%------------------------------------------------------------------------------
% File     : ITP114^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : ringNorm.ax [Gau19]
%          : HL4114^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  491 ( 176 unt; 279 typ;   0 def)
%            Number of atoms       :  383 ( 314 equ;  11 cnn)
%            Maximal formula atoms :   20 (   0 avg)
%            Number of connectives : 11503 (  11   ~;  13   |;  90   &;11348   @)
%                                         (  17 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   5 avg;11348 nst)
%            Number of types       :    8 (   7 usr)
%            Number of type conns  :  466 ( 466   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  274 ( 272 usr; 102 con; 0-6 aty)
%            Number of variables   :  795 (   0   ^ 771   !;  24   ?; 795   :)
% 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_2Equote_2Eindex,type,
    mono_2Etyop_2Equote_2Eindex: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_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(tyop_2Ecanonical_2Ecanonical__sum,type,
    tyop_2Ecanonical_2Ecanonical__sum: d > d ).

thf(tyop_2Ecanonical_2Espolynom,type,
    tyop_2Ecanonical_2Espolynom: d > d ).

thf(tyop_2Eind__type_2Erecspace,type,
    tyop_2Eind__type_2Erecspace: d > d ).

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_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: d > d > d ).

thf(tyop_2Equote_2Eindex,type,
    tyop_2Equote_2Eindex: d ).

thf(tyop_2Equote_2Evarmap,type,
    tyop_2Equote_2Evarmap: d > d ).

thf(tyop_2Ering_2Ering,type,
    tyop_2Ering_2Ering: d > d ).

thf(tyop_2EringNorm_2Epolynom,type,
    tyop_2EringNorm_2Epolynom: d > d ).

thf(tyop_2Esemi__ring_2Esemi__ring,type,
    tyop_2Esemi__ring_2Esemi__ring: d > d ).

thf(tyop_2EternaryComparisons_2Eordering,type,
    tyop_2EternaryComparisons_2Eordering: 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_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: u ).

thf(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: du > 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_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: 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_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: u ).

thf(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

thf(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: du > u ).

thf(c_2Eind__type_2EBOTTOM_2E0,type,
    c_2Eind__type_2EBOTTOM_2E0: 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_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

thf(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: du > du > u ).

thf(c_2Eind__type_2ECONSTR_2E0,type,
    c_2Eind__type_2ECONSTR_2E0: u ).

thf(c_2Eind__type_2ECONSTR_2E3,type,
    c_2Eind__type_2ECONSTR_2E3: du > du > du > u ).

thf(c_2Ecanonical_2ECons__monom_2E0,type,
    c_2Ecanonical_2ECons__monom_2E0: u ).

thf(c_2Ecanonical_2ECons__monom_2E3,type,
    c_2Ecanonical_2ECons__monom_2E3: du > du > du > u ).

thf(c_2Ecanonical_2ECons__varlist_2E0,type,
    c_2Ecanonical_2ECons__varlist_2E0: u ).

thf(c_2Ecanonical_2ECons__varlist_2E2,type,
    c_2Ecanonical_2ECons__varlist_2E2: du > du > u ).

thf(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

thf(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: du > u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Eind__type_2EFCONS_2E0,type,
    c_2Eind__type_2EFCONS_2E0: u ).

thf(c_2Eind__type_2EFCONS_2E2,type,
    c_2Eind__type_2EFCONS_2E2: du > du > u ).

thf(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

thf(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

thf(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: du > u ).

thf(c_2Ecanonical_2ENil__monom_2E0,type,
    c_2Ecanonical_2ENil__monom_2E0: u ).

thf(c_2EringNorm_2EPconst_2E0,type,
    c_2EringNorm_2EPconst_2E0: u ).

thf(c_2EringNorm_2EPconst_2E1,type,
    c_2EringNorm_2EPconst_2E1: du > u ).

thf(c_2EringNorm_2EPmult_2E0,type,
    c_2EringNorm_2EPmult_2E0: u ).

thf(c_2EringNorm_2EPmult_2E2,type,
    c_2EringNorm_2EPmult_2E2: du > du > u ).

thf(c_2EringNorm_2EPopp_2E0,type,
    c_2EringNorm_2EPopp_2E0: u ).

thf(c_2EringNorm_2EPopp_2E1,type,
    c_2EringNorm_2EPopp_2E1: du > u ).

thf(c_2EringNorm_2EPplus_2E0,type,
    c_2EringNorm_2EPplus_2E0: u ).

thf(c_2EringNorm_2EPplus_2E2,type,
    c_2EringNorm_2EPplus_2E2: du > du > u ).

thf(c_2EringNorm_2EPvar_2E0,type,
    c_2EringNorm_2EPvar_2E0: u ).

thf(c_2EringNorm_2EPvar_2E1,type,
    c_2EringNorm_2EPvar_2E1: du > u ).

thf(c_2Ecanonical_2ESPconst_2E0,type,
    c_2Ecanonical_2ESPconst_2E0: u ).

thf(c_2Ecanonical_2ESPconst_2E1,type,
    c_2Ecanonical_2ESPconst_2E1: du > u ).

thf(c_2Ecanonical_2ESPmult_2E0,type,
    c_2Ecanonical_2ESPmult_2E0: u ).

thf(c_2Ecanonical_2ESPmult_2E2,type,
    c_2Ecanonical_2ESPmult_2E2: du > du > u ).

thf(c_2Ecanonical_2ESPplus_2E0,type,
    c_2Ecanonical_2ESPplus_2E0: u ).

thf(c_2Ecanonical_2ESPplus_2E2,type,
    c_2Ecanonical_2ESPplus_2E2: du > du > u ).

thf(c_2Ecanonical_2ESPvar_2E0,type,
    c_2Ecanonical_2ESPvar_2E0: u ).

thf(c_2Ecanonical_2ESPvar_2E1,type,
    c_2Ecanonical_2ESPvar_2E1: du > u ).

thf(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: u ).

thf(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).

thf(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: 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_2Ecanonical_2Ecanonical__sum__merge_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__merge_2E0: u ).

thf(c_2Ecanonical_2Ecanonical__sum__merge_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__merge_2E1: du > u ).

thf(c_2Ecanonical_2Ecanonical__sum__prod_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__prod_2E0: u ).

thf(c_2Ecanonical_2Ecanonical__sum__prod_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__prod_2E1: du > u ).

thf(c_2Ecanonical_2Ecanonical__sum__scalar_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__scalar_2E0: u ).

thf(c_2Ecanonical_2Ecanonical__sum__scalar_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__scalar_2E1: du > u ).

thf(c_2Ecanonical_2Ecanonical__sum__scalar2_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__scalar2_2E0: u ).

thf(c_2Ecanonical_2Ecanonical__sum__scalar2_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__scalar2_2E1: du > u ).

thf(c_2Ecanonical_2Ecanonical__sum__scalar3_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__scalar3_2E0: u ).

thf(c_2Ecanonical_2Ecanonical__sum__scalar3_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__scalar3_2E1: du > u ).

thf(c_2Ecanonical_2Ecanonical__sum__simplify_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__simplify_2E0: u ).

thf(c_2Ecanonical_2Ecanonical__sum__simplify_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__simplify_2E1: du > u ).

thf(c_2Ecanonical_2Eics__aux_2E0,type,
    c_2Ecanonical_2Eics__aux_2E0: u ).

thf(c_2Ecanonical_2Eics__aux_2E1,type,
    c_2Ecanonical_2Eics__aux_2E1: du > u ).

