ITP001 Axioms: ITP097^4.ax
%------------------------------------------------------------------------------
% File : ITP097^4 : TPTP v9.0.0. 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 : comparison.ax [Gau19]
% : HL4097^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 475 ( 198 unt; 233 typ; 0 def)
% Number of atoms : 473 ( 331 equ; 4 cnn)
% Maximal formula atoms : 30 ( 0 avg)
% Number of connectives : 8623 ( 4 ~; 3 |; 64 &;8461 @)
% ( 37 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg;8461 nst)
% Number of types : 9 ( 8 usr)
% Number of type conns : 624 ( 624 >; 0 *; 0 +; 0 <<)
% Number of symbols : 227 ( 225 usr; 67 con; 0-5 aty)
% Number of variables : 658 ( 0 ^ 657 !; 1 ?; 658 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
u: $tType ).
thf(d,type,
d: $tType ).
thf(du,type,
du: $tType ).
thf(mono_2Etyop_2Estring_2Echar,type,
mono_2Etyop_2Estring_2Echar: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Etyop_2EternaryComparisons_2Eordering: $tType ).
thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,type,
mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: d > d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: d ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: d > d ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(tyop_2Estring_2Echar,type,
tyop_2Estring_2Echar: d ).
thf(tyop_2EternaryComparisons_2Eordering,type,
tyop_2EternaryComparisons_2Eordering: d ).
thf(tyop_2Etoto_2Etoto,type,
tyop_2Etoto_2Etoto: d > d ).
thf(s,type,
s: d > u > du ).
thf(app_2E2,type,
app_2E2: du > du > u ).
thf(combin_i_2E0,type,
combin_i_2E0: u ).
thf(combin_k_2E0,type,
combin_k_2E0: u ).
thf(combin_s_2E0,type,
combin_s_2E0: u ).
thf(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: u ).
thf(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: u ).
thf(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: du > du > u ).
thf(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Epair_2ECURRY_2E0,type,
c_2Epair_2ECURRY_2E0: u ).
thf(c_2Epair_2ECURRY_2E1,type,
c_2Epair_2ECURRY_2E1: du > u ).
thf(c_2EternaryComparisons_2EEQUAL_2E0,type,
c_2EternaryComparisons_2EEQUAL_2E0: u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0: u ).
thf(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1: du > u ).
thf(c_2EternaryComparisons_2EGREATER_2E0,type,
c_2EternaryComparisons_2EGREATER_2E0: u ).
thf(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0: u ).
thf(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2: du > du > u ).
thf(c_2EternaryComparisons_2ELESS_2E0,type,
c_2EternaryComparisons_2ELESS_2E0: u ).
thf(c_2Elist_2ELIST__REL_2E0,type,
c_2Elist_2ELIST__REL_2E0: u ).
thf(c_2Elist_2ELIST__REL_2E3,type,
c_2Elist_2ELIST__REL_2E3: du > du > du > u ).
thf(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0: u ).
thf(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1: du > u ).
thf(c_2Elist_2ELLEX_2E0,type,
c_2Elist_2ELLEX_2E0: u ).
thf(c_2Elist_2ELLEX_2E1,type,
c_2Elist_2ELLEX_2E1: du > u ).
thf(c_2Etoto_2EListOrd_2E0,type,
c_2Etoto_2EListOrd_2E0: u ).
thf(c_2Etoto_2EListOrd_2E1,type,
c_2Etoto_2EListOrd_2E1: du > u ).
thf(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0: u ).
thf(c_2Estring_2EORD_2E0,type,
c_2Estring_2EORD_2E0: u ).
thf(c_2Estring_2EORD_2E1,type,
c_2Estring_2EORD_2E1: du > u ).
thf(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0: u ).
thf(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1: du > u ).
thf(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0: u ).
thf(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1: du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Etoto_2ETO_2E0,type,
c_2Etoto_2ETO_2E0: u ).
thf(c_2Etoto_2ETO_2E1,type,
c_2Etoto_2ETO_2E1: du > u ).
thf(c_2Etoto_2ETO__inv_2E0,type,
c_2Etoto_2ETO__inv_2E0: u ).
thf(c_2Etoto_2ETO__inv_2E1,type,
c_2Etoto_2ETO__inv_2E1: du > u ).
thf(c_2Etoto_2ETO__of__LinearOrder_2E0,type,
c_2Etoto_2ETO__of__LinearOrder_2E0: u ).
thf(c_2Etoto_2ETO__of__LinearOrder_2E1,type,
c_2Etoto_2ETO__of__LinearOrder_2E1: du > u ).
thf(c_2Etoto_2ETotOrd_2E0,type,
c_2Etoto_2ETotOrd_2E0: u ).
thf(c_2Etoto_2ETotOrd_2E1,type,
c_2Etoto_2ETotOrd_2E1: du > u ).
thf(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_2E0: u ).
thf(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1: du > u ).
thf(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(c_2Etoto_2Eapto_2E0,type,
c_2Etoto_2Eapto_2E0: u ).
