ) ) ).
tff(thm_2EHolSmt_2Er147,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( V6a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V6a_2E0) ) ) ).
tff(thm_2EHolSmt_2Er148,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__neg_2E1(V6a_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = V6a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er149,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__neg_2E1(V6a_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = V6a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er150,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__neg_2E1(V6a_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = V6a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er151,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__neg_2E1(V6a_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = V6a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er152,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4u_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( ( V5a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V5a_2E0) ) ) ).
tff(thm_2EHolSmt_2Er153,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4u_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( ( V5a_2E0 = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V5a_2E0) ) ) ).
tff(thm_2EHolSmt_2Er154,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)) = c_2Erealax_2Ereal__neg_2E1(V4a_2E0) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)) = V4a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er155,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V5a_2E0) )
<=> ( c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = V5a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er156,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V6a_2E0) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = V6a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er157,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V6a_2E0) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = V6a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er158,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))) = c_2Erealax_2Ereal__neg_2E1(V6a_2E0) )
<=> ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))) = V6a_2E0 ) ) ).
tff(thm_2EHolSmt_2Er159,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ereal_2Ereal__lte_2E2(V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er160,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__ge_2E2(V1x_2E0,V0y_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er161,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__gt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er162,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(V1x_2E0,V0y_2E0) = c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er163,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,V0z_2E0)) = c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0)),V1y_2E0) ) ).
tff(thm_2EHolSmt_2Er164,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1u_2E0: tyop_2Erealax_2Ereal,V2a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V1u_2E0),V0x_2E0),V2a_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__mul_2E2(V1u_2E0,V0x_2E0),c_2Erealax_2Ereal__neg_2E1(V2a_2E0)) ) ).
tff(thm_2EHolSmt_2Er165,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1u_2E0: tyop_2Erealax_2Ereal,V2a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V1u_2E0),V0x_2E0),c_2Erealax_2Ereal__neg_2E1(V2a_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__mul_2E2(V1u_2E0,V0x_2E0),V2a_2E0) ) ).
tff(thm_2EHolSmt_2Er166,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er167,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),V4a_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),c_2Erealax_2Ereal__neg_2E1(V4a_2E0)) ) ).
tff(thm_2EHolSmt_2Er168,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),c_2Erealax_2Ereal__neg_2E1(V4a_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),V4a_2E0) ) ).
tff(thm_2EHolSmt_2Er169,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),V4a_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),c_2Erealax_2Ereal__neg_2E1(V4a_2E0)) ) ).
tff(thm_2EHolSmt_2Er170,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),c_2Erealax_2Ereal__neg_2E1(V4a_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),V4a_2E0) ) ).
tff(thm_2EHolSmt_2Er171,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er172,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er173,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er174,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Er175,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V6a_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)) ) ).
tff(thm_2EHolSmt_2Er176,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V6a_2E0) ) ).
tff(thm_2EHolSmt_2Er177,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V6a_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)) ) ).
tff(thm_2EHolSmt_2Er178,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V6a_2E0) ) ).
tff(thm_2EHolSmt_2Er179,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V6a_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)) ) ).
tff(thm_2EHolSmt_2Er180,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V6a_2E0) ) ).
tff(thm_2EHolSmt_2Er181,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V6a_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)) ) ).
tff(thm_2EHolSmt_2Er182,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V6a_2E0) ) ).
tff(thm_2EHolSmt_2Er183,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0)) = c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V5a_2E0) ) ).
tff(thm_2EHolSmt_2Er184,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(V1x_2E0,V0y_2E0))
<=> ~ p(c_2Ereal_2Ereal__ge_2E2(V1x_2E0,V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Er185,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1u_2E0: tyop_2Erealax_2Ereal,V2a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V1u_2E0),V0x_2E0),V2a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__mul_2E2(V1u_2E0,V0x_2E0),c_2Erealax_2Ereal__neg_2E1(V2a_2E0))) ) ).