thf(c_2Equote_2Eindex__compare_2E0,type,
    c_2Equote_2Eindex__compare_2E0: u ).

thf(c_2Equote_2Eindex__lt_2E0,type,
    c_2Equote_2Eindex__lt_2E0: u ).

thf(c_2Equote_2Eindex__size_2E0,type,
    c_2Equote_2Eindex__size_2E0: u ).

thf(c_2Equote_2Eindex__size_2E1,type,
    c_2Equote_2Eindex__size_2E1: du > u ).

thf(c_2Ecanonical_2Einterp__cs_2E0,type,
    c_2Ecanonical_2Einterp__cs_2E0: u ).

thf(c_2Ecanonical_2Einterp__cs_2E1,type,
    c_2Ecanonical_2Einterp__cs_2E1: du > u ).

thf(c_2Ecanonical_2Einterp__m_2E0,type,
    c_2Ecanonical_2Einterp__m_2E0: u ).

thf(c_2Ecanonical_2Einterp__m_2E1,type,
    c_2Ecanonical_2Einterp__m_2E1: du > u ).

thf(c_2EringNorm_2Einterp__p_2E0,type,
    c_2EringNorm_2Einterp__p_2E0: u ).

thf(c_2EringNorm_2Einterp__p_2E3,type,
    c_2EringNorm_2Einterp__p_2E3: du > du > du > u ).

thf(c_2Ecanonical_2Einterp__sp_2E0,type,
    c_2Ecanonical_2Einterp__sp_2E0: u ).

thf(c_2Ecanonical_2Einterp__sp_2E1,type,
    c_2Ecanonical_2Einterp__sp_2E1: du > u ).

thf(c_2Ecanonical_2Einterp__vl_2E0,type,
    c_2Ecanonical_2Einterp__vl_2E0: u ).

thf(c_2Ecanonical_2Einterp__vl_2E1,type,
    c_2Ecanonical_2Einterp__vl_2E1: du > u ).

thf(c_2Ering_2Eis__ring_2E0,type,
    c_2Ering_2Eis__ring_2E0: u ).

thf(c_2Ering_2Eis__ring_2E1,type,
    c_2Ering_2Eis__ring_2E1: du > u ).

thf(c_2Ecanonical_2Eivl__aux_2E0,type,
    c_2Ecanonical_2Eivl__aux_2E0: u ).

thf(c_2Ecanonical_2Eivl__aux_2E1,type,
    c_2Ecanonical_2Eivl__aux_2E1: du > u ).

thf(c_2EternaryComparisons_2Elist__compare_2E0,type,
    c_2EternaryComparisons_2Elist__compare_2E0: u ).

thf(c_2EternaryComparisons_2Elist__compare_2E3,type,
    c_2EternaryComparisons_2Elist__compare_2E3: du > du > du > u ).

thf(c_2EternaryComparisons_2Elist__merge_2E0,type,
    c_2EternaryComparisons_2Elist__merge_2E0: u ).

thf(c_2EternaryComparisons_2Elist__merge_2E3,type,
    c_2EternaryComparisons_2Elist__merge_2E3: du > du > du > u ).

thf(c_2Ecanonical_2Emonom__insert_2E0,type,
    c_2Ecanonical_2Emonom__insert_2E0: u ).

thf(c_2Ecanonical_2Emonom__insert_2E1,type,
    c_2Ecanonical_2Emonom__insert_2E1: 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_2EringNorm_2Epolynom__CASE_2E0,type,
    c_2EringNorm_2Epolynom__CASE_2E0: u ).

thf(c_2EringNorm_2Epolynom__CASE_2E6,type,
    c_2EringNorm_2Epolynom__CASE_2E6: du > du > du > du > du > du > u ).

thf(c_2EringNorm_2Epolynom__normalize_2E0,type,
    c_2EringNorm_2Epolynom__normalize_2E0: u ).

thf(c_2EringNorm_2Epolynom__normalize_2E2,type,
    c_2EringNorm_2Epolynom__normalize_2E2: du > du > u ).

thf(c_2EringNorm_2Epolynom__simplify_2E0,type,
    c_2EringNorm_2Epolynom__simplify_2E0: u ).

thf(c_2EringNorm_2Epolynom__simplify_2E2,type,
    c_2EringNorm_2Epolynom__simplify_2E2: du > du > u ).

thf(c_2EringNorm_2Epolynom__size_2E0,type,
    c_2EringNorm_2Epolynom__size_2E0: u ).

thf(c_2EringNorm_2Epolynom__size_2E2,type,
    c_2EringNorm_2Epolynom__size_2E2: du > du > u ).

thf(c_2EringNorm_2Er__canonical__sum__merge_2E0,type,
    c_2EringNorm_2Er__canonical__sum__merge_2E0: u ).

thf(c_2EringNorm_2Er__canonical__sum__merge_2E1,type,
    c_2EringNorm_2Er__canonical__sum__merge_2E1: du > u ).

thf(c_2EringNorm_2Er__canonical__sum__merge_2E3,type,
    c_2EringNorm_2Er__canonical__sum__merge_2E3: du > du > du > u ).

thf(c_2EringNorm_2Er__canonical__sum__prod_2E0,type,
    c_2EringNorm_2Er__canonical__sum__prod_2E0: u ).

thf(c_2EringNorm_2Er__canonical__sum__prod_2E1,type,
    c_2EringNorm_2Er__canonical__sum__prod_2E1: du > u ).

thf(c_2EringNorm_2Er__canonical__sum__prod_2E3,type,
    c_2EringNorm_2Er__canonical__sum__prod_2E3: du > du > du > u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar_2E0,type,
    c_2EringNorm_2Er__canonical__sum__scalar_2E0: u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar_2E1,type,
    c_2EringNorm_2Er__canonical__sum__scalar_2E1: du > u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar_2E3,type,
    c_2EringNorm_2Er__canonical__sum__scalar_2E3: du > du > du > u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar2_2E0,type,
    c_2EringNorm_2Er__canonical__sum__scalar2_2E0: u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar2_2E1,type,
    c_2EringNorm_2Er__canonical__sum__scalar2_2E1: du > u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar2_2E3,type,
    c_2EringNorm_2Er__canonical__sum__scalar2_2E3: du > du > du > u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar3_2E0,type,
    c_2EringNorm_2Er__canonical__sum__scalar3_2E0: u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar3_2E1,type,
    c_2EringNorm_2Er__canonical__sum__scalar3_2E1: du > u ).

thf(c_2EringNorm_2Er__canonical__sum__scalar3_2E4,type,
    c_2EringNorm_2Er__canonical__sum__scalar3_2E4: du > du > du > du > u ).

thf(c_2EringNorm_2Er__canonical__sum__simplify_2E0,type,
    c_2EringNorm_2Er__canonical__sum__simplify_2E0: u ).

thf(c_2EringNorm_2Er__canonical__sum__simplify_2E1,type,
    c_2EringNorm_2Er__canonical__sum__simplify_2E1: du > u ).

thf(c_2EringNorm_2Er__canonical__sum__simplify_2E2,type,
    c_2EringNorm_2Er__canonical__sum__simplify_2E2: du > du > u ).

thf(c_2EringNorm_2Er__ics__aux_2E0,type,
    c_2EringNorm_2Er__ics__aux_2E0: u ).

thf(c_2EringNorm_2Er__ics__aux_2E1,type,
    c_2EringNorm_2Er__ics__aux_2E1: du > u ).

