ITP001 Axioms: ITP117_7.ax


%------------------------------------------------------------------------------
% File     : ITP117_7 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : numRing.ax [Gau19]
%          : HL4117_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  285 (  93 unt; 175 typ;   0 def)
%            Number of atoms       :  281 ( 234 equ)
%            Maximal formula atoms :   91 (   0 avg)
%            Number of connectives :  175 (   4   ~;   3   |; 132   &)
%                                         (  29 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   65 (   4 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  136 (  83   >;  53   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  170 ( 170 usr;  47 con; 0-5 aty)
%            Number of variables   :  462 ( 378   !;   1   ?; 462   :)
%                                         (  83  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Ecanonical_2Ecanonical__sum,type,
    tyop_2Ecanonical_2Ecanonical__sum: $tType > $tType ).

tff(tyop_2Ecanonical_2Espolynom,type,
    tyop_2Ecanonical_2Espolynom: $tType > $tType ).

tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

tff(tyop_2Equote_2Eindex,type,
    tyop_2Equote_2Eindex: $tType ).

tff(tyop_2Equote_2Evarmap,type,
    tyop_2Equote_2Evarmap: $tType > $tType ).

tff(tyop_2Esemi__ring_2Esemi__ring,type,
    tyop_2Esemi__ring_2Esemi__ring: $tType > $tType ).

tff(tyop_2EternaryComparisons_2Eordering,type,
    tyop_2EternaryComparisons_2Eordering: $tType ).

tff(app_2E2,type,
    app_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(p,type,
    p: tyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(combin_k_2E0,type,
    combin_k_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(combin_s_2E0,type,
    combin_s_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2A_2E2,type,
    c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3E_2E0,type,
    c_2Earithmetic_2E_3E_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3E_2E2,type,
    c_2Earithmetic_2E_3E_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3E_3D_2E0,type,
    c_2Earithmetic_2E_3E_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3E_3D_2E2,type,
    c_2Earithmetic_2E_3E_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).

tff(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Ecanonical_2ECons__monom_2E0,type,
    c_2Ecanonical_2ECons__monom_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2ECons__monom_2E3,type,
    c_2Ecanonical_2ECons__monom_2E3: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(A_27a) ) > tyop_2Ecanonical_2Ecanonical__sum(A_27a) ) ).

tff(c_2Ecanonical_2ECons__varlist_2E0,type,
    c_2Ecanonical_2ECons__varlist_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ).

tff(c_2Ecanonical_2ECons__varlist_2E2,type,
    c_2Ecanonical_2ECons__varlist_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(A_27a) ) > tyop_2Ecanonical_2Ecanonical__sum(A_27a) ) ).

tff(c_2Earithmetic_2EEVEN_2E0,type,
    c_2Earithmetic_2EEVEN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EEVEN_2E1,type,
    c_2Earithmetic_2EEVEN_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2EEXP_2E0,type,
    c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EEXP_2E2,type,
    c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Equote_2EEmpty__vm_2E0,type,
    c_2Equote_2EEmpty__vm_2E0: 
      !>[A_27a: $tType] : tyop_2Equote_2Evarmap(A_27a) ).

tff(c_2Equote_2EEnd__idx_2E0,type,
    c_2Equote_2EEnd__idx_2E0: tyop_2Equote_2Eindex ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Equote_2ELeft__idx_2E0,type,
    c_2Equote_2ELeft__idx_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex) ).

tff(c_2Equote_2ELeft__idx_2E1,type,
    c_2Equote_2ELeft__idx_2E1: tyop_2Equote_2Eindex > tyop_2Equote_2Eindex ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: 
      !>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ecanonical_2ENil__monom_2E0,type,
    c_2Ecanonical_2ENil__monom_2E0: 
      !>[A_27a: $tType] : tyop_2Ecanonical_2Ecanonical__sum(A_27a) ).

tff(c_2Equote_2ENode__vm_2E0,type,
    c_2Equote_2ENode__vm_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)))) ).

tff(c_2Equote_2ENode__vm_2E3,type,
    c_2Equote_2ENode__vm_2E3: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Equote_2Evarmap(A_27a) * tyop_2Equote_2Evarmap(A_27a) ) > tyop_2Equote_2Evarmap(A_27a) ) ).