tff(thm_2EHolSmt_2Er186,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1u_2E0: tyop_2Erealax_2Ereal,V2a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V1u_2E0),V0x_2E0),c_2Erealax_2Ereal__neg_2E1(V2a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__mul_2E2(V1u_2E0,V0x_2E0),V2a_2E0)) ) ).
tff(thm_2EHolSmt_2Er187,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er188,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er189,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),V4a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),c_2Erealax_2Ereal__neg_2E1(V4a_2E0))) ) ).
tff(thm_2EHolSmt_2Er190,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),c_2Erealax_2Ereal__neg_2E1(V4a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),V4a_2E0)) ) ).
tff(thm_2EHolSmt_2Er191,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),V4a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),c_2Erealax_2Ereal__neg_2E1(V4a_2E0))) ) ).
tff(thm_2EHolSmt_2Er192,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2v_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal,V4a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V1x_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2v_2E0),V0y_2E0)),c_2Erealax_2Ereal__neg_2E1(V4a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V1x_2E0),c_2Erealax_2Ereal__mul_2E2(V2v_2E0,V0y_2E0)),V4a_2E0)) ) ).
tff(thm_2EHolSmt_2Er193,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V6a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0))) ) ).
tff(thm_2EHolSmt_2Er194,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V6a_2E0)) ) ).
tff(thm_2EHolSmt_2Er195,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V6a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0))) ) ).
tff(thm_2EHolSmt_2Er196,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V6a_2E0)) ) ).
tff(thm_2EHolSmt_2Er197,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V6a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0))) ) ).
tff(thm_2EHolSmt_2Er198,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V6a_2E0)) ) ).
tff(thm_2EHolSmt_2Er199,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V6a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0))) ) ).
tff(thm_2EHolSmt_2Er200,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal,V6a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V6a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V6a_2E0)) ) ).
tff(thm_2EHolSmt_2Er201,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er202,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5u_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V5u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V5u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Er203,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V5a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0))) ) ).
tff(thm_2EHolSmt_2Er204,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V5a_2E0)) ) ).
tff(thm_2EHolSmt_2Er205,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V5a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0))) ) ).
tff(thm_2EHolSmt_2Er206,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V5a_2E0)) ) ).
tff(thm_2EHolSmt_2Er207,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V5a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0))) ) ).
tff(thm_2EHolSmt_2Er208,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V5a_2E0)) ) ).
tff(thm_2EHolSmt_2Er209,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),V5a_2E0))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0))) ) ).
tff(thm_2EHolSmt_2Er210,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4v_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4v_2E0),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V5a_2E0)) ) ).
tff(thm_2EHolSmt_2Er211,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3w_2E0: tyop_2Erealax_2Ereal,V4u_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3w_2E0),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__mul_2E2(V3w_2E0,V0z_2E0))),V5a_2E0)) ) ).
tff(thm_2EHolSmt_2Er212,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3v_2E0: tyop_2Erealax_2Ereal,V4u_2E0: tyop_2Erealax_2Ereal,V5a_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V4u_2E0),V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V3v_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0))),c_2Erealax_2Ereal__neg_2E1(V5a_2E0)))
<=> ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(V4u_2E0,V2x_2E0),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3v_2E0),V1y_2E0),V0z_2E0)),V5a_2E0)) ) ).
tff(thm_2EHolSmt_2Er213,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er214,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(V0x_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er215,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(V1x_2E0,V0y_2E0) = c_2Erealax_2Ereal__add_2E2(V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er216,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(V0x_2E0,V0x_2E0) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V0x_2E0) ) ).
tff(thm_2EHolSmt_2Er217,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0) = c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,V0z_2E0)) ) ).
tff(thm_2EHolSmt_2Er218,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0) = c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V0z_2E0,V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er219,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,V0z_2E0)) = c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__add_2E2(V0z_2E0,V2x_2E0)) ) ).