thf(c_2Etoto_2Eapto_2E1,type,
c_2Etoto_2Eapto_2E1: du > u ).
thf(c_2EternaryComparisons_2Ebool__compare_2E0,type,
c_2EternaryComparisons_2Ebool__compare_2E0: u ).
thf(c_2EternaryComparisons_2Ebool__compare_2E2,type,
c_2EternaryComparisons_2Ebool__compare_2E2: du > du > u ).
thf(c_2Etoto_2EcharOrd_2E0,type,
c_2Etoto_2EcharOrd_2E0: u ).
thf(c_2EternaryComparisons_2Echar__compare_2E0,type,
c_2EternaryComparisons_2Echar__compare_2E0: u ).
thf(c_2EternaryComparisons_2Echar__compare_2E2,type,
c_2EternaryComparisons_2Echar__compare_2E2: du > du > u ).
thf(c_2Ecomparison_2Eequiv__inj_2E0,type,
c_2Ecomparison_2Eequiv__inj_2E0: u ).
thf(c_2Ecomparison_2Eequiv__inj_2E3,type,
c_2Ecomparison_2Eequiv__inj_2E3: du > du > du > u ).
thf(c_2Ecomparison_2Egood__cmp_2E0,type,
c_2Ecomparison_2Egood__cmp_2E0: u ).
thf(c_2Ecomparison_2Egood__cmp_2E1,type,
c_2Ecomparison_2Egood__cmp_2E1: du > u ).
thf(c_2EternaryComparisons_2Einvert__comparison_2E0,type,
c_2EternaryComparisons_2Einvert__comparison_2E0: u ).
thf(c_2Erelation_2Eirreflexive_2E0,type,
c_2Erelation_2Eirreflexive_2E0: u ).
thf(c_2Erelation_2Eirreflexive_2E1,type,
c_2Erelation_2Eirreflexive_2E1: du > u ).
thf(c_2Etoto_2ElexTO_2E0,type,
c_2Etoto_2ElexTO_2E0: u ).
thf(c_2Etoto_2ElexTO_2E2,type,
c_2Etoto_2ElexTO_2E2: du > du > u ).
thf(c_2EternaryComparisons_2Elist__compare_2E0,type,
c_2EternaryComparisons_2Elist__compare_2E0: u ).
thf(c_2EternaryComparisons_2Elist__compare_2E1,type,
c_2EternaryComparisons_2Elist__compare_2E1: du > u ).
thf(c_2EternaryComparisons_2Elist__compare_2E3,type,
c_2EternaryComparisons_2Elist__compare_2E3: du > du > du > u ).
thf(c_2Etoto_2EnumOrd_2E0,type,
c_2Etoto_2EnumOrd_2E0: u ).
thf(c_2EternaryComparisons_2Enum__compare_2E0,type,
c_2EternaryComparisons_2Enum__compare_2E0: u ).
thf(c_2EternaryComparisons_2Enum__compare_2E2,type,
c_2EternaryComparisons_2Enum__compare_2E2: du > du > u ).
thf(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0: u ).
thf(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2: du > du > u ).
thf(c_2Ecomparison_2Eoption__cmp2_2E0,type,
c_2Ecomparison_2Eoption__cmp2_2E0: u ).
thf(c_2Ecomparison_2Eoption__cmp2_2E1,type,
c_2Ecomparison_2Eoption__cmp2_2E1: du > u ).
thf(c_2Ecomparison_2Eoption__cmp2_2E3,type,
c_2Ecomparison_2Eoption__cmp2_2E3: du > du > du > u ).
thf(c_2EternaryComparisons_2Eoption__compare_2E0,type,
c_2EternaryComparisons_2Eoption__compare_2E0: u ).
thf(c_2EternaryComparisons_2Eoption__compare_2E1,type,
c_2EternaryComparisons_2Eoption__compare_2E1: du > u ).
thf(c_2EternaryComparisons_2Eoption__compare_2E3,type,
c_2EternaryComparisons_2Eoption__compare_2E3: du > du > du > u ).
thf(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
c_2EternaryComparisons_2Eordering__CASE_2E0: u ).
thf(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
c_2EternaryComparisons_2Eordering__CASE_2E4: du > du > du > du > u ).
thf(c_2EternaryComparisons_2Epair__compare_2E0,type,
c_2EternaryComparisons_2Epair__compare_2E0: u ).
thf(c_2EternaryComparisons_2Epair__compare_2E2,type,
c_2EternaryComparisons_2Epair__compare_2E2: du > du > u ).
thf(c_2EternaryComparisons_2Epair__compare_2E4,type,
c_2EternaryComparisons_2Epair__compare_2E4: du > du > du > du > u ).
thf(c_2Ecomparison_2Eresp__equiv_2E0,type,
c_2Ecomparison_2Eresp__equiv_2E0: u ).
