ITP001 Axioms: ITP096^4.ax
%------------------------------------------------------------------------------
% File : ITP096^4 : 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 : canonical.ax [Gau19]
% : HL4096^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 423 ( 134 unt; 229 typ; 0 def)
% Number of atoms : 443 ( 317 equ; 10 cnn)
% Maximal formula atoms : 32 ( 1 avg)
% Number of connectives : 13292 ( 10 ~; 16 |; 110 &;13063 @)
% ( 20 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg;13063 nst)
% Number of types : 8 ( 7 usr)
% Number of type conns : 462 ( 462 >; 0 *; 0 +; 0 <<)
% Number of symbols : 224 ( 222 usr; 86 con; 0-5 aty)
% Number of variables : 924 ( 0 ^ 886 !; 38 ?; 924 :)
% 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_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_2EternaryComparisons_2EEQUAL_2E0,type,
c_2EternaryComparisons_2EEQUAL_2E0: 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_2EternaryComparisons_2EGREATER_2E0,type,
c_2EternaryComparisons_2EGREATER_2E0: u ).
thf(c_2EternaryComparisons_2ELESS_2E0,type,
c_2EternaryComparisons_2ELESS_2E0: 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_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__CASE_2E0,type,
c_2Ecanonical_2Ecanonical__sum__CASE_2E0: u ).
thf(c_2Ecanonical_2Ecanonical__sum__CASE_2E4,type,
c_2Ecanonical_2Ecanonical__sum__CASE_2E4: du > du > du > du > u ).
thf(c_2Ecanonical_2Ecanonical__sum__merge_2E0,type,
c_2Ecanonical_2Ecanonical__sum__merge_2E0: u ).
thf(c_2Ecanonical_2Ecanonical__sum__merge_2E3,type,
c_2Ecanonical_2Ecanonical__sum__merge_2E3: du > du > du > u ).
thf(c_2Ecanonical_2Ecanonical__sum__prod_2E0,type,
c_2Ecanonical_2Ecanonical__sum__prod_2E0: u ).
thf(c_2Ecanonical_2Ecanonical__sum__prod_2E3,type,
c_2Ecanonical_2Ecanonical__sum__prod_2E3: du > du > du > u ).
thf(c_2Ecanonical_2Ecanonical__sum__scalar_2E0,type,
c_2Ecanonical_2Ecanonical__sum__scalar_2E0: u ).
thf(c_2Ecanonical_2Ecanonical__sum__scalar_2E3,type,
c_2Ecanonical_2Ecanonical__sum__scalar_2E3: du > du > du > u ).
thf(c_2Ecanonical_2Ecanonical__sum__scalar2_2E0,type,
c_2Ecanonical_2Ecanonical__sum__scalar2_2E0: u ).
thf(c_2Ecanonical_2Ecanonical__sum__scalar2_2E3,type,
c_2Ecanonical_2Ecanonical__sum__scalar2_2E3: du > du > du > u ).
thf(c_2Ecanonical_2Ecanonical__sum__scalar3_2E0,type,
c_2Ecanonical_2Ecanonical__sum__scalar3_2E0: u ).
thf(c_2Ecanonical_2Ecanonical__sum__scalar3_2E4,type,
c_2Ecanonical_2Ecanonical__sum__scalar3_2E4: du > du > du > du > u ).
thf(c_2Ecanonical_2Ecanonical__sum__simplify_2E0,type,
c_2Ecanonical_2Ecanonical__sum__simplify_2E0: u ).
thf(c_2Ecanonical_2Ecanonical__sum__simplify_2E2,type,
c_2Ecanonical_2Ecanonical__sum__simplify_2E2: du > du > u ).
thf(c_2Ecanonical_2Ecanonical__sum__size_2E0,type,
c_2Ecanonical_2Ecanonical__sum__size_2E0: u ).
thf(c_2Ecanonical_2Ecanonical__sum__size_2E2,type,
c_2Ecanonical_2Ecanonical__sum__size_2E2: du > du > u ).
thf(c_2Ecanonical_2Eics__aux_2E0,type,
c_2Ecanonical_2Eics__aux_2E0: u ).
thf(c_2Ecanonical_2Eics__aux_2E4,type,
c_2Ecanonical_2Eics__aux_2E4: du > du > du > 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_2E3,type,
c_2Ecanonical_2Einterp__cs_2E3: du > du > du > u ).
thf(c_2Ecanonical_2Einterp__m_2E0,type,
c_2Ecanonical_2Einterp__m_2E0: u ).
thf(c_2Ecanonical_2Einterp__m_2E4,type,
c_2Ecanonical_2Einterp__m_2E4: du > du > du > du > u ).
thf(c_2Ecanonical_2Einterp__sp_2E0,type,
c_2Ecanonical_2Einterp__sp_2E0: u ).
thf(c_2Ecanonical_2Einterp__sp_2E3,type,
c_2Ecanonical_2Einterp__sp_2E3: du > du > du > u ).
thf(c_2Ecanonical_2Einterp__vl_2E0,type,
c_2Ecanonical_2Einterp__vl_2E0: u ).
thf(c_2Ecanonical_2Einterp__vl_2E3,type,
c_2Ecanonical_2Einterp__vl_2E3: du > du > du > u ).
thf(c_2Esemi__ring_2Eis__semi__ring_2E0,type,
c_2Esemi__ring_2Eis__semi__ring_2E0: u ).
thf(c_2Esemi__ring_2Eis__semi__ring_2E1,type,
c_2Esemi__ring_2Eis__semi__ring_2E1: du > u ).
thf(c_2Ecanonical_2Eivl__aux_2E0,type,
c_2Ecanonical_2Eivl__aux_2E0: u ).
thf(c_2Ecanonical_2Eivl__aux_2E4,type,
c_2Ecanonical_2Eivl__aux_2E4: du > du > du > 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_2Elist_2Elist__size_2E0,type,
c_2Elist_2Elist__size_2E0: u ).
thf(c_2Elist_2Elist__size_2E2,type,
c_2Elist_2Elist__size_2E2: du > du > u ).
thf(c_2Ecanonical_2Emonom__insert_2E0,type,
c_2Ecanonical_2Emonom__insert_2E0: u ).
thf(c_2Ecanonical_2Emonom__insert_2E4,type,
c_2Ecanonical_2Emonom__insert_2E4: du > du > du > du > u ).
thf(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
c_2EternaryComparisons_2Eordering__CASE_2E0: u ).