tff(c_2Earithmetic_2EODD_2E0,type,
    c_2Earithmetic_2EODD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EODD_2E1,type,
    c_2Earithmetic_2EODD_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).

tff(c_2Eprim__rec_2EPRE_2E0,type,
    c_2Eprim__rec_2EPRE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Eprim__rec_2EPRE_2E1,type,
    c_2Eprim__rec_2EPRE_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Equote_2ERight__idx_2E0,type,
    c_2Equote_2ERight__idx_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex) ).

tff(c_2Equote_2ERight__idx_2E1,type,
    c_2Equote_2ERight__idx_2E1: tyop_2Equote_2Eindex > tyop_2Equote_2Eindex ).

tff(c_2Ecanonical_2ESPconst_2E0,type,
    c_2Ecanonical_2ESPconst_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Ecanonical_2Espolynom(A_27a)) ).

tff(c_2Ecanonical_2ESPconst_2E1,type,
    c_2Ecanonical_2ESPconst_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Ecanonical_2Espolynom(A_27a) ) ).

tff(c_2Ecanonical_2ESPmult_2E0,type,
    c_2Ecanonical_2ESPmult_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Espolynom(A_27a))) ).

tff(c_2Ecanonical_2ESPmult_2E2,type,
    c_2Ecanonical_2ESPmult_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ecanonical_2Espolynom(A_27a) * tyop_2Ecanonical_2Espolynom(A_27a) ) > tyop_2Ecanonical_2Espolynom(A_27a) ) ).

tff(c_2Ecanonical_2ESPplus_2E0,type,
    c_2Ecanonical_2ESPplus_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Espolynom(A_27a))) ).

tff(c_2Ecanonical_2ESPplus_2E2,type,
    c_2Ecanonical_2ESPplus_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ecanonical_2Espolynom(A_27a) * tyop_2Ecanonical_2Espolynom(A_27a) ) > tyop_2Ecanonical_2Espolynom(A_27a) ) ).

tff(c_2Ecanonical_2ESPvar_2E0,type,
    c_2Ecanonical_2ESPvar_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Ecanonical_2Espolynom(A_27a)) ).

tff(c_2Ecanonical_2ESPvar_2E1,type,
    c_2Ecanonical_2ESPvar_2E1: 
      !>[A_27a: $tType] : ( tyop_2Equote_2Eindex > tyop_2Ecanonical_2Espolynom(A_27a) ) ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Ecanonical_2Ecanonical__sum__merge_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__merge_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2Ecanonical__sum__merge_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__merge_2E1: 
      !>[A_27a: $tType] : ( 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))) ) ).

tff(c_2Ecanonical_2Ecanonical__sum__prod_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__prod_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2Ecanonical__sum__prod_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__prod_2E1: 
      !>[A_27a: $tType] : ( 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))) ) ).

tff(c_2Ecanonical_2Ecanonical__sum__scalar_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__scalar_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2Ecanonical__sum__scalar_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__scalar_2E1: 
      !>[A_27a: $tType] : ( 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))) ) ).

tff(c_2Ecanonical_2Ecanonical__sum__scalar2_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__scalar2_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2Ecanonical__sum__scalar2_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__scalar2_2E1: 
      !>[A_27a: $tType] : ( 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))) ) ).

tff(c_2Ecanonical_2Ecanonical__sum__scalar3_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__scalar3_2E0: 
      !>[A_27a: $tType] : 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))))) ).

tff(c_2Ecanonical_2Ecanonical__sum__scalar3_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__scalar3_2E1: 
      !>[A_27a: $tType] : ( 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)))) ) ).

tff(c_2Ecanonical_2Ecanonical__sum__simplify_2E0,type,
    c_2Ecanonical_2Ecanonical__sum__simplify_2E0: 
      !>[A_27a: $tType] : 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))) ).

tff(c_2Ecanonical_2Ecanonical__sum__simplify_2E1,type,
    c_2Ecanonical_2Ecanonical__sum__simplify_2E1: 
      !>[A_27a: $tType] : ( tyop_2Esemi__ring_2Esemi__ring(A_27a) > tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)) ) ).