thf(c_2Ecomparison_2Eresp__equiv_2E2,type,
c_2Ecomparison_2Eresp__equiv_2E2: du > du > u ).
thf(c_2Ecomparison_2Eresp__equiv2_2E0,type,
c_2Ecomparison_2Eresp__equiv2_2E0: u ).
thf(c_2Ecomparison_2Eresp__equiv2_2E3,type,
c_2Ecomparison_2Eresp__equiv2_2E3: du > du > du > u ).
thf(c_2EternaryComparisons_2Estring__compare_2E0,type,
c_2EternaryComparisons_2Estring__compare_2E0: u ).
thf(c_2EternaryComparisons_2Estring__compare_2E2,type,
c_2EternaryComparisons_2Estring__compare_2E2: du > du > u ).
thf(c_2Etoto_2Estringto_2E0,type,
c_2Etoto_2Estringto_2E0: u ).
thf(c_2Erelation_2Etransitive_2E0,type,
c_2Erelation_2Etransitive_2E0: u ).
thf(c_2Erelation_2Etransitive_2E1,type,
c_2Erelation_2Etransitive_2E1: du > u ).
thf(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
thf(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29: ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2EternaryComparisons_2Eordering: ( $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,type,
mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ) > ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ) > ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ) > ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,type,
mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering: $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2EEQUAL,type,
mono_2Ec_2EternaryComparisons_2EEQUAL: mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2EternaryComparisons_2EGREATER,type,
mono_2Ec_2EternaryComparisons_2EGREATER: mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2ELESS,type,
mono_2Ec_2EternaryComparisons_2ELESS: mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Estring_2EORD,type,
mono_2Ec_2Estring_2EORD: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,type,
mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2Ebool__compare,type,
mono_2Ec_2EternaryComparisons_2Ebool__compare: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Etoto_2EcharOrd,type,
mono_2Ec_2Etoto_2EcharOrd: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2Echar__compare,type,
mono_2Ec_2EternaryComparisons_2Echar__compare: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Emin_2Ebool: ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Estring_2Echar,type,
mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Estring_2Echar: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,type,
mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(mono_2Ec_2EternaryComparisons_2Einvert__comparison,type,
mono_2Ec_2EternaryComparisons_2Einvert__comparison: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,type,
mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Etoto_2EnumOrd,type,
mono_2Ec_2Etoto_2EnumOrd: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2Enum__compare,type,
mono_2Ec_2EternaryComparisons_2Enum__compare: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2Estring__compare,type,
mono_2Ec_2EternaryComparisons_2Estring__compare: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Etoto_2Estringto,type,
mono_2Ec_2Etoto_2Estringto: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 ).
thf(mono_2Ec_2Ebool_2E_7E,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(i_mono_2Etyop_2Estring_2Echar,type,
i_mono_2Etyop_2Estring_2Echar: mono_2Etyop_2Estring_2Echar > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29: ( $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29: ( ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,type,
i_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(i_mono_2Etyop_2EternaryComparisons_2Eordering,type,
i_mono_2Etyop_2EternaryComparisons_2Eordering: mono_2Etyop_2EternaryComparisons_2Eordering > u ).
thf(i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,type,
i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(j_mono_2Etyop_2Estring_2Echar,type,
j_mono_2Etyop_2Estring_2Echar: du > mono_2Etyop_2Estring_2Echar ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29: du > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29: du > ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,type,
j_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2EternaryComparisons_2Eordering,type,
j_mono_2Etyop_2EternaryComparisons_2Eordering: du > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,type,
j_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: du > mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 ).
thf(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
thf(reserved_2Eho_2Ei__thm,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Ek__thm,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Es__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
thf(reserved_2Elogic_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(reserved_2Elogic_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(reserved_2Elogic_2E_7E,axiom,
! [V0: $o] :
( ( mono_2Ec_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ) ).
thf(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Estring_2Echar,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ ( j_mono_2Etyop_2Estring_2Echar @ ( s @ tyop_2Estring_2Echar @ V0_2E0 ) ) ) )
= ( s @ tyop_2Estring_2Echar @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
= ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ V0_2E0 ) ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 @ ( j_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 @ ( s @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ V0_2E0 ) ) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Estring_2Echar,axiom,
! [V0: mono_2Etyop_2Estring_2Echar] :
( ( j_mono_2Etyop_2Estring_2Echar @ ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29] :
( ( j_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 @ ( s @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 @ V0 ) ) )
= V0 ) ).
thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Epair_2ECURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Epair_2ECURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: d,A_27d: d,X0_2E0: u] :
( ( s @ A_27b @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ X0_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ A_27b ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ELIST__REL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Elist_2ELIST__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELLEX_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Elist_2ELLEX_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Elist_2ELLEX_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2EListOrd_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2EListOrd_2E1 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2EListOrd_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u] :
( ( s @ A_27c @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X0_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27c ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: d,A_27d: d,X0_2E0: u] :
( ( s @ A_27d @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ X0_2E0 ) ) )
= ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ A_27d ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2ETO_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( c_2Etoto_2ETO_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Etoto_2Etoto @ A_27a ) ) @ c_2Etoto_2ETO_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2ETO__inv_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__inv_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2ETO__inv_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2ETO__inv_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__inv_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2ETO__inv_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__of__LinearOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2ETO__of__LinearOrder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__of__LinearOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2ETO__of__LinearOrder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Etoto_2ETotOrd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Etoto_2ETotOrd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Etoto_2ETotOrd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ecomparison_2Eequiv__inj_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eequiv__inj_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Ecomparison_2Eequiv__inj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Eirreflexive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2Eirreflexive_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Etoto_2ElexTO_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ElexTO_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ c_2Etoto_2ElexTO_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2EternaryComparisons_2Elist__compare_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Elist__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Elist__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Elist__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Elist__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [A_27a: d,X0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ X0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ecomparison_2Eoption__cmp2_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Ecomparison_2Eoption__cmp2_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Ecomparison_2Eoption__cmp2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ecomparison_2Eoption__cmp2_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Ecomparison_2Eoption__cmp2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ecomparison_2Eoption__cmp2_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Ecomparison_2Eoption__cmp2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2EternaryComparisons_2Eoption__compare_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Eoption__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Eoption__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2EternaryComparisons_2Eoption__compare_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Eoption__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2EternaryComparisons_2Eoption__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Eoption__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2EternaryComparisons_2Eordering,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ c_2EternaryComparisons_2Eordering__CASE_2E0 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2EternaryComparisons_2Epair__compare_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Epair__compare_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ c_2EternaryComparisons_2Epair__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2EternaryComparisons_2Epair__compare_2E4_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Epair__compare_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X3_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ c_2EternaryComparisons_2Epair__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X3_2E0 ) ) ) ) ) ).
thf(arityeq4_2Ec_2EternaryComparisons_2Epair__compare_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Epair__compare_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ X3_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ c_2EternaryComparisons_2Epair__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ X3_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ecomparison_2Eresp__equiv_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eresp__equiv_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ecomparison_2Eresp__equiv_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ecomparison_2Eresp__equiv2_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eresp__equiv2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Ecomparison_2Eresp__equiv2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ecomparison_2Eresp__equiv2_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eresp__equiv2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Ecomparison_2Eresp__equiv2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2Etransitive_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2Etransitive_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Estring_2Echar] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o,V1: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o,V1: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering,V2: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Etoto_2Eapto_2E0_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2Eapto_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Etoto_2Eapto_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ V0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2Eapto_2E1 @ ( s @ ( tyop_2Etoto_2Etoto @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ecomparison_2Egood__cmp_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Emin_2Ebool ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ecomparison_2Egood__cmp_2E0_2Emono_2Etyop_2Estring_2Echar,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Estring_2Echar ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Estring_2Echar @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ecomparison_2Egood__cmp_2E0_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ecomparison_2Egood__cmp_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecomparison_2Egood__cmp_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Elist__compare_2E0_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Elist__compare_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Elist__compare_2E1_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar @ V0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Elist__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Eordering__CASE_2E0_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ c_2EternaryComparisons_2Eordering__CASE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering,V2: mono_2Etyop_2EternaryComparisons_2Eordering,V3: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering @ V0 @ V1 @ V2 @ V3 ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V2 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V3 ) ) ) ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Estring_2Echar] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o,V1: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o,V1: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Ecomparison_2Egood__cmp__def,axiom,
! [A_27a: d,V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
<=> ( ! [V1x_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ! [V2x_2E0: u,V3y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
& ! [V4x_2E0: u,V5y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V5y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER )
<=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V5y_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
& ! [V6x_2E0: u,V7y_2E0: u,V8z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27a @ V7y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V7y_2E0 ) ) ) @ ( s @ A_27a @ V8z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27a @ V8z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
& ! [V9x_2E0: u,V10y_2E0: u,V11z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) ) ) @ ( s @ A_27a @ V10y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V10y_2E0 ) ) ) @ ( s @ A_27a @ V11z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) ) ) @ ( s @ A_27a @ V11z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
& ! [V12x_2E0: u,V13y_2E0: u,V14z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V12x_2E0 ) ) ) @ ( s @ A_27a @ V13y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V13y_2E0 ) ) ) @ ( s @ A_27a @ V14z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V12x_2E0 ) ) ) @ ( s @ A_27a @ V14z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
& ! [V15x_2E0: u,V16y_2E0: u,V17z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V15x_2E0 ) ) ) @ ( s @ A_27a @ V16y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V16y_2E0 ) ) ) @ ( s @ A_27a @ V17z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V15x_2E0 ) ) ) @ ( s @ A_27a @ V17z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) ) ) ) ).