thf(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
c_2EternaryComparisons_2Eordering__CASE_2E4: du > du > du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SR0_2E0,type,
c_2Esemi__ring_2Esemi__ring__SR0_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SR0_2E1,type,
c_2Esemi__ring_2Esemi__ring__SR0_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SR1_2E0,type,
c_2Esemi__ring_2Esemi__ring__SR1_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SR1_2E1,type,
c_2Esemi__ring_2Esemi__ring__SR1_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRM_2E0,type,
c_2Esemi__ring_2Esemi__ring__SRM_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SRM_2E3,type,
c_2Esemi__ring_2Esemi__ring__SRM_2E3: du > du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRP_2E0,type,
c_2Esemi__ring_2Esemi__ring__SRP_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SRP_2E3,type,
c_2Esemi__ring_2Esemi__ring__SRP_2E3: du > du > du > u ).
thf(c_2Ecanonical_2Espolynom__CASE_2E0,type,
c_2Ecanonical_2Espolynom__CASE_2E0: u ).
thf(c_2Ecanonical_2Espolynom__CASE_2E5,type,
c_2Ecanonical_2Espolynom__CASE_2E5: du > du > du > du > du > u ).
thf(c_2Ecanonical_2Espolynom__normalize_2E0,type,
c_2Ecanonical_2Espolynom__normalize_2E0: u ).
thf(c_2Ecanonical_2Espolynom__normalize_2E2,type,
c_2Ecanonical_2Espolynom__normalize_2E2: du > du > u ).
thf(c_2Ecanonical_2Espolynom__simplify_2E0,type,
c_2Ecanonical_2Espolynom__simplify_2E0: u ).
thf(c_2Ecanonical_2Espolynom__simplify_2E2,type,
c_2Ecanonical_2Espolynom__simplify_2E2: du > du > u ).
thf(c_2Ecanonical_2Espolynom__size_2E0,type,
c_2Ecanonical_2Espolynom__size_2E0: u ).
thf(c_2Ecanonical_2Espolynom__size_2E2,type,
c_2Ecanonical_2Espolynom__size_2E2: du > du > u ).
thf(c_2Ecanonical_2Evarlist__insert_2E0,type,
c_2Ecanonical_2Evarlist__insert_2E0: u ).
thf(c_2Ecanonical_2Evarlist__insert_2E3,type,
c_2Ecanonical_2Evarlist__insert_2E3: du > du > 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_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29: ( ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ).
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_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ).
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_2Ebool_2EARB_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,type,
mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ).
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_2EternaryComparisons_2EEQUAL,type,
mono_2Ec_2EternaryComparisons_2EEQUAL: mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2EternaryComparisons_2EGREATER,type,
mono_2Ec_2EternaryComparisons_2EGREATER: mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2EternaryComparisons_2ELESS,type,
mono_2Ec_2EternaryComparisons_2ELESS: mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_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_2Elist_2Elist__size_2Emono_2Etyop_2Equote_2Eindex,type,
mono_2Ec_2Elist_2Elist__size_2Emono_2Etyop_2Equote_2Eindex: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ).
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_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ) > 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_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ) > 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_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29: du > ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ).
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_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum ).
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_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) ) @ 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_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) @ 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_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_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_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_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_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X1 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ X1 ) ) ) ) ) ).
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_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) ) ) @ c_2Eind__type_2ECONSTR_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ 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_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_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 @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) ) ) @ c_2Eind__type_2EFCONS_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ 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_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_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_29_29_20mono_2Etyop_2Ecanonical_2Ecanonical__sum_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 @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Equote_2Eindex_2CA_27a_29_29_20mono_2Etyop_2Ecanonical_2Espolynom_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_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq4_2Ec_2Ecanonical_2Ecanonical__sum__CASE_2E4_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] :
( ( s @ A_27b @ ( c_2Ecanonical_2Ecanonical__sum__CASE_2E4 @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_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 ) @ A_27b ) ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ X3_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ A_27b ) ) ) ) @ c_2Ecanonical_2Ecanonical__sum__CASE_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_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 ) @ A_27b ) ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ X3_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ecanonical_2Ecanonical__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_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ecanonical_2Ecanonical__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_2Ecanonical_2Ecanonical__sum__prod_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ecanonical_2Ecanonical__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_2Ecanonical_2Ecanonical__sum__scalar_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ecanonical_2Ecanonical__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_2Ecanonical_2Ecanonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( 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(arityeq4_2Ec_2Ecanonical_2Ecanonical__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_2Ecanonical_2Ecanonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( 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(arityeq2_2Ec_2Ecanonical_2Ecanonical__sum__simplify_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecanonical_2Ecanonical__sum__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_2Ecanonical_2Ecanonical__sum__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2Ecanonical_2Ecanonical__sum__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq4_2Ec_2Ecanonical_2Eics__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_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X3_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ecanonical_2Einterp__cs_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Ecanonical_2Einterp__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_2Ecanonical_2Einterp__m_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( 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(arityeq3_2Ec_2Ecanonical_2Einterp__sp_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ecanonical_2Einterp__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_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( 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_2Esemi__ring_2Eis__semi__ring_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Esemi__ring_2Eis__semi__ring_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq4_2Ec_2Ecanonical_2Eivl__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_2Ecanonical_2Eivl__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( 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(arityeq4_2Ec_2Ecanonical_2Emonom__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_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( 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(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(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SR0_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ A_27a ) @ c_2Esemi__ring_2Esemi__ring__SR0_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SR1_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ A_27a ) @ c_2Esemi__ring_2Esemi__ring__SR1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Esemi__ring_2Esemi__ring__SRM_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRM_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Esemi__ring_2Esemi__ring__SRP_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRP_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
thf(arityeq5_2Ec_2Ecanonical_2Espolynom__CASE_2E5_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] :
( ( s @ A_27b @ ( c_2Ecanonical_2Espolynom__CASE_2E5 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ X3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ X4_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ A_27b ) ) ) ) ) @ c_2Ecanonical_2Espolynom__CASE_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ X4_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecanonical_2Espolynom__normalize_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecanonical_2Espolynom__simplify_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecanonical_2Espolynom__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_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2Ecanonical_2Espolynom__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ecanonical_2Evarlist__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_2Ecanonical_2Evarlist__insert_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ 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_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 ) ) ) @ ( 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_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_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_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_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_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_2Ebool_2EARB_2E0_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,axiom,
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) )
= ( s @ ( tyop_2Elist_2Elist @ 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(monoeq_2Emono_2Ec_2Elist_2Elist__size_2E0_2Emono_2Etyop_2Equote_2Eindex,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29_29 @ mono_2Ec_2Elist_2Elist__size_2Emono_2Etyop_2Equote_2Eindex ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ tyop_2Enum_2Enum ) ) @ c_2Elist_2Elist__size_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2Elist__size_2E2_2Emono_2Etyop_2Equote_2Eindex,axiom,
! [V0: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Elist_2Elist__size_2Emono_2Etyop_2Equote_2Eindex @ V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2Elist__size_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_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1 ) ) ) ) ) ).