thf(c_2EringNorm_2Er__ics__aux_2E4,type,
    c_2EringNorm_2Er__ics__aux_2E4: du > du > du > du > u ).

thf(c_2EringNorm_2Er__interp__cs_2E0,type,
    c_2EringNorm_2Er__interp__cs_2E0: u ).

thf(c_2EringNorm_2Er__interp__cs_2E1,type,
    c_2EringNorm_2Er__interp__cs_2E1: du > u ).

thf(c_2EringNorm_2Er__interp__cs_2E3,type,
    c_2EringNorm_2Er__interp__cs_2E3: du > du > du > u ).

thf(c_2EringNorm_2Er__interp__m_2E0,type,
    c_2EringNorm_2Er__interp__m_2E0: u ).

thf(c_2EringNorm_2Er__interp__m_2E1,type,
    c_2EringNorm_2Er__interp__m_2E1: du > u ).

thf(c_2EringNorm_2Er__interp__m_2E4,type,
    c_2EringNorm_2Er__interp__m_2E4: du > du > du > du > u ).

thf(c_2EringNorm_2Er__interp__sp_2E0,type,
    c_2EringNorm_2Er__interp__sp_2E0: u ).

thf(c_2EringNorm_2Er__interp__sp_2E1,type,
    c_2EringNorm_2Er__interp__sp_2E1: du > u ).

thf(c_2EringNorm_2Er__interp__sp_2E3,type,
    c_2EringNorm_2Er__interp__sp_2E3: du > du > du > u ).

thf(c_2EringNorm_2Er__interp__vl_2E0,type,
    c_2EringNorm_2Er__interp__vl_2E0: u ).

thf(c_2EringNorm_2Er__interp__vl_2E1,type,
    c_2EringNorm_2Er__interp__vl_2E1: du > u ).

thf(c_2EringNorm_2Er__interp__vl_2E3,type,
    c_2EringNorm_2Er__interp__vl_2E3: du > du > du > u ).

thf(c_2EringNorm_2Er__ivl__aux_2E0,type,
    c_2EringNorm_2Er__ivl__aux_2E0: u ).

thf(c_2EringNorm_2Er__ivl__aux_2E1,type,
    c_2EringNorm_2Er__ivl__aux_2E1: du > u ).

thf(c_2EringNorm_2Er__ivl__aux_2E4,type,
    c_2EringNorm_2Er__ivl__aux_2E4: du > du > du > du > u ).

thf(c_2EringNorm_2Er__monom__insert_2E0,type,
    c_2EringNorm_2Er__monom__insert_2E0: u ).

thf(c_2EringNorm_2Er__monom__insert_2E1,type,
    c_2EringNorm_2Er__monom__insert_2E1: du > u ).

thf(c_2EringNorm_2Er__monom__insert_2E4,type,
    c_2EringNorm_2Er__monom__insert_2E4: du > du > du > du > u ).

thf(c_2EringNorm_2Er__spolynom__normalize_2E0,type,
    c_2EringNorm_2Er__spolynom__normalize_2E0: u ).

thf(c_2EringNorm_2Er__spolynom__normalize_2E1,type,
    c_2EringNorm_2Er__spolynom__normalize_2E1: du > u ).

thf(c_2EringNorm_2Er__spolynom__normalize_2E2,type,
    c_2EringNorm_2Er__spolynom__normalize_2E2: du > du > u ).

thf(c_2EringNorm_2Er__spolynom__simplify_2E0,type,
    c_2EringNorm_2Er__spolynom__simplify_2E0: u ).

thf(c_2EringNorm_2Er__spolynom__simplify_2E1,type,
    c_2EringNorm_2Er__spolynom__simplify_2E1: du > u ).

thf(c_2EringNorm_2Er__spolynom__simplify_2E2,type,
    c_2EringNorm_2Er__spolynom__simplify_2E2: du > du > u ).

thf(c_2EringNorm_2Er__varlist__insert_2E0,type,
    c_2EringNorm_2Er__varlist__insert_2E0: u ).

thf(c_2EringNorm_2Er__varlist__insert_2E1,type,
    c_2EringNorm_2Er__varlist__insert_2E1: du > u ).

thf(c_2EringNorm_2Er__varlist__insert_2E3,type,
    c_2EringNorm_2Er__varlist__insert_2E3: du > du > du > u ).

thf(c_2Ering_2Ering__R0_2E0,type,
    c_2Ering_2Ering__R0_2E0: u ).

thf(c_2Ering_2Ering__R0_2E1,type,
    c_2Ering_2Ering__R0_2E1: du > u ).

thf(c_2Ering_2Ering__R1_2E0,type,
    c_2Ering_2Ering__R1_2E0: u ).

thf(c_2Ering_2Ering__R1_2E1,type,
    c_2Ering_2Ering__R1_2E1: du > u ).

thf(c_2Ering_2Ering__RM_2E0,type,
    c_2Ering_2Ering__RM_2E0: u ).

thf(c_2Ering_2Ering__RM_2E3,type,
    c_2Ering_2Ering__RM_2E3: du > du > du > u ).

thf(c_2Ering_2Ering__RN_2E0,type,
    c_2Ering_2Ering__RN_2E0: u ).

thf(c_2Ering_2Ering__RN_2E2,type,
    c_2Ering_2Ering__RN_2E2: du > du > u ).

thf(c_2Ering_2Ering__RP_2E0,type,
    c_2Ering_2Ering__RP_2E0: u ).

thf(c_2Ering_2Ering__RP_2E3,type,
    c_2Ering_2Ering__RP_2E3: du > du > du > u ).

thf(c_2Ering_2Esemi__ring__of_2E0,type,
    c_2Ering_2Esemi__ring__of_2E0: u ).

thf(c_2Ering_2Esemi__ring__of_2E1,type,
    c_2Ering_2Esemi__ring__of_2E1: du > u ).

thf(c_2Ecanonical_2Espolynom__normalize_2E0,type,
    c_2Ecanonical_2Espolynom__normalize_2E0: u ).

thf(c_2Ecanonical_2Espolynom__normalize_2E1,type,
    c_2Ecanonical_2Espolynom__normalize_2E1: du > u ).

thf(c_2Ecanonical_2Espolynom__simplify_2E0,type,
    c_2Ecanonical_2Espolynom__simplify_2E0: u ).

thf(c_2Ecanonical_2Espolynom__simplify_2E1,type,
    c_2Ecanonical_2Espolynom__simplify_2E1: du > u ).

thf(c_2Ecanonical_2Evarlist__insert_2E0,type,
    c_2Ecanonical_2Evarlist__insert_2E0: u ).

thf(c_2Ecanonical_2Evarlist__insert_2E1,type,
    c_2Ecanonical_2Evarlist__insert_2E1: du > u ).

thf(c_2Equote_2Evarmap__find_2E0,type,
    c_2Equote_2Evarmap__find_2E0: u ).

thf(c_2Equote_2Evarmap__find_2E2,type,
    c_2Equote_2Evarmap__find_2E2: du > 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_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29: ( ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) > ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2E_2B,type,
    mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2E_2F_5C,type,
    mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(mono_2Ec_2Enum_2E0,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Equote_2Eindex,type,
    mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Equote_2Eindex: mono_2Etyop_2Equote_2Eindex ).

thf(mono_2Ec_2Earithmetic_2EBIT1,type,
    mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex,type,
    mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool: $o > $o ).