thf(thm_2Ecomparison_2Eresp__equiv__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0cmp_2E0: u,V1f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eresp__equiv_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V1f_2E0 ) ) ) )
<=> ! [V2k1_2E0: u,V3k2_2E0: u,V4v_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2k1_2E0 ) ) ) @ ( s @ A_27a @ V3k2_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2k1_2E0 ) ) ) @ ( s @ A_27b @ V4v_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V3k2_2E0 ) ) ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Eresp__equiv2__def,axiom,
! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1cmp2_2E0: u,V2f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eresp__equiv2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) )
<=> ! [V3k1_2E0: u,V4k2_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3k1_2E0 ) ) ) @ ( s @ A_27a @ V4k2_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V3k1_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V4k2_2E0 ) ) ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) ) ) ).
thf(thm_2Ecomparison_2Eequiv__inj__def,axiom,
! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1cmp2_2E0: u,V2f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eequiv__inj_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) )
<=> ! [V3k1_2E0: u,V4k2_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V3k1_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V4k2_2E0 ) ) ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3k1_2E0 ) ) ) @ ( s @ A_27a @ V4k2_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) ) ) ).
thf(thm_2Ecomparison_2Egood__cmp__thm,axiom,
! [A_27a: d,V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
<=> ( ! [V1x_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ! [V2x_2E0: u,V3y_2E0: u,V4z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER )
<=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
& ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) @ ( s @ A_27a @ V4z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V4z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
& ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) @ ( s @ A_27a @ V4z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V4z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) ) ) ) ) ).
thf(thm_2Ecomparison_2Ecmp__thms,axiom,
! [A_27a: d] :
( ( (~) @ ( mono_2Ec_2EternaryComparisons_2ELESS = mono_2Ec_2EternaryComparisons_2EEQUAL ) )
& ( (~) @ ( mono_2Ec_2EternaryComparisons_2ELESS = mono_2Ec_2EternaryComparisons_2EGREATER ) )
& ( (~) @ ( mono_2Ec_2EternaryComparisons_2EEQUAL = mono_2Ec_2EternaryComparisons_2EGREATER ) )
& ! [V0v0_2E0: u,V1v1_2E0: u,V2v2_2E0: u] :
( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2ELESS ) ) @ ( s @ A_27a @ V0v0_2E0 ) @ ( s @ A_27a @ V1v1_2E0 ) @ ( s @ A_27a @ V2v2_2E0 ) ) )
= ( s @ A_27a @ V0v0_2E0 ) )
& ! [V3v0_2E0: u,V4v1_2E0: u,V5v2_2E0: u] :
( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2EEQUAL ) ) @ ( s @ A_27a @ V3v0_2E0 ) @ ( s @ A_27a @ V4v1_2E0 ) @ ( s @ A_27a @ V5v2_2E0 ) ) )
= ( s @ A_27a @ V4v1_2E0 ) )
& ! [V6v0_2E0: u,V7v1_2E0: u,V8v2_2E0: u] :
( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) @ ( s @ A_27a @ V6v0_2E0 ) @ ( s @ A_27a @ V7v1_2E0 ) @ ( s @ A_27a @ V8v2_2E0 ) ) )
= ( s @ A_27a @ V8v2_2E0 ) )
& ! [V9a: mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V9a = mono_2Ec_2EternaryComparisons_2ELESS )
| ( V9a = mono_2Ec_2EternaryComparisons_2EEQUAL )
| ( V9a = mono_2Ec_2EternaryComparisons_2EGREATER ) )
& ! [V10cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) ) ) )
<=> ( ! [V11x_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V11x_2E0 ) ) ) @ ( s @ A_27a @ V11x_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ! [V12x_2E0: u,V13y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V12x_2E0 ) ) ) @ ( s @ A_27a @ V13y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V13y_2E0 ) ) ) @ ( s @ A_27a @ V12x_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
& ! [V14x_2E0: u,V15y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V14x_2E0 ) ) ) @ ( s @ A_27a @ V15y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER )
<=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V15y_2E0 ) ) ) @ ( s @ A_27a @ V14x_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
& ! [V16x_2E0: u,V17y_2E0: u,V18z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V16x_2E0 ) ) ) @ ( s @ A_27a @ V17y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V17y_2E0 ) ) ) @ ( s @ A_27a @ V18z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V16x_2E0 ) ) ) @ ( s @ A_27a @ V18z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
& ! [V19x_2E0: u,V20y_2E0: u,V21z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V19x_2E0 ) ) ) @ ( s @ A_27a @ V20y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V20y_2E0 ) ) ) @ ( s @ A_27a @ V21z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V19x_2E0 ) ) ) @ ( s @ A_27a @ V21z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
& ! [V22x_2E0: u,V23y_2E0: u,V24z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V22x_2E0 ) ) ) @ ( s @ A_27a @ V23y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V23y_2E0 ) ) ) @ ( s @ A_27a @ V24z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V22x_2E0 ) ) ) @ ( s @ A_27a @ V24z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
& ! [V25x_2E0: u,V26y_2E0: u,V27z_2E0: u] :
( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V25x_2E0 ) ) ) @ ( s @ A_27a @ V26y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V26y_2E0 ) ) ) @ ( s @ A_27a @ V27z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V10cmp_2E0 ) @ ( s @ A_27a @ V25x_2E0 ) ) ) @ ( s @ A_27a @ V27z_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp__def,axiom,