tff(thm_2EHolSmt_2Er220,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,V0z_2E0)) = c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__add_2E2(V2x_2E0,V0z_2E0)) ) ).
tff(thm_2EHolSmt_2Er221,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V0x_2E0) = c_2Erealax_2Ereal__neg_2E1(V0x_2E0) ) ).
tff(thm_2EHolSmt_2Er222,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Erealax_2Ereal__mul_2E2(V1u_2E0,V0x_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V1u_2E0),V0x_2E0) ) ).
tff(thm_2EHolSmt_2Er223,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(V0x_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0)) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er224,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(V1x_2E0,V0y_2E0) = c_2Erealax_2Ereal__add_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Er225,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(V1x_2E0,V0y_2E0) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0),V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er226,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(V2u_2E0,V0y_2E0)) = c_2Erealax_2Ereal__add_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2u_2E0),V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Er227,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal,V2u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(V2u_2E0,V0y_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V2u_2E0),V0y_2E0),V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er228,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0) = c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0))) ) ).
tff(thm_2EHolSmt_2Er229,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,V1y_2E0),V0z_2E0) = c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0z_2E0),V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er230,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V0z_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V0z_2E0),c_2Erealax_2Ereal__add_2E2(V2x_2E0,V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er231,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V0z_2E0)) = c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V0z_2E0),V1y_2E0)) ) ).
tff(thm_2EHolSmt_2Er232,axiom,
! [V0z_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Erealax_2Ereal,V3u_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__add_2E2(V2x_2E0,V1y_2E0),c_2Erealax_2Ereal__mul_2E2(V3u_2E0,V0z_2E0)) = c_2Erealax_2Ereal__add_2E2(V2x_2E0,c_2Erealax_2Ereal__add_2E2(V1y_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(V3u_2E0),V0z_2E0))) ) ).
tff(thm_2EHolSmt_2Er233,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),V0x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ).
tff(thm_2EHolSmt_2Er234,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er235,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__add_2E2(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er236,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__add_2E2(A_27a,V1x_2E0,V0y_2E0) = c_2Ewords_2Eword__add_2E2(A_27a,V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er237,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__add_2E2(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ewords_2Eword__add_2E2(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0x_2E0)) = c_2Ewords_2Eword__add_2E2(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V0x_2E0) ) ).
tff(thm_2EHolSmt_2Er238,axiom,
! [A_27a: $tType,V0z_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V2x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
( ( c_2Ewords_2Eword__add_2E2(A_27a,V2x_2E0,V0z_2E0) = c_2Ewords_2Eword__add_2E2(A_27a,V1y_2E0,V2x_2E0) )
<=> ( V1y_2E0 = V0z_2E0 ) ) ).
tff(thm_2EHolSmt_2Er239,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,c_2Ewords_2Edimword_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ( c_2Ewords_2Eword__concat_2E2(A_27a,A_27b,A_27c,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0),c_2Ewords_2En2w_2E1(A_27b,V0x_2E0)) = c_2Ewords_2En2w_2E1(A_27c,V0x_2E0) ) ) ) ).
tff(thm_2EHolSmt_2Er240,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
=> ( c_2Ewords_2Ew2w_2E1(A_27a,A_27b,c_2Ewords_2En2w_2E1(A_27a,V0x_2E0)) = c_2Ewords_2En2w_2E1(A_27b,V0x_2E0) ) ) ).
tff(thm_2EHolSmt_2Er241,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c))))
=> ( p(c_2Eprim__rec_2E_3C_2E2(V0y_2E0,c_2Ewords_2Edimword_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ( ( c_2Ewords_2Eword__concat_2E2(A_27a,A_27b,A_27c,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0),V1x_2E0) = c_2Ewords_2En2w_2E1(A_27c,V0y_2E0) )
<=> ( V1x_2E0 = c_2Ewords_2En2w_2E1(A_27b,V0y_2E0) ) ) ) ) ) ).