thf(mono_2Ec_2Ebool_2EF,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex,type,
    mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
    mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Enum_2ESUC,type,
    mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2ET,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(mono_2Ec_2Earithmetic_2EZERO,type,
    mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2E_5C_2F,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(mono_2Ec_2Equote_2Eindex__compare,type,
    mono_2Ec_2Equote_2Eindex__compare: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2Equote_2Eindex__lt,type,
    mono_2Ec_2Equote_2Eindex__lt: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ).

thf(mono_2Ec_2Equote_2Eindex__size,type,
    mono_2Ec_2Equote_2Eindex__size: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex,type,
    mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex,type,
    mono_2Ec_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_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_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_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29: ( ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Equote_2Eindex,type,
    i_mono_2Etyop_2Equote_2Eindex: mono_2Etyop_2Equote_2Eindex > u ).

thf(i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,type,
    i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_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(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

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_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29: du > ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29: du > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Equote_2Eindex,type,
    j_mono_2Etyop_2Equote_2Eindex: du > mono_2Etyop_2Equote_2Eindex ).

thf(j_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,type,
    j_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_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(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_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_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ ( j_mono_2Etyop_2Equote_2Eindex @ ( s @ tyop_2Equote_2Eindex @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Equote_2Eindex @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ 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(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_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_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex] :
      ( ( j_mono_2Etyop_2Equote_2Eindex @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_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(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_2Etyop_2Equote_2Eindex_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Equote_2Eindex,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X0 ) ) ) ) @ ( s @ A_27a @ 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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28A_27a_29,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Equote_2Eindex_2CA_27a_29,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) ) ) @ c_2Eind__type_2ECONSTR_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ecanonical_2ECons__monom_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,X2_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2Ecanonical_2ECons__monom_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecanonical_2ECons__varlist_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,X1_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2Ecanonical_2ECons__varlist_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Equote_2Eindex_2CA_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) ) ) @ c_2Eind__type_2EFCONS_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2EPconst_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ c_2EringNorm_2EPconst_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2EringNorm_2EPmult_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ c_2EringNorm_2EPmult_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2EPopp_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ c_2EringNorm_2EPopp_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2EringNorm_2EPplus_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ c_2EringNorm_2EPplus_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2EPvar_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Equote_2Eindex] :
      ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X0 ) ) ) )
      = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ c_2EringNorm_2EPvar_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2ESPconst_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ c_2Ecanonical_2ESPconst_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecanonical_2ESPmult_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ c_2Ecanonical_2ESPmult_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecanonical_2ESPplus_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ c_2Ecanonical_2ESPplus_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2ESPvar_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Equote_2Eindex] :
      ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X0 ) ) ) )
      = ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ c_2Ecanonical_2ESPvar_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Equote_2Eindex_2CA_27a_29_29_20mono_2Etyop_2EringNorm_2Epolynom_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__merge_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2Ecanonical_2Ecanonical__sum__merge_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__prod_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__prod_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2Ecanonical_2Ecanonical__sum__prod_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2Ecanonical_2Ecanonical__sum__scalar_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar2_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar2_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2Ecanonical_2Ecanonical__sum__scalar2_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar3_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar3_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) ) @ c_2Ecanonical_2Ecanonical__sum__scalar3_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__simplify_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2Ecanonical_2Ecanonical__sum__simplify_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Eics__aux_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ ( c_2Ecanonical_2Eics__aux_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) ) @ c_2Ecanonical_2Eics__aux_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Einterp__cs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) @ ( c_2Ecanonical_2Einterp__cs_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ c_2Ecanonical_2Einterp__cs_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Einterp__m_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( c_2Ecanonical_2Einterp__m_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) ) @ c_2Ecanonical_2Einterp__m_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Einterp__p_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27a ) ) ) @ c_2EringNorm_2Einterp__p_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Einterp__sp_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) @ ( c_2Ecanonical_2Einterp__sp_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) ) @ c_2Ecanonical_2Einterp__sp_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Einterp__vl_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( c_2Ecanonical_2Einterp__vl_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ c_2Ecanonical_2Einterp__vl_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Eis__ring_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Ering_2Eis__ring_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Eivl__aux_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( c_2Ecanonical_2Eivl__aux_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) ) @ c_2Ecanonical_2Eivl__aux_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Emonom__insert_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( c_2Ecanonical_2Emonom__insert_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) ) @ c_2Ecanonical_2Emonom__insert_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28A_27a_29,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2EternaryComparisons_2Eordering,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) ) @ c_2EternaryComparisons_2Eordering__CASE_2E0 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq6_2Ec_2EringNorm_2Epolynom__CASE_2E6_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u,X5_2E0: u] :
      ( ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ X3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ X4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ X5_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ A_27b ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ A_27b ) ) ) ) ) ) @ c_2EringNorm_2Epolynom__CASE_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ X4_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ X5_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2EringNorm_2Epolynom__normalize_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2EringNorm_2Epolynom__normalize_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2EringNorm_2Epolynom__simplify_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2EringNorm_2Epolynom__simplify_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2EringNorm_2Epolynom__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2EringNorm_2Epolynom__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__merge_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__merge_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Er__canonical__sum__merge_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__merge_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__prod_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__prod_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Er__canonical__sum__prod_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__prod_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__scalar_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__scalar_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Er__canonical__sum__scalar_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__scalar_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar2_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__scalar2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Er__canonical__sum__scalar2_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,X2_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__scalar2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar3_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__scalar3_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EringNorm_2Er__canonical__sum__scalar3_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,X3_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) ) @ c_2EringNorm_2Er__canonical__sum__scalar3_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X2 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__simplify_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2EringNorm_2Er__canonical__sum__simplify_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2EringNorm_2Er__canonical__sum__simplify_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2EringNorm_2Er__canonical__sum__simplify_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__ics__aux_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ ( c_2EringNorm_2Er__ics__aux_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) ) @ c_2EringNorm_2Er__ics__aux_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EringNorm_2Er__ics__aux_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ A_27a @ ( c_2EringNorm_2Er__ics__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) ) @ c_2EringNorm_2Er__ics__aux_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__interp__cs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) @ ( c_2EringNorm_2Er__interp__cs_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ c_2EringNorm_2Er__interp__cs_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Er__interp__cs_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__cs_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ c_2EringNorm_2Er__interp__cs_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__interp__m_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( c_2EringNorm_2Er__interp__m_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) ) @ c_2EringNorm_2Er__interp__m_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EringNorm_2Er__interp__m_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__m_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X3 ) ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) ) @ c_2EringNorm_2Er__interp__m_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X3 ) ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__interp__sp_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) @ ( c_2EringNorm_2Er__interp__sp_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) ) @ c_2EringNorm_2Er__interp__sp_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Er__interp__sp_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) ) @ c_2EringNorm_2Er__interp__sp_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__interp__vl_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( c_2EringNorm_2Er__interp__vl_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ c_2EringNorm_2Er__interp__vl_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Er__interp__vl_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__vl_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X2 ) ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ c_2EringNorm_2Er__interp__vl_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X2 ) ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__ivl__aux_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( c_2EringNorm_2Er__ivl__aux_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) ) @ c_2EringNorm_2Er__ivl__aux_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EringNorm_2Er__ivl__aux_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Equote_2Eindex,X3: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ A_27a @ ( c_2EringNorm_2Er__ivl__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X2 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X3 ) ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) ) @ c_2EringNorm_2Er__ivl__aux_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X2 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X3 ) ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__monom__insert_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( c_2EringNorm_2Er__monom__insert_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) ) @ c_2EringNorm_2Er__monom__insert_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EringNorm_2Er__monom__insert_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,X3_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) ) @ c_2EringNorm_2Er__monom__insert_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X2 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__spolynom__normalize_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2EringNorm_2Er__spolynom__normalize_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2EringNorm_2Er__spolynom__normalize_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2EringNorm_2Er__spolynom__normalize_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__spolynom__simplify_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2EringNorm_2Er__spolynom__simplify_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2EringNorm_2Er__spolynom__simplify_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2EringNorm_2Er__spolynom__simplify_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2EringNorm_2Er__spolynom__simplify_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2EringNorm_2Er__varlist__insert_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__varlist__insert_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__varlist__insert_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EringNorm_2Er__varlist__insert_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,X2_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__varlist__insert_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2EringNorm_2Er__varlist__insert_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__R0_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ A_27a ) @ c_2Ering_2Ering__R0_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__R1_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ A_27a ) @ c_2Ering_2Ering__R1_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ering_2Ering__RM_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_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 @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ering_2Ering__RM_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ering_2Ering__RN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__RN_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ c_2Ering_2Ering__RN_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ering_2Ering__RP_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_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 @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ering_2Ering__RP_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Esemi__ring__of_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ c_2Ering_2Esemi__ring__of_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Espolynom__normalize_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2Ecanonical_2Espolynom__normalize_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2Ecanonical_2Espolynom__normalize_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Espolynom__simplify_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2Ecanonical_2Espolynom__simplify_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ c_2Ecanonical_2Espolynom__simplify_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecanonical_2Evarlist__insert_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Evarlist__insert_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ c_2Ecanonical_2Evarlist__insert_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Equote_2Evarmap__find_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Equote_2Eindex,X1_2E0: u] :
      ( ( s @ A_27a @ ( c_2Equote_2Evarmap__find_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X0 ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ A_27a ) ) @ c_2Equote_2Evarmap__find_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ X0 ) ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_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_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V1: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V1: mono_2Etyop_2Equote_2Eindex] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ V0 ) ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Equote_2Eindex] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_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_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EARB_2E0_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ( ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Equote_2Eindex ) )
    = ( s @ tyop_2Equote_2Eindex @ c_2Ebool_2EARB_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29 @ mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ c_2Elist_2ECONS_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EDATATYPE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) )
    = ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ c_2Elist_2ENIL_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Elist__compare_2E0_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Elist__compare_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ V0 @ V1 @ V2 ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Elist__merge_2E0_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_29 @ mono_2Ec_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ c_2EternaryComparisons_2Elist__merge_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Elist__merge_2E3_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex @ V0 @ V1 @ V2 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( c_2EternaryComparisons_2Elist__merge_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2 ) ) ) ) ) ).