! [A_27a: d,A_27b: d,V0v3_2E0: u,V1v2_2E0: u,V2v1_2E0: u,V3v0_2E0: u,V4c_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V3v0_2E0 ) ) ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0v3_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2v1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V1v2_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ A_27a @ V2v1_2E0 ) ) ) @ ( s @ A_27b @ V1v2_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp2__ind,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ( ! [V1c_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [V2c_2E0: u,V3v0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V2c_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V3v0_2E0 ) ) ) ) ) )
& ! [V4c_2E0: u,V5v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5v3_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [V6c_2E0: u,V7v1_2E0: u,V8v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V6c_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7v1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V8v2_2E0 ) ) ) ) ) ) )
=> ! [V9v_2E0: u,V10v1_2E0: u,V11v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V9v_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10v1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V11v2_2E0 ) ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp2__def,axiom,
! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_27_2E0: u,V2x_2E0: u,V3cmp_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V1x_27_2E0 ) ) ) ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS )
& ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0y_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ V0y_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Epair__cmp__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0y_2E0: u,V1x_2E0: u,V2c2_2E0: u,V3c1_2E0: u] :
( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Epair__compare_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3c1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ V2c2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V1x_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V0y_2E0 ) ) ) )
= ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3c1_2E0 ) @ ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V1x_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V0y_2E0 ) ) ) ) ) ) @ mono_2Ec_2EternaryComparisons_2ELESS @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ V2c2_2E0 ) @ ( s @ A_27c @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V1x_2E0 ) ) ) ) ) @ ( s @ A_27d @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V0y_2E0 ) ) ) ) ) ) @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) ).
thf(thm_2Ecomparison_2Ebool__cmp__def,axiom,
( ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ mono_2Ec_2Ebool_2ET @ mono_2Ec_2Ebool_2ET )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ mono_2Ec_2Ebool_2EF @ mono_2Ec_2Ebool_2EF )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
& ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ mono_2Ec_2Ebool_2ET @ mono_2Ec_2Ebool_2EF )
= mono_2Ec_2EternaryComparisons_2EGREATER )
& ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ mono_2Ec_2Ebool_2EF @ mono_2Ec_2Ebool_2ET )
= mono_2Ec_2EternaryComparisons_2ELESS ) ) ).
thf(thm_2Ecomparison_2Enum__cmp__def,axiom,
! [F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V0n1: mono_2Etyop_2Enum_2Enum,V1n2: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V0n1 @ V1n2 )
<=> ( V0n1 = V1n2 ) )
=> ! [V0n1: mono_2Etyop_2Enum_2Enum,V1n2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2EternaryComparisons_2Enum__compare @ V0n1 @ V1n2 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering @ ( F0 @ V0n1 @ V1n2 ) @ mono_2Ec_2EternaryComparisons_2EEQUAL @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n1 @ V1n2 ) @ mono_2Ec_2EternaryComparisons_2ELESS @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) ) ) ).
thf(thm_2Ecomparison_2Echar__cmp__def,axiom,
! [V0c1: mono_2Etyop_2Estring_2Echar,V1c2: mono_2Etyop_2Estring_2Echar] :
( ( mono_2Ec_2EternaryComparisons_2Echar__compare @ V0c1 @ V1c2 )
= ( mono_2Ec_2EternaryComparisons_2Enum__compare @ ( mono_2Ec_2Estring_2EORD @ V0c1 ) @ ( mono_2Ec_2Estring_2EORD @ V1c2 ) ) ) ).
thf(thm_2Ecomparison_2Estring__cmp__def,axiom,
( mono_2Ec_2EternaryComparisons_2Estring__compare
= ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar @ mono_2Ec_2EternaryComparisons_2Echar__compare ) ) ).
thf(thm_2Ecomparison_2ETotOrder__imp__good__cmp,axiom,
! [A_27a: d,V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) ) ) ).
thf(thm_2Ecomparison_2ETO__inv__invert,axiom,
! [A_27a: d,V0c_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__inv_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Epair_2ECURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ mono_2Ec_2EternaryComparisons_2Einvert__comparison ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp2__TO__inv,axiom,
! [A_27a: d,V0c_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Ecomparison_2Eoption__cmp2_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__inv_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Eoption__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__inv_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Elist__cmp__ListOrd,axiom,
! [A_27a: d,V0c_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Elist__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2EListOrd_2E1 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( c_2Etoto_2ETO_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2ETotOrd__list__cmp,axiom,
! [A_27a: d,V0c_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Elist__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Epair__cmp__lexTO,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1V_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0R_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etoto_2ETotOrd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1V_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Epair__compare_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1V_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ElexTO_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1V_2E0 ) ) ) ) ) ).