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_2Emin_2Efun_28tyop_2Equote_2Eindex_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Equote_2Eindex > mono_2Etyop_2Enum_2Enum] :
( ( 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_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 > mono_2Etyop_2Enum_2Enum,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_2Ecanonical_2Ecanonical__sum__TY__DEF,axiom,
! [A_27a: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V11n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11n ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V8n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8n ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V4n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ 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 @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V1a0_27_2E0 ) ) ) )
<=> ! [V2_27canonical__sum_27_2E0: u] :
( ! [V3a0_27_2E0: u] :
( ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V3a0_27_2E0 )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ F1_2E0 ) ) ) )
| ? [V5a0_2E0: u,V6a1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7a2_2E0: u] :
( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V3a0_27_2E0 )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( 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 @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6a1 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V7a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ F2_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27canonical__sum_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V7a2_2E0 ) ) ) ) )
| ? [V9a0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V10a1_2E0: u] :
( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V3a0_27_2E0 )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ ( 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 @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9a0 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V10a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ F3_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27canonical__sum_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ V10a1_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27canonical__sum_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ 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 @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27canonical__sum_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ 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 @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) ) ) ) @ V0rep_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__case__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0v_2E0: u,V1f_2E0: u,V2f1_2E0: u] :
( ( s @ A_27b @ ( c_2Ecanonical_2Ecanonical__sum__CASE_2E4 @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) @ ( s @ A_27b @ V0v_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 ) @ A_27b ) ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V2f1_2E0 ) ) )
= ( s @ A_27b @ V0v_2E0 ) )
& ! [V3a0_2E0: u,V4a1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V5a2_2E0: u,V6v_2E0: u,V7f_2E0: u,V8f1_2E0: u] :
( ( s @ A_27b @ ( c_2Ecanonical_2Ecanonical__sum__CASE_2E4 @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V3a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4a1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5a2_2E0 ) ) ) @ ( s @ A_27b @ V6v_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 ) @ A_27b ) ) ) @ V7f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V8f1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ ( 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 ) @ A_27b ) ) ) @ V7f_2E0 ) @ ( s @ A_27a @ V3a0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4a1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5a2_2E0 ) ) ) )
& ! [V9a0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V10a1_2E0: u,V11v_2E0: u,V12f_2E0: u,V13f1_2E0: u] :
( ( s @ A_27b @ ( c_2Ecanonical_2Ecanonical__sum__CASE_2E4 @ ( 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 @ V9a0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10a1_2E0 ) ) ) @ ( s @ A_27b @ V11v_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 ) @ A_27b ) ) ) @ V12f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V13f1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V13f1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9a0 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10a1_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__size__def,axiom,
! [A_27a: d] :
( ! [V0f_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Ecanonical__sum__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) )
= mono_2Ec_2Enum_2E0 )
& ! [V1f_2E0: u,V2a0_2E0: u,V3a1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4a2_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Ecanonical__sum__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3a1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4a2_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 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Elist_2Elist__size_2Emono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__size @ V3a1 ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Ecanonical__sum__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4a2_2E0 ) ) ) ) ) ) ) )
& ! [V5f_2E0: u,V6a0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7a1_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Ecanonical__sum__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V5f_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 @ V6a0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7a1_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Elist_2Elist__size_2Emono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__size @ V6a0 ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Ecanonical__sum__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V5f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7a1_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__scalar__def,axiom,
! [A_27a: d] :
( ! [V0sr_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_2Ecanonical_2Ecanonical__sum__scalar_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Ecanonical__sum__scalar_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ V1c0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t_2E0 ) ) ) ) ) )
& ! [V5sr_2E0: u,V6c0_2E0: u,V7l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8t_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_2E0 ) @ ( s @ A_27a @ V6c0_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 @ V7l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V6c0_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 ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_2E0 ) @ ( s @ A_27a @ V6c0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t_2E0 ) ) ) ) ) )
& ! [V9sr_2E0: u,V10c0_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_2E0 ) @ ( s @ A_27a @ V10c0_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_2Ecanonical_2Ecanonical__sum__scalar2__def,axiom,
! [A_27a: d] :
( ! [V0sr_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_2Ecanonical_2Ecanonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Ecanonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) ) ) ) ) )
& ! [V5sr_2E0: u,V6l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8t_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l0 ) ) @ ( 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 @ V7l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Evarlist__insert_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_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 @ V6l0 @ V7l ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t_2E0 ) ) ) ) ) )
& ! [V9sr_2E0: u,V10l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V10l0 ) ) @ ( 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_2Ecanonical_2Ecanonical__sum__scalar3__def,axiom,
! [A_27a: d] :
( ! [V0sr_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_2Ecanonical_2Ecanonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Ecanonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) ) ) ) ) )
& ! [V6sr_2E0: u,V7c0_2E0: u,V8l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V9l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V10t_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ A_27a @ V7c0_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_2ECons__varlist_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ A_27a @ V7c0_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 @ V8l0 @ V9l ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ A_27a @ V7c0_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 ) @ V10t_2E0 ) ) ) ) ) )
& ! [V11sr_2E0: u,V12c0_2E0: u,V13l0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V11sr_2E0 ) @ ( s @ A_27a @ V12c0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V13l0 ) ) @ ( 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_2Ecanonical_2Ecanonical__sum__prod__def,axiom,
! [A_27a: d] :
( ! [V0sr_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_2Ecanonical_2Ecanonical__sum__prod_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Ecanonical__sum__prod_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4s2_2E0 ) ) ) ) ) )
& ! [V5sr_2E0: u,V6l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7t1_2E0: u,V8s2_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__prod_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_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 @ V6l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8s2_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V6l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8s2_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__prod_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8s2_2E0 ) ) ) ) ) )
& ! [V9sr_2E0: u,V10s2_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__prod_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10s2_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__simplify__def,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V1c_2E0: u,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ A_27a @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V1c_2E0 )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) ) )
=> ( ! [V1c_2E0: u,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V1c_2E0 )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) ) )
=> ( ! [V0sr_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_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ A_27a @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3t_2E0 ) ) ) ) ) ) ) ) ) )
& ! [V4sr_2E0: u,V5l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V6t_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V4sr_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 @ ( 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 ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V4sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t_2E0 ) ) ) ) ) )
& ! [V7sr_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_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_2Ecanonical_2Eivl__aux__def,axiom,
! [A_27a: d] :
( ! [V0sr_2E0: u,V1vm_2E0: u,V2x: mono_2Etyop_2Equote_2Eindex] :
( ( s @ A_27a @ ( c_2Ecanonical_2Eivl__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) ) ) )