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_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V1: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V1: mono_2Etyop_2Equote_2Eindex] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Equote_2Eindex] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2EringNorm_2Er__interp__sp__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) @ ( c_2EringNorm_2Er__interp__sp_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27a ) ) @ ( c_2Ecanonical_2Einterp__sp_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__spolynom__simplify__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2EringNorm_2Er__spolynom__simplify_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2Ecanonical_2Espolynom__simplify_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__spolynom__normalize__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2Ecanonical_2Espolynom__normalize_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__interp__cs__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) @ ( c_2EringNorm_2Er__interp__cs_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) @ ( c_2Ecanonical_2Einterp__cs_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__ics__aux__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ ( c_2EringNorm_2Er__ics__aux_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27a ) ) ) @ ( c_2Ecanonical_2Eics__aux_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__interp__m__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( c_2EringNorm_2Er__interp__m_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( c_2Ecanonical_2Einterp__m_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__interp__vl__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( c_2EringNorm_2Er__interp__vl_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) @ ( c_2Ecanonical_2Einterp__vl_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__ivl__aux__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( c_2EringNorm_2Er__ivl__aux_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Equote_2Evarmap @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ A_27a ) ) ) @ ( c_2Ecanonical_2Eivl__aux_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__canonical__sum__simplify__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__canonical__sum__prod__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__prod_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__canonical__sum__scalar3__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar3_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__canonical__sum__scalar2__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar2_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__canonical__sum__scalar__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__scalar_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__varlist__insert__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__varlist__insert_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Evarlist__insert_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__monom__insert__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( c_2EringNorm_2Er__monom__insert_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) ) @ ( c_2Ecanonical_2Emonom__insert_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Er__canonical__sum__merge__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__TY__DEF,axiom,
    ! [A_27a: d,F5_2E0: u,F4_2E0: u,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V15n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F5_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V15n ) ) ) )
          = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
     => ( ! [V13n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F4_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V13n ) ) ) )
            = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
       => ( ! [V10n: mono_2Etyop_2Enum_2Enum] :
              ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10n ) ) ) )
              = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
         => ( ! [V7n: mono_2Etyop_2Enum_2Enum] :
                ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7n ) ) ) )
                = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
           => ( ! [V5n: mono_2Etyop_2Enum_2Enum] :
                  ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5n ) ) ) )
                  = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
             => ( ! [V1a0_27_2E0: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V1a0_27_2E0 ) ) ) )
                  <=> ! [V2_27polynom_27_2E0: u] :
                        ( ! [V3a0_27_2E0: u] :
                            ( ( ? [V4a: mono_2Etyop_2Equote_2Eindex] :
                                  ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V3a0_27_2E0 )
                                  = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V4a ) ) @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F1_2E0 ) ) ) )
                              | ? [V6a_2E0: u] :
                                  ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V3a0_27_2E0 )
                                  = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Equote_2Eindex ) ) @ ( s @ A_27a @ V6a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F2_2E0 ) ) ) )
                              | ? [V8a0_2E0: u,V9a1_2E0: u] :
                                  ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V3a0_27_2E0 )
                                    = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Equote_2Eindex ) ) @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V8a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V9a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F3_2E0 ) ) ) ) ) ) ) )
                                  & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V2_27polynom_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V8a0_2E0 ) ) ) )
                                  & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V2_27polynom_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V9a1_2E0 ) ) ) ) )
                              | ? [V11a0_2E0: u,V12a1_2E0: u] :
                                  ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V3a0_27_2E0 )
                                    = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Equote_2Eindex ) ) @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V11a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V12a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F4_2E0 ) ) ) ) ) ) ) )
                                  & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V2_27polynom_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V11a0_2E0 ) ) ) )
                                  & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V2_27polynom_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V12a1_2E0 ) ) ) ) )
                              | ? [V14a_2E0: u] :
                                  ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V3a0_27_2E0 )
                                    = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Equote_2Eindex ) ) @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V14a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ F5_2E0 ) ) ) ) ) )
                                  & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V2_27polynom_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V14a_2E0 ) ) ) ) ) )
                           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V2_27polynom_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V3a0_27_2E0 ) ) ) ) )
                       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V2_27polynom_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V1a0_27_2E0 ) ) ) ) ) )
               => ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ V0rep_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__case__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0a: mono_2Etyop_2Equote_2Eindex,V1f_2E0: u,V2f1_2E0: u,V3f2_2E0: u,V4f3_2E0: u,V5f4_2E0: u] :
          ( ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V0a ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V3f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V4f3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5f4_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V1f_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V0a ) ) ) ) )
      & ! [V6a_2E0: u,V7f_2E0: u,V8f1_2E0: u,V9f2_2E0: u,V10f3_2E0: u,V11f4_2E0: u] :
          ( ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V6a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V7f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V8f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V9f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V10f3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V11f4_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V8f1_2E0 ) @ ( s @ A_27a @ V6a_2E0 ) ) ) )
      & ! [V12a0_2E0: u,V13a1_2E0: u,V14f_2E0: u,V15f1_2E0: u,V16f2_2E0: u,V17f3_2E0: u,V18f4_2E0: u] :
          ( ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V14f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V15f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V16f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V17f3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V18f4_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V16f2_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12a0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13a1_2E0 ) ) ) )
      & ! [V19a0_2E0: u,V20a1_2E0: u,V21f_2E0: u,V22f1_2E0: u,V23f2_2E0: u,V24f3_2E0: u,V25f4_2E0: u] :
          ( ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V19a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V20a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V21f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V23f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V24f3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V25f4_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V24f3_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V19a0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V20a1_2E0 ) ) ) )
      & ! [V26a_2E0: u,V27f_2E0: u,V28f1_2E0: u,V29f2_2E0: u,V30f3_2E0: u,V31f4_2E0: u] :
          ( ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V26a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V27f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V28f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V29f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V30f3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V31f4_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V31f4_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V26a_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__size__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u,V1a: mono_2Etyop_2Equote_2Eindex] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1a ) ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Equote_2Eindex__size @ V1a ) ) )
      & ! [V2f_2E0: u,V3a_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V2f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V2f_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) )
      & ! [V4f_2E0: u,V5a0_2E0: u,V6a1_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6a1_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5a0_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6a1_2E0 ) ) ) ) ) ) )
      & ! [V7f_2E0: u,V8a0_2E0: u,V9a1_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V7f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9a1_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V7f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8a0_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V7f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9a1_2E0 ) ) ) ) ) ) )
      & ! [V10f_2E0: u,V11a_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V10f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11a_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2EringNorm_2Epolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V10f_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11a_2E0 ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__normalize__def,axiom,
    ! [A_27a: d] :
      ( ! [V0r_2E0: u,V1i: mono_2Etyop_2Equote_2Eindex] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1i ) ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex @ V1i @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) )
      & ! [V2r_2E0: u,V3c_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V2r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V3c_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V3c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) )
      & ! [V4r_2E0: u,V5pl_2E0: u,V6pr_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V4r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5pl_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6pr_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V4r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V4r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5pl_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V4r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6pr_2E0 ) ) ) ) ) )
      & ! [V7r_2E0: u,V8pl_2E0: u,V9pr_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V7r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8pl_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9pr_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V7r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V7r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8pl_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V7r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9pr_2E0 ) ) ) ) ) )
      & ! [V10r_2E0: u,V11p_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11p_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RN_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11p_2E0 ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__simplify__def,axiom,
    ! [A_27a: d,V0r_2E0: u,V1x_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V1x_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V1x_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Einterp__p__def,axiom,
    ! [A_27a: d] :
      ( ! [V0r_2E0: u,V1vm_2E0: u,V2c_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V2c_2E0 ) ) ) ) )
          = ( s @ A_27a @ V2c_2E0 ) )
      & ! [V3r_2E0: u,V4vm_2E0: u,V5i: mono_2Etyop_2Equote_2Eindex] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V3r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V5i ) ) ) ) ) )
          = ( s @ A_27a @ ( c_2Equote_2Evarmap__find_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V5i ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) ) ) )
      & ! [V6r_2E0: u,V7vm_2E0: u,V8p1_2E0: u,V9p2_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8p1_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9p2_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8p1_2E0 ) ) ) @ ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9p2_2E0 ) ) ) ) ) )
      & ! [V10r_2E0: u,V11vm_2E0: u,V12p1_2E0: u,V13p2_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V11vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12p1_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13p2_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V11vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12p1_2E0 ) ) ) @ ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V11vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13p2_2E0 ) ) ) ) ) )
      & ! [V14r_2E0: u,V15vm_2E0: u,V16p1_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V14r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V15vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V16p1_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RN_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V14r_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V14r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V15vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V16p1_2E0 ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Einterp__sp__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1vm_2E0: u,V2c_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V2c_2E0 ) ) ) ) )
          = ( s @ A_27a @ V2c_2E0 ) )
      & ! [V3vm_2E0: u,V4i: mono_2Etyop_2Equote_2Eindex] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V4i ) ) ) ) ) )
          = ( s @ A_27a @ ( c_2Equote_2Evarmap__find_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V4i ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) ) ) )
      & ! [V5vm_2E0: u,V6p1_2E0: u,V7p2_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V5vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6p1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V7p2_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V5vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6p1_2E0 ) ) ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V5vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V7p2_2E0 ) ) ) ) ) )
      & ! [V8vm_2E0: u,V9p1_2E0: u,V10p2_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V8vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9p1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10p2_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V8vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9p1_2E0 ) ) ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__interp__sp_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V8vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10p2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Ecanonical__sum__merge__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1t2_2E0: u,V2t1_2E0: u,V3l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V5c2_2E0: u,V6c1_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V6c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V5c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V4l1 @ V3l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V6c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V5c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V6c1_2E0 ) @ ( s @ A_27a @ V5c2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V5c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V6c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) ) ) ) )
      & ! [V7t2_2E0: u,V8t1_2E0: u,V9l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V10l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V11c1_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V11c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V10l1 @ V9l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V11c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V11c1_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V11c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) ) )
      & ! [V12t2_2E0: u,V13t1_2E0: u,V14l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V15l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V16c2_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V15l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V16c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V14l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V12t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V15l1 @ V14l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V15l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V16c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V14l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V12t2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V16c2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V15l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V12t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V16c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V14l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V15l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V12t2_2E0 ) ) ) ) ) ) ) )
      & ! [V17t2_2E0: u,V18t1_2E0: u,V19l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V20l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V20l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V19l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V17t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V20l1 @ V19l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V20l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V19l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V17t2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V20l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V17t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V19l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V20l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V17t2_2E0 ) ) ) ) ) ) ) )
      & ! [V21s1_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V21s1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V21s1_2E0 ) )
      & ! [V22v6_2E0: u,V23v5: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V24v4_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V24v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V23v5 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V22v6_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V24v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V23v5 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V22v6_2E0 ) ) ) )
      & ! [V25v8_2E0: u,V26v7: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V26v7 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V25v8_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V26v7 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V25v8_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Emonom__insert__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1t2_2E0: u,V2l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4c2_2E0: u,V5c1_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V5c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V4c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V3l1 @ V2l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V5c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V4c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V5c1_2E0 ) @ ( s @ A_27a @ V4c2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V4c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V5c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) ) ) ) )
      & ! [V6t2_2E0: u,V7l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V9c1_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V9c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V8l1 @ V7l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V9c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V9c1_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V9c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t2_2E0 ) ) ) ) ) ) ) )
      & ! [V10l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V11c1_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V11c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V11c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Evarlist__insert__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1t2_2E0: u,V2l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4c2_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__varlist__insert_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V4c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V3l1 @ V2l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V4c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V4c2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V4c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__varlist__insert_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t2_2E0 ) ) ) ) ) ) ) )
      & ! [V5t2_2E0: u,V6l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__varlist__insert_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V7l1 @ V6l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__varlist__insert_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t2_2E0 ) ) ) ) ) ) ) )
      & ! [V8l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__varlist__insert_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Ecanonical__sum__scalar__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1c0_2E0: u,V2c_2E0: u,V3l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4t_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1c0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V2c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1c0_2E0 ) @ ( s @ A_27a @ V2c_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1c0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t_2E0 ) ) ) ) ) )
      & ! [V5c0_2E0: u,V6l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7t_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V5c0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V5c0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V5c0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t_2E0 ) ) ) ) ) )
      & ! [V8c0_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V8c0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ).