tff(thm_2EHolSmt_2Er242,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c))))
=> ( p(c_2Eprim__rec_2E_3C_2E2(V0y_2E0,c_2Ewords_2Edimword_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ( ( c_2Ewords_2Eword__concat_2E2(A_27a,A_27b,A_27c,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0),V1x_2E0) = c_2Ewords_2En2w_2E1(A_27c,V0y_2E0) )
<=> ( c_2Ewords_2En2w_2E1(A_27b,V0y_2E0) = V1x_2E0 ) ) ) ) ) ).
tff(thm_2EHolSmt_2Er243,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c))))
=> ( p(c_2Eprim__rec_2E_3C_2E2(V0y_2E0,c_2Ewords_2Edimword_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ( ( c_2Ewords_2En2w_2E1(A_27c,V0y_2E0) = c_2Ewords_2Eword__concat_2E2(A_27a,A_27b,A_27c,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0),V1x_2E0) )
<=> ( V1x_2E0 = c_2Ewords_2En2w_2E1(A_27b,V0y_2E0) ) ) ) ) ) ).
tff(thm_2EHolSmt_2Er244,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c))))
=> ( p(c_2Eprim__rec_2E_3C_2E2(V0y_2E0,c_2Ewords_2Edimword_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ( ( c_2Ewords_2En2w_2E1(A_27c,V0y_2E0) = c_2Ewords_2Eword__concat_2E2(A_27a,A_27b,A_27c,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0),V1x_2E0) )
<=> ( c_2Ewords_2En2w_2E1(A_27b,V0y_2E0) = V1x_2E0 ) ) ) ) ) ).
tff(thm_2EHolSmt_2Er245,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__and_2E2(A_27a,V1x_2E0,V0y_2E0) = c_2Ewords_2Eword__and_2E2(A_27a,V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er246,axiom,
! [A_27a: $tType,V0z_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V2x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__and_2E2(A_27a,V2x_2E0,c_2Ewords_2Eword__and_2E2(A_27a,V1y_2E0,V0z_2E0)) = c_2Ewords_2Eword__and_2E2(A_27a,V1y_2E0,c_2Ewords_2Eword__and_2E2(A_27a,V2x_2E0,V0z_2E0)) ) ).
tff(thm_2EHolSmt_2Er247,axiom,
! [A_27a: $tType,V0z_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V2x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__and_2E2(A_27a,V2x_2E0,c_2Ewords_2Eword__and_2E2(A_27a,V1y_2E0,V0z_2E0)) = c_2Ewords_2Eword__and_2E2(A_27a,c_2Ewords_2Eword__and_2E2(A_27a,V2x_2E0,V1y_2E0),V0z_2E0) ) ).
tff(thm_2EHolSmt_2Er248,axiom,
! [V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Ewords_2Eword__and_2E2(tyop_2Eone_2Eone,V1x_2E0,V0y_2E0) )
<=> ( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V1x_2E0 )
& ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V0y_2E0 ) ) ) ).
tff(thm_2EHolSmt_2Er249,axiom,
! [V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Ewords_2Eword__and_2E2(tyop_2Eone_2Eone,V1x_2E0,V0y_2E0) )
<=> ( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V0y_2E0 )
& ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V1x_2E0 ) ) ) ).
tff(thm_2EHolSmt_2Er250,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] : ( c_2Ewords_2Eword__extract_2E3(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Enum_2E0_2E0,V0x_2E0) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er251,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
( p(c_2Ewords_2Eword__lo_2E2(A_27a,V1x_2E0,V0y_2E0))
<=> ~ p(c_2Ewords_2Eword__ls_2E2(A_27a,V0y_2E0,V1x_2E0)) ) ).