tff(c_2Enumeral_2EiDUB_2E0,type,
    c_2Enumeral_2EiDUB_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enumeral_2EiDUB_2E1,type,
    c_2Enumeral_2EiDUB_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Enumeral_2EiZ_2E0,type,
    c_2Enumeral_2EiZ_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enumeral_2EiZ_2E1,type,
    c_2Enumeral_2EiZ_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ecanonical_2Eics__aux_2E0,type,
    c_2Ecanonical_2Eics__aux_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2Eics__aux_2E1,type,
    c_2Ecanonical_2Eics__aux_2E1: 
      !>[A_27a: $tType] : ( 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))) ) ).

tff(c_2Enumeral_2EiiSUC_2E0,type,
    c_2Enumeral_2EiiSUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enumeral_2EiiSUC_2E1,type,
    c_2Enumeral_2EiiSUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Equote_2Eindex__compare_2E0,type,
    c_2Equote_2Eindex__compare_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)) ).

tff(c_2Equote_2Eindex__lt_2E0,type,
    c_2Equote_2Eindex__lt_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)) ).

tff(c_2Ecanonical_2Einterp__cs_2E0,type,
    c_2Ecanonical_2Einterp__cs_2E0: 
      !>[A_27a: $tType] : 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))) ).

tff(c_2Ecanonical_2Einterp__cs_2E1,type,
    c_2Ecanonical_2Einterp__cs_2E1: 
      !>[A_27a: $tType] : ( 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)) ) ).

tff(c_2Ecanonical_2Einterp__m_2E0,type,
    c_2Ecanonical_2Einterp__m_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2Einterp__m_2E1,type,
    c_2Ecanonical_2Einterp__m_2E1: 
      !>[A_27a: $tType] : ( 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))) ) ).

tff(c_2Ecanonical_2Einterp__sp_2E0,type,
    c_2Ecanonical_2Einterp__sp_2E0: 
      !>[A_27a: $tType] : 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))) ).

tff(c_2Ecanonical_2Einterp__sp_2E1,type,
    c_2Ecanonical_2Einterp__sp_2E1: 
      !>[A_27a: $tType] : ( 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)) ) ).

tff(c_2Ecanonical_2Einterp__vl_2E0,type,
    c_2Ecanonical_2Einterp__vl_2E0: 
      !>[A_27a: $tType] : 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))) ).

tff(c_2Ecanonical_2Einterp__vl_2E1,type,
    c_2Ecanonical_2Einterp__vl_2E1: 
      !>[A_27a: $tType] : ( 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)) ) ).

tff(c_2Esemi__ring_2Eis__semi__ring_2E0,type,
    c_2Esemi__ring_2Eis__semi__ring_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2Esemi__ring_2Eis__semi__ring_2E1,type,
    c_2Esemi__ring_2Eis__semi__ring_2E1: 
      !>[A_27a: $tType] : ( tyop_2Esemi__ring_2Esemi__ring(A_27a) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecanonical_2Eivl__aux_2E0,type,
    c_2Ecanonical_2Eivl__aux_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2Eivl__aux_2E1,type,
    c_2Ecanonical_2Eivl__aux_2E1: 
      !>[A_27a: $tType] : ( 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))) ) ).

tff(c_2EternaryComparisons_2Elist__compare_2E0,type,
    c_2EternaryComparisons_2Elist__compare_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering))) ).

tff(c_2EternaryComparisons_2Elist__compare_2E3,type,
    c_2EternaryComparisons_2Elist__compare_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2EternaryComparisons_2Eordering ) ).

tff(c_2EternaryComparisons_2Elist__merge_2E0,type,
    c_2EternaryComparisons_2Elist__merge_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2EternaryComparisons_2Elist__merge_2E3,type,
    c_2EternaryComparisons_2Elist__merge_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Ecanonical_2Emonom__insert_2E0,type,
    c_2Ecanonical_2Emonom__insert_2E0: 
      !>[A_27a: $tType] : 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))))) ).

tff(c_2Ecanonical_2Emonom__insert_2E1,type,
    c_2Ecanonical_2Emonom__insert_2E1: 
      !>[A_27a: $tType] : ( 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)))) ) ).

tff(c_2EnumRing_2Enum__canonical__sum__merge_2E0,type,
    c_2EnumRing_2Enum__canonical__sum__merge_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))) ).

tff(c_2EnumRing_2Enum__canonical__sum__merge_2E2,type,
    c_2EnumRing_2Enum__canonical__sum__merge_2E2: ( tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__canonical__sum__prod_2E0,type,
    c_2EnumRing_2Enum__canonical__sum__prod_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))) ).