thf(thm_2EringNorm_2Ecanonical__sum__scalar2__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V2c_2E0: u,V3l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4t_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V2c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__lt @ V1l0 @ V3l ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t_2E0 ) ) ) ) ) )
      & ! [V5l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V6l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7t_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V5l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__varlist__insert_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__lt @ V5l0 @ V6l ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V5l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t_2E0 ) ) ) ) ) )
      & ! [V8l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ).

thf(thm_2EringNorm_2Ecanonical__sum__scalar3__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1c0_2E0: u,V2l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3c_2E0: u,V4l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V5t_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1c0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V3c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1c0_2E0 ) @ ( s @ A_27a @ V3c_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__lt @ V2l0 @ V4l ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1c0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t_2E0 ) ) ) ) ) )
      & ! [V6c0_2E0: u,V7l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V9t_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V6c0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V9t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__monom__insert_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V6c0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__lt @ V7l0 @ V8l ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V6c0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V9t_2E0 ) ) ) ) ) )
      & ! [V10c0_2E0: u,V11l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V10c0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V11l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ).

thf(thm_2EringNorm_2Ecanonical__sum__prod__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1c1_2E0: u,V2l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3t1_2E0: u,V4s2_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V1c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4s2_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4s2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4s2_2E0 ) ) ) ) ) )
      & ! [V5l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V6t1_2E0: u,V7s2_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V5l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7s2_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V5l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7s2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7s2_2E0 ) ) ) ) ) )
      & ! [V8s2_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8s2_2E0 ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ).