tff(thm_2EHolSmt_2Er252,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__mul_2E2(A_27a,V1x_2E0,V0y_2E0) = c_2Ewords_2Eword__mul_2E2(A_27a,V0y_2E0,V1x_2E0) ) ).
tff(thm_2EHolSmt_2Er253,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] : ( c_2Ewords_2Eword__extract_2E3(tyop_2Eone_2Eone,tyop_2Eone_2Eone,c_2Enum_2E0_2E0,c_2Enum_2E0_2E0,V0x_2E0) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Er254,axiom,
! [A_27a: $tType,V0z_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V2x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__and_2E2(A_27a,c_2Ewords_2Eword__and_2E2(A_27a,V2x_2E0,V1y_2E0),V0z_2E0) = c_2Ewords_2Eword__and_2E2(A_27a,V2x_2E0,c_2Ewords_2Eword__and_2E2(A_27a,V1y_2E0,V0z_2E0)) ) ).
tff(thm_2EHolSmt_2Er255,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Eword__or_2E2(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2EHolSmt_2Et001,axiom,
! [A_27a: $tType,A_27b: $tType,V0z_2E0: A_27b,V1y_2E0: A_27a,V2x_2E0: A_27a,V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( V2x_2E0 = V1y_2E0 )
| ( app_2E2(A_27a,A_27b,V3f_2E0,V2x_2E0) = c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V1y_2E0,V0z_2E0,V3f_2E0,V2x_2E0) ) ) ).
tff(thm_2EHolSmt_2Et002,axiom,
! [A_27a: $tType,A_27b: $tType,V0z_2E0: A_27b,V1y_2E0: A_27a,V2x_2E0: A_27a,V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( V2x_2E0 = V1y_2E0 )
| ( app_2E2(A_27a,A_27b,V3f_2E0,V1y_2E0) = c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V2x_2E0,V0z_2E0,V3f_2E0,V1y_2E0) ) ) ).
tff(thm_2EHolSmt_2Et003,axiom,
! [A_27a: $tType,A_27b: $tType,V0z_2E0: A_27b,V1y_2E0: A_27a,V2x_2E0: A_27a,V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( V2x_2E0 = V1y_2E0 )
| ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V1y_2E0,V0z_2E0,V3f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V3f_2E0,V2x_2E0) ) ) ).
tff(thm_2EHolSmt_2Et004,axiom,
! [A_27a: $tType,A_27b: $tType,V0z_2E0: A_27b,V1y_2E0: A_27a,V2x_2E0: A_27a,V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( V2x_2E0 = V1y_2E0 )
| ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V2x_2E0,V0z_2E0,V3f_2E0,V1y_2E0) = app_2E2(A_27a,A_27b,V3f_2E0,V1y_2E0) ) ) ).
tff(thm_2EHolSmt_2Et005,axiom,
! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( V1f_2E0 = V0g_2E0 )
| ( app_2E2(A_27a,A_27b,V1f_2E0,c_2EHolSmt_2Earray__ext_2E2(A_27a,A_27b,V1f_2E0,V0g_2E0)) != app_2E2(A_27a,A_27b,V0g_2E0,c_2EHolSmt_2Earray__ext_2E2(A_27a,A_27b,V1f_2E0,V0g_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et006,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( ( V1x_2E0 != V0y_2E0 )
| p(c_2Einteger_2Eint__le_2E2(V1x_2E0,V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Et007,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( ( V1x_2E0 != V0y_2E0 )
| p(c_2Einteger_2Eint__ge_2E2(V1x_2E0,V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Et008,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( ( V1x_2E0 != V0y_2E0 )
| p(c_2Einteger_2Eint__ge_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Et009,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( ( V1x_2E0 != V0y_2E0 )
| p(c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Et010,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( ( V1x_2E0 = V0y_2E0 )
| ~ p(c_2Einteger_2Eint__le_2E2(V1x_2E0,V0y_2E0))
| ~ p(c_2Einteger_2Eint__ge_2E2(V1x_2E0,V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Et011,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] :
( ~ p(c_2Einteger_2Eint__le_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)))
| p(c_2Einteger_2Eint__le_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2EHolSmt_2Et012,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] :
( ~ p(c_2Einteger_2Eint__le_2E2(V0x_2E0,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
| p(c_2Einteger_2Eint__le_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Et013,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] :
( ~ p(c_2Einteger_2Eint__ge_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)))
| p(c_2Einteger_2Eint__ge_2E2(V0x_2E0,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) ).