tff(c_2EnumRing_2Enum__canonical__sum__prod_2E2,type,
    c_2EnumRing_2Enum__canonical__sum__prod_2E2: ( tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__canonical__sum__scalar_2E0,type,
    c_2EnumRing_2Enum__canonical__sum__scalar_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))) ).

tff(c_2EnumRing_2Enum__canonical__sum__scalar_2E2,type,
    c_2EnumRing_2Enum__canonical__sum__scalar_2E2: ( tyop_2Enum_2Enum * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__canonical__sum__scalar2_2E0,type,
    c_2EnumRing_2Enum__canonical__sum__scalar2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))) ).

tff(c_2EnumRing_2Enum__canonical__sum__scalar2_2E2,type,
    c_2EnumRing_2Enum__canonical__sum__scalar2_2E2: ( tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__canonical__sum__scalar3_2E0,type,
    c_2EnumRing_2Enum__canonical__sum__scalar3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))) ).

tff(c_2EnumRing_2Enum__canonical__sum__scalar3_2E3,type,
    c_2EnumRing_2Enum__canonical__sum__scalar3_2E3: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__canonical__sum__simplify_2E0,type,
    c_2EnumRing_2Enum__canonical__sum__simplify_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)) ).

tff(c_2EnumRing_2Enum__canonical__sum__simplify_2E1,type,
    c_2EnumRing_2Enum__canonical__sum__simplify_2E1: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__ics__aux_2E0,type,
    c_2EnumRing_2Enum__ics__aux_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum))) ).

tff(c_2EnumRing_2Enum__ics__aux_2E3,type,
    c_2EnumRing_2Enum__ics__aux_2E3: ( tyop_2Equote_2Evarmap(tyop_2Enum_2Enum) * tyop_2Enum_2Enum * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Enum_2Enum ).

tff(c_2EnumRing_2Enum__interp__cs_2E0,type,
    c_2EnumRing_2Enum__interp__cs_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)) ).

tff(c_2EnumRing_2Enum__interp__cs_2E2,type,
    c_2EnumRing_2Enum__interp__cs_2E2: ( tyop_2Equote_2Evarmap(tyop_2Enum_2Enum) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Enum_2Enum ).

tff(c_2EnumRing_2Enum__interp__m_2E0,type,
    c_2EnumRing_2Enum__interp__m_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))) ).

tff(c_2EnumRing_2Enum__interp__m_2E3,type,
    c_2EnumRing_2Enum__interp__m_2E3: ( tyop_2Equote_2Evarmap(tyop_2Enum_2Enum) * tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) ) > tyop_2Enum_2Enum ).

tff(c_2EnumRing_2Enum__interp__sp_2E0,type,
    c_2EnumRing_2Enum__interp__sp_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum)) ).

tff(c_2EnumRing_2Enum__interp__sp_2E2,type,
    c_2EnumRing_2Enum__interp__sp_2E2: ( tyop_2Equote_2Evarmap(tyop_2Enum_2Enum) * tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum) ) > tyop_2Enum_2Enum ).

tff(c_2EnumRing_2Enum__interp__vl_2E0,type,
    c_2EnumRing_2Enum__interp__vl_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)) ).

tff(c_2EnumRing_2Enum__interp__vl_2E2,type,
    c_2EnumRing_2Enum__interp__vl_2E2: ( tyop_2Equote_2Evarmap(tyop_2Enum_2Enum) * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) ) > tyop_2Enum_2Enum ).

tff(c_2EnumRing_2Enum__ivl__aux_2E0,type,
    c_2EnumRing_2Enum__ivl__aux_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))) ).

tff(c_2EnumRing_2Enum__ivl__aux_2E3,type,
    c_2EnumRing_2Enum__ivl__aux_2E3: ( tyop_2Equote_2Evarmap(tyop_2Enum_2Enum) * tyop_2Equote_2Eindex * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) ) > tyop_2Enum_2Enum ).

tff(c_2EnumRing_2Enum__monom__insert_2E0,type,
    c_2EnumRing_2Enum__monom__insert_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))) ).

tff(c_2EnumRing_2Enum__monom__insert_2E3,type,
    c_2EnumRing_2Enum__monom__insert_2E3: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__spolynom__normalize_2E0,type,
    c_2EnumRing_2Enum__spolynom__normalize_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)) ).