thf(thm_2EringNorm_2Ecanonical__sum__simplify__def,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1c_2E0: u,V0r_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ A_27a @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V1c_2E0 )
            = ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) )
     => ( ! [V1c_2E0: u,V0r_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
          <=> ( ( s @ A_27a @ V1c_2E0 )
              = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) )
       => ! [V0r_2E0: u] :
            ( ! [V1c_2E0: u,V2l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3t_2E0: u] :
                ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V1c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3t_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ A_27a @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3t_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V1c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3t_2E0 ) ) ) ) ) ) ) ) ) )
            & ! [V4l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V5t_2E0: u] :
                ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t_2E0 ) ) ) ) ) )
            & ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
              = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Eivl__aux__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1vm_2E0: u,V2x: mono_2Etyop_2Equote_2Eindex] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__ivl__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V2x ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) ) ) )
          = ( s @ A_27a @ ( c_2Equote_2Evarmap__find_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V2x ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) ) ) )
      & ! [V3vm_2E0: u,V4x: mono_2Etyop_2Equote_2Eindex,V5x_27: mono_2Etyop_2Equote_2Eindex,V6t_27: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__ivl__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V4x ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex @ V5x_27 @ V6t_27 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Equote_2Evarmap__find_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V4x ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) ) ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__ivl__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V5x_27 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6t_27 ) ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Einterp__vl__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1vm_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__vl_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
      & ! [V2vm_2E0: u,V3x: mono_2Etyop_2Equote_2Eindex,V4t: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__vl_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V2vm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex @ V3x @ V4t ) ) ) ) )
          = ( s @ A_27a @ ( c_2EringNorm_2Er__ivl__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V2vm_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V3x ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4t ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Einterp__m__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1vm_2E0: u,V2c_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__m_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ A_27a @ V2c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) ) ) )
          = ( s @ A_27a @ V2c_2E0 ) )
      & ! [V3vm_2E0: u,V4c_2E0: u,V5x: mono_2Etyop_2Equote_2Eindex,V6t: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__m_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ A_27a @ V4c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex @ V5x @ V6t ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V4c_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__ivl__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V5x ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6t ) ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Eics__aux__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1vm_2E0: u,V2a_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__ics__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
          = ( s @ A_27a @ V2a_2E0 ) )
      & ! [V3vm_2E0: u,V4a_2E0: u,V5l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V6t_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__ics__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V5l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__ics__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__interp__vl_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V5l ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t_2E0 ) ) ) ) ) )
      & ! [V7vm_2E0: u,V8a_2E0: u,V9c_2E0: u,V10l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V11t_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__ics__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V9c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V11t_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__ics__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__interp__m_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ A_27a @ V9c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V11t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Einterp__cs__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1vm_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__cs_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
      & ! [V2vm_2E0: u,V3l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4t_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__cs_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V2vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2EringNorm_2Er__ics__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V2vm_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__interp__vl_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V2vm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t_2E0 ) ) ) )
      & ! [V5vm_2E0: u,V6c_2E0: u,V7l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8t_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__cs_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V5vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V6c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2EringNorm_2Er__ics__aux_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V5vm_2E0 ) @ ( s @ A_27a @ ( c_2EringNorm_2Er__interp__m_2E4 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V5vm_2E0 ) @ ( s @ A_27a @ V6c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7l ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Espolynom__normalize__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ! [V1i: mono_2Etyop_2Equote_2Eindex] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1i ) ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex @ V1i @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) )
      & ! [V2c_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V2c_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V2c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Equote_2Eindex ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) )
      & ! [V3l_2E0: u,V4r_27_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V3l_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4r_27_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__merge_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V3l_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4r_27_2E0 ) ) ) ) ) )
      & ! [V5l_2E0: u,V6r_27_2E0: u] :
          ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5l_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6r_27_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__prod_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5l_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6r_27_2E0 ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Espolynom__simplify__def,axiom,
    ! [A_27a: d,V0r_2E0: u,V1x_2E0: u] :
      ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V1x_2E0 ) ) )
      = ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__canonical__sum__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Er__spolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V1x_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Edatatype__polynom,axiom,
    ! [A_27a: d,V0polynom_2E0: u] : ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ V0polynom_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ c_2EringNorm_2EPvar_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ c_2EringNorm_2EPconst_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ c_2EringNorm_2EPplus_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ) @ c_2EringNorm_2EPmult_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2EringNorm_2Epolynom @ A_27a ) ) @ c_2EringNorm_2EPopp_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__11,axiom,
    ! [A_27a: d] :
      ( ! [V0a: mono_2Etyop_2Equote_2Eindex,V1a_27: mono_2Etyop_2Equote_2Eindex] :
          ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V0a ) ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1a_27 ) ) ) ) )
        <=> ( V0a = V1a_27 ) )
      & ! [V2a_2E0: u,V3a_27_2E0: u] :
          ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V3a_27_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V2a_2E0 )
            = ( s @ A_27a @ V3a_27_2E0 ) ) )
      & ! [V4a0_2E0: u,V5a1_2E0: u,V6a0_27_2E0: u,V7a1_27_2E0: u] :
          ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V4a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5a1_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6a0_27_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V7a1_27_2E0 ) ) ) )
        <=> ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V4a0_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6a0_27_2E0 ) )
            & ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5a1_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V7a1_27_2E0 ) ) ) )
      & ! [V8a0_2E0: u,V9a1_2E0: u,V10a0_27_2E0: u,V11a1_27_2E0: u] :
          ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9a1_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V10a0_27_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11a1_27_2E0 ) ) ) )
        <=> ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8a0_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V10a0_27_2E0 ) )
            & ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9a1_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11a1_27_2E0 ) ) ) )
      & ! [V12a_2E0: u,V13a_27_2E0: u] :
          ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12a_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13a_27_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12a_2E0 )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13a_27_2E0 ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__distinct,axiom,
    ! [A_27a: d] :
      ( ! [V0a_27_2E0: u,V1a: mono_2Etyop_2Equote_2Eindex] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1a ) ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V0a_27_2E0 ) ) ) ) )
      & ! [V2a1_2E0: u,V3a0_2E0: u,V4a: mono_2Etyop_2Equote_2Eindex] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V4a ) ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V3a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V2a1_2E0 ) ) ) ) )
      & ! [V5a1_2E0: u,V6a0_2E0: u,V7a: mono_2Etyop_2Equote_2Eindex] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V7a ) ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5a1_2E0 ) ) ) ) )
      & ! [V8a_27_2E0: u,V9a: mono_2Etyop_2Equote_2Eindex] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V9a ) ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8a_27_2E0 ) ) ) ) )