tff(thm_2EHolSmt_2Et014,axiom,
! [V0x_2E0: tyop_2Einteger_2Eint] :
( ~ p(c_2Einteger_2Eint__ge_2E2(V0x_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)))
| ~ p(c_2Einteger_2Eint__le_2E2(V0x_2E0,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) ).
tff(thm_2EHolSmt_2Et015,axiom,
! [V0y_2E0: tyop_2Einteger_2Eint,V1x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__ge_2E2(V1x_2E0,V0y_2E0))
| p(c_2Einteger_2Eint__le_2E2(V1x_2E0,V0y_2E0)) ) ).
tff(thm_2EHolSmt_2Et016,axiom,
! [V0y_2E0: tyop_2Erealax_2Ereal,V1x_2E0: tyop_2Erealax_2Ereal] :
( ( V1x_2E0 != V0y_2E0 )
| p(c_2Ereal_2Ereal__ge_2E2(c_2Erealax_2Ereal__add_2E2(V1x_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0y_2E0)),c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) ) ).
tff(thm_2EHolSmt_2Et017,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( V0x_2E0 != c_2Ewords_2Eword__1comp_2E1(A_27a,V0x_2E0) ) ).
tff(thm_2EHolSmt_2Et018,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V2i_2E0: tyop_2Enum_2Enum] :
( ( V1x_2E0 = V0y_2E0 )
=> ( p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,A_27a,V1x_2E0,V2i_2E0))
=> p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,A_27a,V0y_2E0,V2i_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et019,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Ewords_2Eword__1comp_2E1(tyop_2Eone_2Eone,V0x_2E0) )
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V0x_2E0,c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Et020,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V0x_2E0,c_2Enum_2E0_2E0))
=> ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0) = c_2Ewords_2Eword__1comp_2E1(tyop_2Eone_2Eone,V0x_2E0) ) ) ).
tff(thm_2EHolSmt_2Et021,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V0x_2E0,c_2Enum_2E0_2E0))
=> ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V0x_2E0 ) ) ).
tff(thm_2EHolSmt_2Et022,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V0x_2E0,c_2Enum_2E0_2E0))
=> ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0) = V0x_2E0 ) ) ).
tff(thm_2EHolSmt_2Et023,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V0x_2E0,c_2Enum_2E0_2E0))
=> ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Ewords_2Eword__1comp_2E1(tyop_2Eone_2Eone,V0x_2E0) ) ) ).
tff(thm_2EHolSmt_2Et024,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0) = c_2Ewords_2Eword__1comp_2E1(tyop_2Eone_2Eone,V0x_2E0) )
| ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V0x_2E0,c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Et025,axiom,
! [V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Ewords_2Eword__or_2E2(tyop_2Eone_2Eone,c_2Ewords_2Eword__1comp_2E1(tyop_2Eone_2Eone,V1x_2E0),c_2Ewords_2Eword__1comp_2E1(tyop_2Eone_2Eone,V0y_2E0)) )
| ~ ( ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V1x_2E0,c_2Enum_2E0_2E0))
| ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V0y_2E0,c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et026,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] :
( ( c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),c_2Enum_2E0_2E0) = V0x_2E0 )
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Enum_2E0_2E0))
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))
| p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) ).