tff(c_2EnumRing_2Enum__spolynom__normalize_2E1,type,
    c_2EnumRing_2Enum__spolynom__normalize_2E1: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__spolynom__simplify_2E0,type,
    c_2EnumRing_2Enum__spolynom__simplify_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)) ).

tff(c_2EnumRing_2Enum__spolynom__simplify_2E1,type,
    c_2EnumRing_2Enum__spolynom__simplify_2E1: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EnumRing_2Enum__varlist__insert_2E0,type,
    c_2EnumRing_2Enum__varlist__insert_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))) ).

tff(c_2EnumRing_2Enum__varlist__insert_2E2,type,
    c_2EnumRing_2Enum__varlist__insert_2E2: ( tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum) ).

tff(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
    c_2EternaryComparisons_2Eordering__CASE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))) ).

tff(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
    c_2EternaryComparisons_2Eordering__CASE_2E4: 
      !>[A_27a: $tType] : ( ( tyop_2EternaryComparisons_2Eordering * A_27a * A_27a * A_27a ) > A_27a ) ).

tff(c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E0,type,
    c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Esemi__ring_2Esemi__ring(A_27a))))) ).

tff(c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4,type,
    c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4: 
      !>[A_27a: $tType] : ( ( A_27a * A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) ) > tyop_2Esemi__ring_2Esemi__ring(A_27a) ) ).

tff(c_2Ecanonical_2Espolynom__normalize_2E0,type,
    c_2Ecanonical_2Espolynom__normalize_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ).

tff(c_2Ecanonical_2Espolynom__normalize_2E1,type,
    c_2Ecanonical_2Espolynom__normalize_2E1: 
      !>[A_27a: $tType] : ( tyop_2Esemi__ring_2Esemi__ring(A_27a) > tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)) ) ).

tff(c_2Ecanonical_2Espolynom__simplify_2E0,type,
    c_2Ecanonical_2Espolynom__simplify_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ).

tff(c_2Ecanonical_2Espolynom__simplify_2E1,type,
    c_2Ecanonical_2Espolynom__simplify_2E1: 
      !>[A_27a: $tType] : ( tyop_2Esemi__ring_2Esemi__ring(A_27a) > tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)) ) ).

tff(c_2Ecanonical_2Evarlist__insert_2E0,type,
    c_2Ecanonical_2Evarlist__insert_2E0: 
      !>[A_27a: $tType] : 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)))) ).

tff(c_2Ecanonical_2Evarlist__insert_2E1,type,
    c_2Ecanonical_2Evarlist__insert_2E1: 
      !>[A_27a: $tType] : ( 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))) ) ).

tff(c_2Equote_2Evarmap__find_2E0,type,
    c_2Equote_2Evarmap__find_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27a)) ).

tff(c_2Equote_2Evarmap__find_2E2,type,
    c_2Equote_2Evarmap__find_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Equote_2Eindex * tyop_2Equote_2Evarmap(A_27a) ) > A_27a ) ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
     => ( V0f_2E0 = V1g_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Eboolext,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Etruth,axiom,
    p(c_2Ebool_2ET_2E0) ).

tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
    ~ p(c_2Ebool_2EF_2E0) ).

tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Es__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).

tff(logicdef_2E_2F_5C,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(logicdef_2E_5C_2F,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(logicdef_2E_7E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(logicdef_2E_3D_3D_3E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
      ( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
    <=> ( V0_2E0 = V1_2E0 ) ) ).