      & ! [V10a1_2E0: u,V11a0_2E0: u,V12a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V12a_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V10a1_2E0 ) ) ) ) )
      & ! [V13a1_2E0: u,V14a0_2E0: u,V15a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V15a_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V14a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13a1_2E0 ) ) ) ) )
      & ! [V16a_27_2E0: u,V17a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V17a_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V16a_27_2E0 ) ) ) ) )
      & ! [V18a1_27_2E0: u,V19a1_2E0: u,V20a0_27_2E0: u,V21a0_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V21a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V19a1_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V20a0_27_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V18a1_27_2E0 ) ) ) ) )
      & ! [V22a1_2E0: u,V23a0_2E0: u,V24a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V23a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V22a1_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V24a_2E0 ) ) ) ) )
      & ! [V25a1_2E0: u,V26a0_2E0: u,V27a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V26a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V25a1_2E0 ) ) )
            = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V27a_2E0 ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__nchotomy,axiom,
    ! [A_27a: d,V0pp_2E0: u] :
      ( ? [V1i: mono_2Etyop_2Equote_2Eindex] :
          ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0pp_2E0 )
          = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1i ) ) ) ) )
      | ? [V2a_2E0: u] :
          ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0pp_2E0 )
          = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) )
      | ? [V3p_2E0: u,V4p0_2E0: u] :
          ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0pp_2E0 )
          = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V3p_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V4p0_2E0 ) ) ) )
      | ? [V5p_2E0: u,V6p0_2E0: u] :
          ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0pp_2E0 )
          = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5p_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6p0_2E0 ) ) ) )
      | ? [V7p_2E0: u] :
          ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0pp_2E0 )
          = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V7p_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u,V2f2_2E0: u,V3f3_2E0: u,V4f4_2E0: u] :
    ? [V5fn_2E0: u] :
      ( ! [V6a: mono_2Etyop_2Equote_2Eindex] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V6a ) ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V0f0_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V6a ) ) ) ) )
      & ! [V7a_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V7a_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f1_2E0 ) @ ( s @ A_27a @ V7a_2E0 ) ) ) )
      & ! [V8a0_2E0: u,V9a1_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9a1_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ V2f2_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8a0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9a1_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8a0_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9a1_2E0 ) ) ) ) ) )
      & ! [V10a0_2E0: u,V11a1_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V10a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11a1_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ V3f3_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V10a0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11a1_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V10a0_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11a1_2E0 ) ) ) ) ) )
      & ! [V12a_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12a_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V4f4_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12a_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V5fn_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12a_2E0 ) ) ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1i: mono_2Etyop_2Equote_2Eindex] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1i ) ) ) ) ) ) )
        & ! [V2a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) ) ) )
        & ! [V3p_2E0: u,V4p0_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V3p_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V4p0_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V3p_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V4p0_2E0 ) ) ) ) ) ) )
        & ! [V5p_2E0: u,V6p0_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5p_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6p0_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5p_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6p0_2E0 ) ) ) ) ) ) )
        & ! [V7p_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V7p_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V7p_2E0 ) ) ) ) ) ) ) )
     => ! [V8p_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V8p_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0f4_27_2E0: u,V1f3_27_2E0: u,V2f2_27_2E0: u,V3f1_27_2E0: u,V4f_27_2E0: u,V5M_2E0: u,V6M_27_2E0: u,V7f_2E0: u,V8f1_2E0: u,V9f2_2E0: u,V10f3_2E0: u,V11f4_2E0: u] :
      ( ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5M_2E0 )
          = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6M_27_2E0 ) )
        & ! [V12a: mono_2Etyop_2Equote_2Eindex] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6M_27_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V12a ) ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V7f_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V12a ) ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V4f_27_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V12a ) ) ) ) ) )
        & ! [V13a_2E0: u] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6M_27_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V13a_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V8f1_2E0 ) @ ( s @ A_27a @ V13a_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V3f1_27_2E0 ) @ ( s @ A_27a @ V13a_2E0 ) ) ) ) )
        & ! [V14a0_2E0: u,V15a1_2E0: u] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6M_27_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V14a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V15a1_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V9f2_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V14a0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V15a1_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V2f2_27_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V14a0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V15a1_2E0 ) ) ) ) )
        & ! [V16a0_2E0: u,V17a1_2E0: u] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6M_27_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V16a0_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V17a1_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V10f3_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V16a0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V17a1_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V1f3_27_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V16a0_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V17a1_2E0 ) ) ) ) )
        & ! [V18a_2E0: u] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6M_27_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V18a_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V11f4_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V18a_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V0f4_27_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V18a_2E0 ) ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V5M_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V7f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V8f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V9f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V10f3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V11f4_2E0 ) ) )
        = ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V6M_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V4f_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V3f1_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V2f2_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V1f3_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V0f4_27_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_2E0: u,V2f4_2E0: u,V3f3_2E0: u,V4f2_2E0: u,V5f1_2E0: u,V6f_2E0: u] :
      ( ( ( s @ A_27b @ ( c_2EringNorm_2Epolynom__CASE_2E6 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V5f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V4f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V3f3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V2f4_2E0 ) ) )
        = ( s @ A_27b @ V1v_2E0 ) )
    <=> ( ? [V7i: mono_2Etyop_2Equote_2Eindex] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V7i ) ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V6f_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V7i ) ) ) )
              = ( s @ A_27b @ V1v_2E0 ) ) )
        | ? [V8a_2E0: u] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPconst_2E1 @ ( s @ A_27a @ V8a_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V5f1_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) ) )
              = ( s @ A_27b @ V1v_2E0 ) ) )
        | ? [V9p_2E0: u,V10p0_2E0: u] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPplus_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9p_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V10p0_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V4f2_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V9p_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V10p0_2E0 ) ) )
              = ( s @ A_27b @ V1v_2E0 ) ) )
        | ? [V11p_2E0: u,V12p0_2E0: u] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPmult_2E2 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11p_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12p0_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) ) @ V3f3_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V11p_2E0 ) ) ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V12p0_2E0 ) ) )
              = ( s @ A_27b @ V1v_2E0 ) ) )
        | ? [V13p_2E0: u] :
            ( ( ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ ( c_2EringNorm_2EPopp_2E1 @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13p_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ A_27b ) @ V2f4_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V13p_2E0 ) ) )
              = ( s @ A_27b @ V1v_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__normalize__ok,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1vm_2E0: u,V2p_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__cs_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__normalize_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V2p_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V2p_2E0 ) ) ) ) ) ).

thf(thm_2EringNorm_2Epolynom__simplify__ok,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1vm_2E0: u,V2p_2E0: u] :
          ( ( s @ A_27a @ ( c_2EringNorm_2Er__interp__cs_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2EringNorm_2Epolynom__simplify_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V2p_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2EringNorm_2Einterp__p_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2EringNorm_2Epolynom @ A_27a ) @ V2p_2E0 ) ) ) ) ) ).

%------------------------------------------------------------------------------