thf(thm_2Ecomparison_2Enum__cmp__numOrd,axiom,
mono_2Ec_2EternaryComparisons_2Enum__compare = mono_2Ec_2Etoto_2EnumOrd ).
thf(thm_2Ecomparison_2Echar__cmp__charOrd,axiom,
mono_2Ec_2EternaryComparisons_2Echar__compare = mono_2Ec_2Etoto_2EcharOrd ).
thf(thm_2Ecomparison_2Estring__cmp__stringto,axiom,
( mono_2Ec_2EternaryComparisons_2Estring__compare
= ( mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ mono_2Ec_2Etoto_2Estringto ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp__good,axiom,
! [A_27a: d,V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Eoption__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp2__good,axiom,
! [A_27a: d,V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Ecomparison_2Eoption__cmp2_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Elist__cmp__good,axiom,
! [A_27a: d,V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Elist__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Epair__cmp__good,axiom,
! [A_27a: d,A_27b: d,V0cmp1_2E0: u,V1cmp2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Epair__compare_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Ebool__cmp__good,axiom,
mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Emin_2Ebool @ mono_2Ec_2EternaryComparisons_2Ebool__compare ).
thf(thm_2Ecomparison_2Enum__cmp__good,axiom,
mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2EternaryComparisons_2Enum__compare ).
thf(thm_2Ecomparison_2Echar__cmp__good,axiom,
mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Estring_2Echar @ mono_2Ec_2EternaryComparisons_2Echar__compare ).
thf(thm_2Ecomparison_2Estring__cmp__good,axiom,
mono_2Ec_2Ecomparison_2Egood__cmp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 @ mono_2Ec_2EternaryComparisons_2Estring__compare ).
thf(thm_2Ecomparison_2Elist__cmp__cong,axiom,
! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l1_2E0: u,V2l2_2E0: u,V3cmp_27_2E0: u,V4l1_27_2E0: u,V5l2_27_2E0: u] :
( ( ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l1_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l1_27_2E0 ) )
& ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l2_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V5l2_27_2E0 ) )
& ! [V6x_2E0: u,V7x_27_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l1_27_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V7x_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V5l2_27_2E0 ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27b @ V7x_27_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_27_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27b @ V7x_27_2E0 ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_27_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l1_27_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V5l2_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp__cong,axiom,
! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1v1_2E0: u,V2v2_2E0: u,V3cmp_27_2E0: u,V4v1_27_2E0: u,V5v2_27_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1v1_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V4v1_27_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2v2_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V5v2_27_2E0 ) )
& ! [V6x_2E0: u,V7x_27_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V4v1_27_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V5v2_27_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V7x_27_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27b @ V7x_27_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_27_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27b @ V7x_27_2E0 ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1v1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2v2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_27_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V4v1_27_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V5v2_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp2__cong,axiom,
! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1v1_2E0: u,V2v2_2E0: u,V3cmp_27_2E0: u,V4v1_27_2E0: u,V5v2_27_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1v1_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V4v1_27_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2v2_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V5v2_27_2E0 ) )
& ! [V6x_2E0: u,V7x_27_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V4v1_27_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V5v2_27_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V7x_27_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27b @ V7x_27_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_27_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27b @ V7x_27_2E0 ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1v1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2v2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_27_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V4v1_27_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V5v2_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Epair__cmp__cong,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0cmp1_2E0: u,V1cmp2_2E0: u,V2v1_2E0: u,V3v2_2E0: u,V4cmp1_27_2E0: u,V5cmp2_27_2E0: u,V6v1_27_2E0: u,V7v2_27_2E0: u] :
( ( ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V2v1_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V6v1_27_2E0 ) )
& ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V3v2_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V7v2_27_2E0 ) )
& ! [V8a_2E0: u,V9b_2E0: u,V10c_2E0: u,V11d_2E0: u] :
( ( ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V6v1_27_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ A_27c @ V9b_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V7v2_27_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V10c_2E0 ) @ ( s @ A_27d @ V11d_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp1_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) ) ) @ ( s @ A_27b @ V10c_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4cmp1_27_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) ) ) @ ( s @ A_27b @ V10c_2E0 ) ) ) ) ) )
& ! [V12a_2E0: u,V13b_2E0: u,V14c_2E0: u,V15d_2E0: u] :
( ( ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V6v1_27_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V12a_2E0 ) @ ( s @ A_27c @ V13b_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V7v2_27_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V14c_2E0 ) @ ( s @ A_27d @ V15d_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) @ ( s @ A_27c @ V13b_2E0 ) ) ) @ ( s @ A_27d @ V15d_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ V5cmp2_27_2E0 ) @ ( s @ A_27c @ V13b_2E0 ) ) ) @ ( s @ A_27d @ V15d_2E0 ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Epair__compare_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V2v1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V3v2_2E0 ) ) ) )
= ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Epair__compare_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4cmp1_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ V5cmp2_27_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V6v1_27_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ V7v2_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Egood__cmp__trans,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V0cmp_2E0: u,V1k_2E0: u,V3k_27_2E0: u,V4v_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27a @ V3k_27_2E0 ) ) ) @ ( s @ A_27b @ V4v_27_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27a @ V3k_27_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ( ! [V0cmp_2E0: u,V1k_2E0: u,V2v_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27b @ V2v_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) )
=> ! [V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Egood__cmp__Less__trans,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0cmp_2E0: u,V1k_2E0: u,V2k_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27a @ V2k_27_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27a @ V2k_27_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ! [V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Egood__cmp__Less__irrefl__trans,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V0cmp_2E0: u,V3k_2E0: u,V4k_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3k_2E0 ) ) ) @ ( s @ A_27a @ V4k_27_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3k_2E0 ) ) ) @ ( s @ A_27a @ V4k_27_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ( ! [V0cmp_2E0: u,V1k_2E0: u,V2k_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27a @ V2k_27_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27a @ V2k_27_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) )
=> ! [V0cmp_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Eirreflexive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Ebool__cmp__antisym,axiom,
! [V0x: $o,V1y: $o] :
( ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ V0x @ V1y )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( V0x = V1y ) ) ).