& ! [V3sr_2E0: u,V4vm_2E0: u,V5x: mono_2Etyop_2Equote_2Eindex,V6x_27: mono_2Etyop_2Equote_2Eindex,V7t_27: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ A_27a @ ( c_2Ecanonical_2Eivl__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_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 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex @ V6x_27 @ V7t_27 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ A_27a @ ( c_2Equote_2Evarmap__find_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V5x ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Eivl__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V6x_27 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7t_27 ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Einterp__vl__def,axiom,
! [A_27a: d] :
( ! [V0sr_2E0: u,V1vm_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
& ! [V2sr_2E0: u,V3vm_2E0: u,V4x: mono_2Etyop_2Equote_2Eindex,V5t: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_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 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Equote_2Eindex @ V4x @ V5t ) ) ) ) )
= ( s @ A_27a @ ( c_2Ecanonical_2Eivl__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_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 @ V5t ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Einterp__m__def,axiom,
! [A_27a: d] :
( ! [V0sr_2E0: u,V1vm_2E0: u,V2c_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__m_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) )
& ! [V3sr_2E0: u,V4vm_2E0: u,V5c_2E0: u,V6x: mono_2Etyop_2Equote_2Eindex,V7t: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__m_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) @ ( s @ A_27a @ V5c_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 @ V6x @ V7t ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ A_27a @ V5c_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Eivl__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V6x ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7t ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Eics__aux__def,axiom,
! [A_27a: d] :
( ! [V0sr_2E0: u,V1vm_2E0: u,V2a_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) )
& ! [V3sr_2E0: u,V4vm_2E0: u,V5a_2E0: u,V6l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7t_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) @ ( s @ A_27a @ V5a_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 @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_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 ) @ V7t_2E0 ) ) ) ) ) )
& ! [V8sr_2E0: u,V9vm_2E0: u,V10a_2E0: u,V11c_2E0: u,V12l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V13t_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V9vm_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V11c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V12l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8sr_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V9vm_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__m_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V9vm_2E0 ) @ ( s @ A_27a @ V11c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V12l ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Einterp__cs__def,axiom,
! [A_27a: d] :
( ! [V0sr_2E0: u,V1vm_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
& ! [V2sr_2E0: u,V3vm_2E0: u,V4l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V5t_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_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 @ A_27a @ ( c_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V3vm_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_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 @ V4l ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t_2E0 ) ) ) )
& ! [V6sr_2E0: u,V7vm_2E0: u,V8c_2E0: u,V9l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V10t_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V8c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10t_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__m_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ A_27a @ V8c_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10t_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__TY__DEF,axiom,
! [A_27a: d,F4_2E0: u,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [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_27spolynom_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_27spolynom_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_27spolynom_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_27spolynom_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_27spolynom_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) @ V12a1_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_27spolynom_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_27spolynom_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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Equote_2Eindex @ A_27a ) ) ) @ V0rep_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__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] :
( ( s @ A_27b @ ( c_2Ecanonical_2Espolynom__CASE_2E5 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V3f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V4f3_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 ) ) ) ) )
& ! [V5a_2E0: u,V6f_2E0: u,V7f1_2E0: u,V8f2_2E0: u,V9f3_2E0: u] :
( ( s @ A_27b @ ( c_2Ecanonical_2Espolynom__CASE_2E5 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V5a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V8f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V9f3_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7f1_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) ) ) )
& ! [V10a0_2E0: u,V11a1_2E0: u,V12f_2E0: u,V13f1_2E0: u,V14f2_2E0: u,V15f3_2E0: u] :
( ( s @ A_27b @ ( c_2Ecanonical_2Espolynom__CASE_2E5 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V11a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V12f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V13f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V14f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V15f3_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V14f2_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10a0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V11a1_2E0 ) ) ) )
& ! [V16a0_2E0: u,V17a1_2E0: u,V18f_2E0: u,V19f1_2E0: u,V20f2_2E0: u,V21f3_2E0: u] :
( ( s @ A_27b @ ( c_2Ecanonical_2Espolynom__CASE_2E5 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V16a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V17a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V18f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V19f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V20f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V21f3_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V21f3_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V16a0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V17a1_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__size__def,axiom,
! [A_27a: d] :
( ! [V0f_2E0: u,V1a: mono_2Etyop_2Equote_2Eindex] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_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_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V2f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_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_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5a0_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6a1_2E0 ) ) ) ) ) ) )
& ! [V7f_2E0: u,V8a0_2E0: u,V9a1_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V7f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ 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_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V7f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8a0_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ecanonical_2Espolynom__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V7f_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9a1_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__normalize__def,axiom,
! [A_27a: d] :
( ! [V0sr_2E0: u,V1i: mono_2Etyop_2Equote_2Eindex] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) ) ) )
& ! [V2sr_2E0: u,V3c_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_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 ) ) ) )
& ! [V4sr_2E0: u,V5l_2E0: u,V6r_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V4sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5l_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V4sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V4sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5l_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V4sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6r_2E0 ) ) ) ) ) )
& ! [V7sr_2E0: u,V8l_2E0: u,V9r_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8l_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__prod_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8l_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9r_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__simplify__def,axiom,
! [A_27a: d,V0sr_2E0: u,V1x_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V1x_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Einterp__sp__def,axiom,
! [A_27a: d] :
( ! [V0sr_2E0: u,V1vm_2E0: u,V2c_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) )
& ! [V3sr_2E0: u,V4vm_2E0: u,V5i: mono_2Etyop_2Equote_2Eindex] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V4vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_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 ) ) ) )
& ! [V6sr_2E0: u,V7vm_2E0: u,V8p1_2E0: u,V9p2_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8p1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9p2_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8p1_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V7vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9p2_2E0 ) ) ) ) ) )
& ! [V10sr_2E0: u,V11vm_2E0: u,V12p1_2E0: u,V13p2_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V10sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V11vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V12p1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V13p2_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V10sr_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V10sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V11vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V12p1_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V10sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V11vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V13p2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Edatatype__canonical__sum,axiom,
! [A_27a: d,V0canonical__sum_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_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0canonical__sum_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_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_2ECons__monom_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_2ECons__varlist_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__11,axiom,
! [A_27a: d] :
( ! [V0a0_2E0: u,V1a1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V2a2_2E0: u,V3a0_27_2E0: u,V4a1_27: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V5a2_27_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1a1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2a2_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V3a0_27_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4a1_27 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5a2_27_2E0 ) ) ) )