tff(thm_2EHolSmt_2Et027,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1p_2E0: tyop_2Emin_2Ebool] :
( ( ( V0x_2E0 = c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
<=> p(V1p_2E0) )
<=> ( V0x_2E0 = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1p_2E0,c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et028,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1p_2E0: tyop_2Emin_2Ebool] :
( ( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V0x_2E0 )
<=> p(V1p_2E0) )
<=> ( V0x_2E0 = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1p_2E0,c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et029,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
<=> ( V0x_2E0 = c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
<=> ( V0x_2E0 = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1p_2E0,c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et030,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
<=> ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V0x_2E0 ) )
<=> ( V0x_2E0 = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1p_2E0,c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et031,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] :
( ( c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Enum_2E0_2E0) = c_2Ewords_2Eword__mul_2E2(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))))))))))))))),c_2Ewords_2Esw2sw_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),V0x_2E0)) )
=> ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Enum_2E0_2E0)) ) ).
tff(thm_2EHolSmt_2Et032,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] :
( ( c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Enum_2E0_2E0) = c_2Ewords_2Eword__mul_2E2(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))))))))))))))),c_2Ewords_2Esw2sw_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),V0x_2E0)) )
=> ~ ( p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))
<=> ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et033,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))] :
( ( c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Enum_2E0_2E0) = c_2Ewords_2Eword__mul_2E2(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Ewords_2En2w_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))))))))))))))),c_2Ewords_2Esw2sw_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),V0x_2E0)) )
=> ~ ( p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))
<=> ( ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Enum_2E0_2E0))
& ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),V0x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ) ).
tff(thm_2EHolSmt_2Et034,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
( ( c_2Ewords_2Eword__add_2E2(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1x_2E0) = V0y_2E0 )
=> ( p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,A_27a,V1x_2E0,c_2Enum_2E0_2E0))
=> ~ p(c_2Efcp_2Efcp__index_2E2(tyop_2Emin_2Ebool,A_27a,V0y_2E0,c_2Enum_2E0_2E0)) ) ) ).
tff(thm_2EHolSmt_2Et035,axiom,
! [V0x_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)] :
( ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = V0x_2E0 )
| ( c_2Ewords_2Eword__extract_2E3(tyop_2Eone_2Eone,tyop_2Eone_2Eone,c_2Enum_2E0_2E0,c_2Enum_2E0_2E0,V0x_2E0) != c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2EHolSmt_2Ep001,axiom,
! [A_27a: $tType] : p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ).
tff(thm_2EHolSmt_2Ep002,axiom,
! [A_27a: $tType] : p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ).
tff(thm_2EHolSmt_2Ep003,axiom,
p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Ewords_2Edimword_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),c_2Ebool_2Ethe__value_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))))) ).
tff(thm_2EHolSmt_2Ep004,axiom,
p(c_2Epred__set_2EFINITE_2E1(tyop_2Eone_2Eone,c_2Epred__set_2EUNIV_2E0(tyop_2Eone_2Eone))) ).
tff(thm_2EHolSmt_2Ep005,axiom,
p(c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone)))),c_2Epred__set_2EUNIV_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))))) ).
tff(thm_2EHolSmt_2Ep006,axiom,
p(c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),c_2Epred__set_2EUNIV_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone))))))) ).
tff(thm_2EHolSmt_2Ep007,axiom,
p(c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),c_2Epred__set_2EUNIV_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone))))))) ).
tff(thm_2EHolSmt_2Ep008,axiom,
p(c_2Epred__set_2EFINITE_2E1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone)))),c_2Epred__set_2EUNIV_2E0(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Efcp_2Ebit1(tyop_2Eone_2Eone))))))) ).
tff(thm_2EHolSmt_2Ep009,axiom,
p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))),c_2Ebool_2Ethe__value_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Efcp_2Edimindex_2E1(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))),c_2Ebool_2Ethe__value_2E0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Efcp_2Ebit0(tyop_2Eone_2Eone))))))))) ).
%------------------------------------------------------------------------------