thf(thm_2Ecomparison_2Enum__cmp__antisym,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2EternaryComparisons_2Enum__compare @ V0x @ V1y )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( V0x = V1y ) ) ).
thf(thm_2Ecomparison_2Echar__cmp__antisym,axiom,
! [V0x: mono_2Etyop_2Estring_2Echar,V1y: mono_2Etyop_2Estring_2Echar] :
( ( ( mono_2Ec_2EternaryComparisons_2Echar__compare @ V0x @ V1y )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( V0x = V1y ) ) ).
thf(thm_2Ecomparison_2Elist__cmp__antisym,axiom,
! [A_27a: d,V0cmp_2E0: u,V1x_2E0: u,V2y_2E0: u] :
( ! [V3x_2E0: u,V4y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V4y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ A_27a @ V3x_2E0 )
= ( s @ A_27a @ V4y_2E0 ) ) )
=> ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1x_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2y_2E0 ) ) ) ) ).
thf(thm_2Ecomparison_2Estring__cmp__antisym,axiom,
! [V0x: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,V1y: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29] :
( ( ( mono_2Ec_2EternaryComparisons_2Estring__compare @ V0x @ V1y )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( V0x = V1y ) ) ).
thf(thm_2Ecomparison_2Epair__cmp__antisym,axiom,
! [A_27a: d,A_27b: d,V0cmp1_2E0: u,V1cmp2_2E0: u,V2x_2E0: u,V3y_2E0: u] :
( ( ! [V4x_2E0: u,V5y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp1_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V5y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ A_27a @ V4x_2E0 )
= ( s @ A_27a @ V5y_2E0 ) ) )
& ! [V6x_2E0: u,V7y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) @ ( s @ A_27b @ V6x_2E0 ) ) ) @ ( s @ A_27b @ V7y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ A_27b @ V6x_2E0 )
= ( s @ A_27b @ V7y_2E0 ) ) ) )
=> ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Epair__compare_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V2x_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V2x_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3y_2E0 ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp__antisym,axiom,
! [A_27a: d,V0cmp_2E0: u,V1x_2E0: u,V2y_2E0: u] :
( ! [V3x_2E0: u,V4y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V4y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ A_27a @ V3x_2E0 )
= ( s @ A_27a @ V4y_2E0 ) ) )
=> ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V2y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V2y_2E0 ) ) ) ) ).
thf(thm_2Ecomparison_2Eoption__cmp2__antisym,axiom,
! [A_27a: d,V0cmp_2E0: u,V1x_2E0: u,V2y_2E0: u] :
( ! [V3x_2E0: u,V4y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V4y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ A_27a @ V3x_2E0 )
= ( s @ A_27a @ V4y_2E0 ) ) )
=> ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ecomparison_2Eoption__cmp2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V2y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V2y_2E0 ) ) ) ) ).
thf(thm_2Ecomparison_2Eantisym__resp__equiv,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0cmp_2E0: u,V1f_2E0: u] :
( ! [V2x_2E0: u,V3y_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( ( s @ A_27a @ V2x_2E0 )
= ( s @ A_27a @ V3y_2E0 ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eresp__equiv_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V1f_2E0 ) ) ) )
& ! [V4cmp2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Egood__cmp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ V4cmp2_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecomparison_2Eresp__equiv2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ tyop_2EternaryComparisons_2Eordering ) ) @ V4cmp2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V1f_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2Elist__cmp__equal__list__rel,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0cmp_2E0: u,V3x_2E0: u,V4y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27b @ V4y_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27b @ V4y_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) )
=> ! [V0cmp_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l2_2E0 ) ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ELIST__REL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l2_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecomparison_2ETO__of__LinearOrder__LLEX,axiom,
! [A_27a: d,V0R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Eirreflexive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__of__LinearOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Elist_2ELLEX_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Elist__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__of__LinearOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------