<=> ( ( ( s @ A_27a @ V0a0_2E0 )
= ( s @ A_27a @ V3a0_27_2E0 ) )
& ( V1a1 = V4a1_27 )
& ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2a2_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5a2_27_2E0 ) ) ) )
& ! [V6a0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7a1_2E0: u,V8a0_27: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V9a1_27_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 @ V6a0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7a1_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 @ V8a0_27 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V9a1_27_2E0 ) ) ) )
<=> ( ( V6a0 = V8a0_27 )
& ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7a1_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V9a1_27_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__distinct,axiom,
! [A_27a: d] :
( ! [V0a2_2E0: u,V1a1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V2a0_2E0: u] :
( (~)
@ ( ( 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 @ V2a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V1a1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0a2_2E0 ) ) ) ) )
& ! [V3a1_2E0: u,V4a0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( (~)
@ ( ( 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 @ V4a0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3a1_2E0 ) ) ) ) )
& ! [V5a2_2E0: u,V6a1_27_2E0: u,V7a1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8a0_27: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V9a0_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V9a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7a1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5a2_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 @ V8a0_27 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6a1_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__nchotomy,axiom,
! [A_27a: d,V0cc_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0cc_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) )
| ? [V1a_2E0: u,V2l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3c_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0cc_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V1a_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 ) @ V3c_2E0 ) ) ) )
| ? [V4l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V5c_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0cc_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 ) @ V5c_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__Axiom,axiom,
! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u,V2f2_2E0: u] :
? [V3fn_2E0: u] :
( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
= ( s @ A_27b @ V0f0_2E0 ) )
& ! [V4a0_2E0: u,V5a1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V6a2_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V4a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V5a1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6a2_2E0 ) ) ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( 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_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ V1f1_2E0 ) @ ( s @ A_27a @ V4a0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V5a1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6a2_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6a2_2E0 ) ) ) ) ) )
& ! [V7a0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8a1_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ V3fn_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 @ V7a0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8a1_2E0 ) ) ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ V2f2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V7a0 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8a1_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8a1_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__induction,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) )
& ! [V1c_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1c_2E0 ) ) ) )
=> ! [V2l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V3a_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 ) @ V1c_2E0 ) ) ) ) ) ) )
& ! [V4c_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4c_2E0 ) ) ) )
=> ! [V5l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_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 ) @ V4c_2E0 ) ) ) ) ) ) ) )
=> ! [V6c_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6c_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__case__cong,axiom,
! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f1_27_2E0: u,V2f_27_2E0: u,V3M_2E0: u,V4M_27_2E0: u,V5v_2E0: u,V6f_2E0: u,V7f1_2E0: u] :
( ( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3M_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4M_27_2E0 ) )
& ( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4M_27_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) )
=> ( ( s @ A_27b @ V5v_2E0 )
= ( s @ A_27b @ V0v_27_2E0 ) ) )
& ! [V8a0_2E0: u,V9a1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V10a2_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4M_27_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V8a0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9a1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10a2_2E0 ) ) ) )
=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ ( 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 ) @ A_27b ) ) ) @ V6f_2E0 ) @ ( s @ A_27a @ V8a0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9a1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10a2_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ ( 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 ) @ A_27b ) ) ) @ V2f_27_2E0 ) @ ( s @ A_27a @ V8a0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9a1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V10a2_2E0 ) ) ) ) )
& ! [V11a0: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V12a1_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4M_27_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 @ V11a0 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V12a1_2E0 ) ) ) )
=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V7f1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V11a0 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V12a1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V1f1_27_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V11a0 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V12a1_2E0 ) ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Ecanonical_2Ecanonical__sum__CASE_2E4 @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3M_2E0 ) @ ( s @ A_27b @ V5v_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 ) @ A_27b ) ) ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V7f1_2E0 ) ) )
= ( s @ A_27b @ ( c_2Ecanonical_2Ecanonical__sum__CASE_2E4 @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4M_27_2E0 ) @ ( s @ A_27b @ V0v_27_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 ) @ A_27b ) ) ) @ V2f_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V1f1_27_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__case__eq,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_27_2E0: u,V2v_2E0: u,V3f1_2E0: u,V4f_2E0: u] :
( ( ( s @ A_27b @ ( c_2Ecanonical_2Ecanonical__sum__CASE_2E4 @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0x_2E0 ) @ ( s @ A_27b @ V2v_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 ) @ A_27b ) ) ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V3f1_2E0 ) ) )
= ( s @ A_27b @ V1v_27_2E0 ) )
<=> ( ( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) )
& ( ( s @ A_27b @ V2v_2E0 )
= ( s @ A_27b @ V1v_27_2E0 ) ) )
| ? [V5a_2E0: u,V6l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7c_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V5a_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 ) @ V7c_2E0 ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ ( 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 ) @ A_27b ) ) ) @ V4f_2E0 ) @ ( s @ A_27a @ V5a_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 ) @ V7c_2E0 ) ) )
= ( s @ A_27b @ V1v_27_2E0 ) ) )
| ? [V8l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V9c_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0x_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 @ V8l ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V9c_2E0 ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ A_27b ) ) @ V3f1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V8l ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V9c_2E0 ) ) )
= ( s @ A_27b @ V1v_27_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__merge__ind,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ! [V1sr_2E0: u,V2c1_2E0: u,V3l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4t1_2E0: u,V5c2_2E0: u,V6l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V7t2_2E0: u] :
( ( ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V3l1 @ V6l2 )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) )
& ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V3l1 @ V6l2 )
= mono_2Ec_2EternaryComparisons_2EGREATER )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V2c1_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 ) @ V4t1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) )
& ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V3l1 @ V6l2 )
= mono_2Ec_2EternaryComparisons_2ELESS )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4t1_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 @ V6l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V2c1_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 ) @ V4t1_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 @ V6l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) )
& ! [V8sr_2E0: u,V9c1_2E0: u,V10l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V11t1_2E0: u,V12l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V13t2_2E0: u] :
( ( ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V10l1 @ V12l2 )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V11t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t2_2E0 ) ) ) ) )
& ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V10l1 @ V12l2 )
= mono_2Ec_2EternaryComparisons_2EGREATER )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8sr_2E0 ) ) ) @ ( 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 @ V10l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V11t1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t2_2E0 ) ) ) ) )
& ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V10l1 @ V12l2 )
= mono_2Ec_2EternaryComparisons_2ELESS )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V11t1_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 @ V12l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t2_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8sr_2E0 ) ) ) @ ( 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 @ V10l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V11t1_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 @ V12l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t2_2E0 ) ) ) ) ) ) )
& ! [V14sr_2E0: u,V15l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V16t1_2E0: u,V17c2_2E0: u,V18l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V19t2_2E0: u] :
( ( ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V15l1 @ V18l2 )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V14sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V16t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V19t2_2E0 ) ) ) ) )
& ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V15l1 @ V18l2 )
= mono_2Ec_2EternaryComparisons_2EGREATER )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V14sr_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 ) @ V16t1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V19t2_2E0 ) ) ) ) )
& ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V15l1 @ V18l2 )
= mono_2Ec_2EternaryComparisons_2ELESS )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V14sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V16t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V17c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V18l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V19t2_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V14sr_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 ) @ V16t1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V17c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V18l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V19t2_2E0 ) ) ) ) ) ) )
& ! [V20sr_2E0: u,V21l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V22t1_2E0: u,V23l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V24t2_2E0: u] :
( ( ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V21l1 @ V23l2 )
= mono_2Ec_2EternaryComparisons_2EEQUAL )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V20sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V22t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V24t2_2E0 ) ) ) ) )
& ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V21l1 @ V23l2 )
= mono_2Ec_2EternaryComparisons_2EGREATER )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V20sr_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 @ V21l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V22t1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V24t2_2E0 ) ) ) ) )
& ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V21l1 @ V23l2 )
= mono_2Ec_2EternaryComparisons_2ELESS )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V20sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V22t1_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 @ V23l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V24t2_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V20sr_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 @ V21l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V22t1_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 @ V23l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V24t2_2E0 ) ) ) ) ) ) )
& ! [V25sr_2E0: u,V26s1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V25sr_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V26s1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) )
& ! [V27sr_2E0: u,V28v4_2E0: u,V29v5: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V30v6_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V27sr_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 @ V28v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V29v5 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V30v6_2E0 ) ) ) ) ) )
& ! [V31sr_2E0: u,V32v7: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V33v8_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V31sr_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 @ V32v7 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V33v8_2E0 ) ) ) ) ) ) )
=> ! [V34v_2E0: u,V35v1_2E0: u,V36v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V34v_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V35v1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V36v2_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__merge__def,axiom,
! [A_27a: d] :
( ! [V0t2_2E0: u,V1t1_2E0: u,V2sr_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_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_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 ) @ V1t1_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 ) @ V0t2_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_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t1_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 ) @ V0t2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_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_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0t2_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_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2sr_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 ) @ V1t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ) ) )
& ! [V7t2_2E0: u,V8t1_2E0: u,V9sr_2E0: u,V10l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V11l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V12c1_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V12c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V11l1 ) ) @ ( 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 @ V10l2 ) ) @ ( 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 @ V11l1 @ V10l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V12c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V11l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_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 @ V10l2 ) ) @ ( 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_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_2E0 ) @ ( s @ A_27a @ V12c1_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V11l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_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 @ V10l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V12c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V11l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V8t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) ) )
& ! [V13t2_2E0: u,V14t1_2E0: u,V15sr_2E0: u,V16l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V17l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V18c2_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15sr_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 @ V17l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V14t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V18c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V16l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t2_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 @ V17l1 @ V16l2 ) ) ) @ ( 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 @ V17l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V14t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V18c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V16l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15sr_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15sr_2E0 ) ) ) @ ( s @ A_27a @ V18c2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V17l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V14t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V18c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V16l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15sr_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 @ V17l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V14t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V13t2_2E0 ) ) ) ) ) ) ) )
& ! [V19t2_2E0: u,V20t1_2E0: u,V21sr_2E0: u,V22l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V23l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V21sr_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 @ V23l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V20t1_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 @ V22l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V19t2_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 @ V23l1 @ V22l2 ) ) ) @ ( 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 @ V23l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V21sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V20t1_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 @ V22l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V19t2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V21sr_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V21sr_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V21sr_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V23l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V21sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V20t1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V19t2_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 @ V22l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V21sr_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 @ V23l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V20t1_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V19t2_2E0 ) ) ) ) ) ) ) )
& ! [V24sr_2E0: u,V25s1_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V24sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V25s1_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V25s1_2E0 ) )
& ! [V26v6_2E0: u,V27v5: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V28v4_2E0: u,V29sr_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V29sr_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 @ V28v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V27v5 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V26v6_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V28v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V27v5 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V26v6_2E0 ) ) ) )
& ! [V30v8_2E0: u,V31v7: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V32sr_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V32sr_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 @ V31v7 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V30v8_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 @ V31v7 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V30v8_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Emonom__insert__ind,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ! [V1sr_2E0: u,V2c1_2E0: u,V3l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4c2_2E0: u,V5l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V6t2_2E0: u] :
( ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V3l1 @ V5l2 )
= mono_2Ec_2EternaryComparisons_2EGREATER )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ ( 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_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_2E0 ) ) ) @ ( s @ A_27a @ V2c1_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 ) @ V6t2_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ ( 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_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_2E0 ) ) ) @ ( s @ A_27a @ V2c1_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 @ V5l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t2_2E0 ) ) ) ) ) ) )
& ! [V7sr_2E0: u,V8c1_2E0: u,V9l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V10l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V11t2_2E0: u] :
( ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V9l1 @ V10l2 )
= mono_2Ec_2EternaryComparisons_2EGREATER )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ ( 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_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) ) ) @ ( s @ A_27a @ V8c1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V11t2_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ ( 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_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) ) ) @ ( s @ A_27a @ V8c1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l1 ) ) ) ) @ ( 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 @ V10l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V11t2_2E0 ) ) ) ) ) ) )
& ! [V12sr_2E0: u,V13c1_2E0: u,V14l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ ( 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_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V12sr_2E0 ) ) ) @ ( s @ A_27a @ V13c1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V14l1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ) )
=> ! [V15v_2E0: u,V16v1_2E0: u,V17v2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V18v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ ( 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_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15v_2E0 ) ) ) @ ( s @ A_27a @ V16v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V17v2 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V18v3_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Emonom__insert__def,axiom,
! [A_27a: d] :
( ! [V0t2_2E0: u,V1sr_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_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_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 ) @ V0t2_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 ) @ V0t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_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 ) @ V0t2_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_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_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 ) @ V0t2_2E0 ) ) ) ) ) ) ) )
& ! [V6t2_2E0: u,V7sr_2E0: u,V8l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V9l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V10c1_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) @ ( s @ A_27a @ V10c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l1 ) ) @ ( 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 @ V8l2 ) ) @ ( 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 @ V9l1 @ V8l2 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V10c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l1 ) ) @ ( 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 @ V8l2 ) ) @ ( 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_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) @ ( s @ A_27a @ V10c1_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l1 ) ) @ ( 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 @ V8l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V7sr_2E0 ) @ ( s @ A_27a @ V10c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V9l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V6t2_2E0 ) ) ) ) ) ) ) )
& ! [V11sr_2E0: u,V12l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V13c1_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V11sr_2E0 ) @ ( s @ A_27a @ V13c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V12l1 ) ) @ ( 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 @ V13c1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V12l1 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Evarlist__insert__ind,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ! [V1sr_2E0: u,V2l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3c2_2E0: u,V4l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V5t2_2E0: u] :
( ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V2l1 @ V4l2 )
= mono_2Ec_2EternaryComparisons_2EGREATER )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_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 ) @ V5t2_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_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 ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ V3c2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V4l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V5t2_2E0 ) ) ) ) ) ) )
& ! [V6sr_2E0: u,V7l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V9t2_2E0: u] :
( ( ( ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__compare @ V7l1 @ V8l2 )
= mono_2Ec_2EternaryComparisons_2EGREATER )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_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 ) @ V9t2_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_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 @ V8l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V9t2_2E0 ) ) ) ) ) ) )
& ! [V10sr_2E0: u,V11l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V10sr_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V11l1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ c_2Ecanonical_2ENil__monom_2E0 ) ) ) ) )
=> ! [V12v_2E0: u,V13v1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V14v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V12v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V13v1 ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V14v2_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Evarlist__insert__def,axiom,
! [A_27a: d] :
( ! [V0t2_2E0: u,V1sr_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_2Ecanonical_2Evarlist__insert_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_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 ) @ V0t2_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 ) @ V0t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_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 ) @ V0t2_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_2Ecanonical_2Evarlist__insert_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1sr_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 ) @ V0t2_2E0 ) ) ) ) ) ) ) )
& ! [V5t2_2E0: u,V6sr_2E0: u,V7l2: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V8l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Evarlist__insert_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_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 ) @ 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 @ V8l1 @ V7l2 ) ) ) @ ( 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_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 ) @ V5t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2ECons__monom_2E3 @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_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 ) @ 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 @ V7l2 ) ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Evarlist__insert_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6sr_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 ) @ V5t2_2E0 ) ) ) ) ) ) ) )
& ! [V9sr_2E0: u,V10l1: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Evarlist__insert_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9sr_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__varlist_2E2 @ ( 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_2Ecanonical_2Eivl__aux__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2v: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3i: mono_2Etyop_2Equote_2Eindex] :
( ( s @ A_27a @ ( c_2Ecanonical_2Eivl__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V3i ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V2v ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Equote_2Evarmap__find_2E2 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V3i ) ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 @ V2v ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Evarlist__merge__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2x: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3y: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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_2EternaryComparisons_2Elist__merge_2Emono_2Etyop_2Equote_2Eindex @ mono_2Ec_2Equote_2Eindex__lt @ V2x @ V3y ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 @ V2x ) ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 @ V3y ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Eics__aux__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2x_2E0: u,V3s_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Eics__aux_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3s_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Einterp__m__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2x_2E0: u,V3l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__m_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29 @ V3l ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 @ V3l ) ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__merge__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2x_2E0: u,V3y_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__merge_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3y_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2x_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Emonom__insert__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2a_2E0: u,V3l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4s_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Emonom__insert_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ V2a_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 ) @ V4s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 @ V3l ) ) ) ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Evarlist__insert__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3s_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Evarlist__insert_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) @ V3s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 @ V2l ) ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__scalar__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2a_2E0: u,V3s_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__scalar2__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V3s_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar2_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) @ V3s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 @ V2l ) ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__scalar3__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2c_2E0: u,V3l: mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29,V4s_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__scalar3_2E4 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 ) @ V4s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ V2c_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__vl_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_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 @ V3l ) ) ) ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V4s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__prod__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2x_2E0: u,V3y_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__prod_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3y_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2x_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V3y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Ecanonical__sum__simplify__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2s_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Ecanonical__sum__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ V2s_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Edatatype__spolynom,axiom,
! [A_27a: d,V0spolynom_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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ V0spolynom_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ c_2Ecanonical_2ESPvar_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) @ c_2Ecanonical_2ESPconst_2E0 ) ) ) @ ( 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_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) ) ) @ c_2Ecanonical_2ESPmult_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__11,axiom,
! [A_27a: d] :
( ! [V0a: mono_2Etyop_2Equote_2Eindex,V1a_27: mono_2Etyop_2Equote_2Eindex] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V0a ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1a_27 ) ) ) ) )
<=> ( V0a = V1a_27 ) )
& ! [V2a_2E0: u,V3a_27_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_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_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5a1_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6a0_27_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V7a1_27_2E0 ) ) ) )
<=> ( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4a0_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6a0_27_2E0 ) )
& ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5a1_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V7a1_27_2E0 ) ) ) )
& ! [V8a0_2E0: u,V9a1_2E0: u,V10a0_27_2E0: u,V11a1_27_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9a1_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10a0_27_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V11a1_27_2E0 ) ) ) )
<=> ( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8a0_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10a0_27_2E0 ) )
& ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9a1_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V11a1_27_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__distinct,axiom,
! [A_27a: d] :
( ! [V0a_27_2E0: u,V1a: mono_2Etyop_2Equote_2Eindex] :
( (~)
@ ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1a ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V0a_27_2E0 ) ) ) ) )
& ! [V2a1_2E0: u,V3a0_2E0: u,V4a: mono_2Etyop_2Equote_2Eindex] :
( (~)
@ ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V4a ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V3a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V2a1_2E0 ) ) ) ) )
& ! [V5a1_2E0: u,V6a0_2E0: u,V7a: mono_2Etyop_2Equote_2Eindex] :
( (~)
@ ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V7a ) ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5a1_2E0 ) ) ) ) )
& ! [V8a1_2E0: u,V9a0_2E0: u,V10a_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V10a_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8a1_2E0 ) ) ) ) )
& ! [V11a1_2E0: u,V12a0_2E0: u,V13a_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V13a_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V12a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V11a1_2E0 ) ) ) ) )
& ! [V14a1_27_2E0: u,V15a1_2E0: u,V16a0_27_2E0: u,V17a0_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V17a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V15a1_2E0 ) ) )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V16a0_27_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V14a1_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__nchotomy,axiom,
! [A_27a: d,V0ss_2E0: u] :
( ? [V1i: mono_2Etyop_2Equote_2Eindex] :
( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0ss_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V1i ) ) ) ) )
| ? [V2a_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0ss_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) )
| ? [V3s_2E0: u,V4s0_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0ss_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V3s_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4s0_2E0 ) ) ) )
| ? [V5s_2E0: u,V6s0_2E0: u] :
( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0ss_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5s_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6s0_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__Axiom,axiom,
! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u,V2f2_2E0: u,V3f3_2E0: u] :
? [V4fn_2E0: u] :
( ! [V5a: mono_2Etyop_2Equote_2Eindex] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V5a ) ) ) ) ) )
= ( 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 @ V5a ) ) ) ) )
& ! [V6a_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V6a_2E0 ) ) ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f1_2E0 ) @ ( s @ A_27a @ V6a_2E0 ) ) ) )
& ! [V7a0_2E0: u,V8a1_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V7a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8a1_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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ V2f2_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V7a0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8a1_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V7a0_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8a1_2E0 ) ) ) ) ) )
& ! [V9a0_2E0: u,V10a1_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10a1_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_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ V3f3_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9a0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10a1_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9a0_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10a1_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__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_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_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_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) ) ) )
& ! [V3s_2E0: u,V4s0_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V3s_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4s0_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V3s_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4s0_2E0 ) ) ) ) ) ) )
& ! [V5s_2E0: u,V6s0_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5s_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6s0_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5s_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V6s0_2E0 ) ) ) ) ) ) ) )
=> ! [V7s_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V7s_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__case__cong,axiom,
! [A_27a: d,A_27b: d,V0f3_27_2E0: u,V1f2_27_2E0: u,V2f1_27_2E0: u,V3f_27_2E0: u,V4M_2E0: u,V5M_27_2E0: u,V6f_2E0: u,V7f1_2E0: u,V8f2_2E0: u,V9f3_2E0: u] :
( ( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4M_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5M_27_2E0 ) )
& ! [V10a: mono_2Etyop_2Equote_2Eindex] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5M_27_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V10a ) ) ) ) )
=> ( ( 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 @ V10a ) ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V3f_27_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V10a ) ) ) ) ) )
& ! [V11a_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5M_27_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V11a_2E0 ) ) ) )
=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7f1_2E0 ) @ ( s @ A_27a @ V11a_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f1_27_2E0 ) @ ( s @ A_27a @ V11a_2E0 ) ) ) ) )
& ! [V12a0_2E0: u,V13a1_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5M_27_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V12a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V13a1_2E0 ) ) ) )
=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V8f2_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V12a0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V13a1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V1f2_27_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V12a0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V13a1_2E0 ) ) ) ) )
& ! [V14a0_2E0: u,V15a1_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5M_27_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V14a0_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V15a1_2E0 ) ) ) )
=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V9f3_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V14a0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V15a1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V0f3_27_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V14a0_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V15a1_2E0 ) ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Ecanonical_2Espolynom__CASE_2E5 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V4M_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V8f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V9f3_2E0 ) ) )
= ( s @ A_27b @ ( c_2Ecanonical_2Espolynom__CASE_2E5 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V5M_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V3f_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f1_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V1f2_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V0f3_27_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynom__case__eq,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_2E0: u,V2f3_2E0: u,V3f2_2E0: u,V4f1_2E0: u,V5f_2E0: u] :
( ( ( s @ A_27b @ ( c_2Ecanonical_2Espolynom__CASE_2E5 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V5f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V3f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V2f3_2E0 ) ) )
= ( s @ A_27b @ V1v_2E0 ) )
<=> ( ? [V6i: mono_2Etyop_2Equote_2Eindex] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPvar_2E1 @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V6i ) ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Equote_2Eindex @ A_27b ) @ V5f_2E0 ) @ ( s @ tyop_2Equote_2Eindex @ ( i_mono_2Etyop_2Equote_2Eindex @ V6i ) ) ) )
= ( s @ A_27b @ V1v_2E0 ) ) )
| ? [V7a_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPconst_2E1 @ ( s @ A_27a @ V7a_2E0 ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4f1_2E0 ) @ ( s @ A_27a @ V7a_2E0 ) ) )
= ( s @ A_27b @ V1v_2E0 ) ) )
| ? [V8s_2E0: u,V9s0_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPplus_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8s_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9s0_2E0 ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V3f2_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V8s_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V9s0_2E0 ) ) )
= ( s @ A_27b @ V1v_2E0 ) ) )
| ? [V10s_2E0: u,V11s0_2E0: u] :
( ( ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( c_2Ecanonical_2ESPmult_2E2 @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10s_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V11s0_2E0 ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ A_27b ) ) @ V2f3_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V10s_2E0 ) ) ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V11s0_2E0 ) ) )
= ( s @ A_27b @ V1v_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynomial__normalize__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2p_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__normalize_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V2p_2E0 ) ) ) ) ) ).
thf(thm_2Ecanonical_2Espolynomial__simplify__ok,axiom,
! [A_27a: d,V0sr_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) ) ) )
=> ! [V1vm_2E0: u,V2p_2E0: u] :
( ( s @ A_27a @ ( c_2Ecanonical_2Einterp__cs_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) @ ( c_2Ecanonical_2Espolynom__simplify_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Ecanonical_2Einterp__sp_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0sr_2E0 ) @ ( s @ ( tyop_2Equote_2Evarmap @ A_27a ) @ V1vm_2E0 ) @ ( s @ ( tyop_2Ecanonical_2Espolynom @ A_27a ) @ V2p_2E0 ) ) ) ) ) ).
%------------------------------------------------------------------------------