tff(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
    <=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
    <=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
      ( ( X0_2E0 = X1_2E0 )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Emin_2E_40_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2Ebool_2ECOND_2E3(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ! [X0_2E0: tyop_2Equote_2Eindex,X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex),app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex)),c_2Elist_2ECONS_2E0(tyop_2Equote_2Eindex),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Ecanonical_2ECons__monom_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2ECons__monom_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ecanonical_2ECons__varlist_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2ECons__varlist_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Equote_2ELeft__idx_2E1,axiom,
    ! [X0_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2ELeft__idx_2E1(X0_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2ELeft__idx_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Equote_2ENode__vm_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Equote_2Evarmap(A_27a),X2_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( c_2Equote_2ENode__vm_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a),app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a))),c_2Equote_2ENode__vm_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EODD_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EODD_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Equote_2ERight__idx_2E1,axiom,
    ! [X0_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2ERight__idx_2E1(X0_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2ERight__idx_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2ESPconst_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ecanonical_2ESPconst_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPconst_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecanonical_2ESPmult_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X1_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2ESPmult_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),app_2E2(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)),c_2Ecanonical_2ESPmult_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecanonical_2ESPplus_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X1_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2ESPplus_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),app_2E2(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)),c_2Ecanonical_2ESPplus_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2ESPvar_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Equote_2Eindex] : ( c_2Ecanonical_2ESPvar_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPvar_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__merge_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Ecanonical__sum__merge_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__merge_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__prod_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Ecanonical__sum__prod_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__prod_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Ecanonical__sum__scalar_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__scalar_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar2_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Ecanonical__sum__scalar2_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__scalar2_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar3_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Ecanonical__sum__scalar3_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Ecanonical__sum__scalar3_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__simplify_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Ecanonical__sum__simplify_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Ecanonical__sum__simplify_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Enumeral_2EiDUB_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiDUB_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Enumeral_2EiZ_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiZ_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Eics__aux_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Eics__aux_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Ecanonical_2Eics__aux_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Enumeral_2EiiSUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiiSUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Einterp__cs_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Einterp__cs_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__cs_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Einterp__m_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Einterp__m_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2Ecanonical_2Einterp__m_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Einterp__sp_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Einterp__sp_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__sp_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Einterp__vl_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Einterp__vl_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__vl_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Esemi__ring_2Eis__semi__ring_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Esemi__ring_2Eis__semi__ring_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Esemi__ring_2Eis__semi__ring_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Eivl__aux_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Eivl__aux_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2Ecanonical_2Eivl__aux_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering),app_2E2(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(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2EternaryComparisons_2Elist__merge_2E3_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex)),app_2E2(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(tyop_2Equote_2Eindex),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Emonom__insert_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Emonom__insert_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Emonom__insert_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2EnumRing_2Enum__canonical__sum__merge_2E2,axiom,
    ! [X0_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__merge_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__canonical__sum__merge_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EnumRing_2Enum__canonical__sum__prod_2E2,axiom,
    ! [X0_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__prod_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__canonical__sum__prod_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EnumRing_2Enum__canonical__sum__scalar_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__canonical__sum__scalar_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EnumRing_2Enum__canonical__sum__scalar2_2E2,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__canonical__sum__scalar2_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EnumRing_2Enum__canonical__sum__scalar3_2E3,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__scalar3_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EnumRing_2Enum__canonical__sum__simplify_2E1,axiom,
    ! [X0_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__simplify_2E1(X0_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2EnumRing_2Enum__ics__aux_2E3,axiom,
    ! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__ics__aux_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__ics__aux_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2EnumRing_2Enum__interp__cs_2E2,axiom,
    ! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__cs_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2EnumRing_2Enum__interp__cs_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EnumRing_2Enum__interp__m_2E3,axiom,
    ! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__interp__m_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum),app_2E2(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__interp__m_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2EnumRing_2Enum__interp__sp_2E2,axiom,
    ! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X1_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__sp_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2EnumRing_2Enum__interp__sp_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EnumRing_2Enum__interp__vl_2E2,axiom,
    ! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__interp__vl_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum,app_2E2(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum),c_2EnumRing_2Enum__interp__vl_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2EnumRing_2Enum__ivl__aux_2E3,axiom,
    ! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X1_2E0: tyop_2Equote_2Eindex,X2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__ivl__aux_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum),app_2E2(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__ivl__aux_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2EnumRing_2Enum__monom__insert_2E3,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__monom__insert_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__monom__insert_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2EnumRing_2Enum__spolynom__normalize_2E1,axiom,
    ! [X0_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__spolynom__normalize_2E1(X0_2E0) = app_2E2(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EnumRing_2Enum__spolynom__simplify_2E1,axiom,
    ! [X0_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__spolynom__simplify_2E1(X0_2E0) = app_2E2(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__simplify_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2EnumRing_2Enum__varlist__insert_2E2,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__varlist__insert_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__varlist__insert_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X3_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq4_2Ec_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)))),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Espolynom__normalize_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Espolynom__normalize_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Espolynom__normalize_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Espolynom__simplify_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Espolynom__simplify_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Espolynom__simplify_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecanonical_2Evarlist__insert_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)] : ( c_2Ecanonical_2Evarlist__insert_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Evarlist__insert_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2Equote_2Evarmap__find_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Equote_2Eindex,X1_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( c_2Equote_2Evarmap__find_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27a,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27a),c_2Equote_2Evarmap__find_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Equote_2Evarmap__find_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Equote_2Eindex,X1_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum)] : ( c_2Equote_2Evarmap__find_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Equote_2Evarmap__find_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(thm_2EnumRing_2Enum__interp__sp__def,axiom,
    c_2EnumRing_2Enum__interp__sp_2E0 = c_2Ecanonical_2Einterp__sp_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__spolynom__simplify__def,axiom,
    c_2EnumRing_2Enum__spolynom__simplify_2E0 = c_2Ecanonical_2Espolynom__simplify_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__spolynom__normalize__def,axiom,
    c_2EnumRing_2Enum__spolynom__normalize_2E0 = c_2Ecanonical_2Espolynom__normalize_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__interp__cs__def,axiom,
    c_2EnumRing_2Enum__interp__cs_2E0 = c_2Ecanonical_2Einterp__cs_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__ics__aux__def,axiom,
    c_2EnumRing_2Enum__ics__aux_2E0 = c_2Ecanonical_2Eics__aux_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__interp__m__def,axiom,
    c_2EnumRing_2Enum__interp__m_2E0 = c_2Ecanonical_2Einterp__m_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__interp__vl__def,axiom,
    c_2EnumRing_2Enum__interp__vl_2E0 = c_2Ecanonical_2Einterp__vl_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__ivl__aux__def,axiom,
    c_2EnumRing_2Enum__ivl__aux_2E0 = c_2Ecanonical_2Eivl__aux_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__canonical__sum__simplify__def,axiom,
    c_2EnumRing_2Enum__canonical__sum__simplify_2E0 = c_2Ecanonical_2Ecanonical__sum__simplify_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__canonical__sum__prod__def,axiom,
    c_2EnumRing_2Enum__canonical__sum__prod_2E0 = c_2Ecanonical_2Ecanonical__sum__prod_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__canonical__sum__scalar3__def,axiom,
    c_2EnumRing_2Enum__canonical__sum__scalar3_2E0 = c_2Ecanonical_2Ecanonical__sum__scalar3_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__canonical__sum__scalar2__def,axiom,
    c_2EnumRing_2Enum__canonical__sum__scalar2_2E0 = c_2Ecanonical_2Ecanonical__sum__scalar2_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__canonical__sum__scalar__def,axiom,
    c_2EnumRing_2Enum__canonical__sum__scalar_2E0 = c_2Ecanonical_2Ecanonical__sum__scalar_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__varlist__insert__def,axiom,
    c_2EnumRing_2Enum__varlist__insert_2E0 = c_2Ecanonical_2Evarlist__insert_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__monom__insert__def,axiom,
    c_2EnumRing_2Enum__monom__insert_2E0 = c_2Ecanonical_2Emonom__insert_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__canonical__sum__merge__def,axiom,
    c_2EnumRing_2Enum__canonical__sum__merge_2E0 = c_2Ecanonical_2Ecanonical__sum__merge_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)) ).

tff(thm_2EnumRing_2Enum__semi__ring,axiom,
    p(c_2Esemi__ring_2Eis__semi__ring_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0))) ).

tff(thm_2EnumRing_2Enum__ring__thms,axiom,
    ! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V105c_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V105c_2E0))
        <=> ( V105c_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
     => ( ! [V105c_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V105c_2E0))
          <=> ( V105c_2E0 = c_2Enum_2E0_2E0 ) )
       => ( ! [V24x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,F0_2E0,V24x_2E0) = c_2Ebool_2ET_2E0 )
         => ( p(c_2Esemi__ring_2Eis__semi__ring_2E1(tyop_2Enum_2Enum,c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E0,c_2Earithmetic_2E_2A_2E0)))
            & ! [V0vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V1p_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__sp_2E2(V0vm_2E0,V1p_2E0) = c_2EnumRing_2Enum__interp__cs_2E2(V0vm_2E0,c_2EnumRing_2Enum__spolynom__simplify_2E1(V1p_2E0)) )
            & ! [V2vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V3c_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__interp__sp_2E2(V2vm_2E0,c_2Ecanonical_2ESPconst_2E1(tyop_2Enum_2Enum,V3c_2E0)) = V3c_2E0 )
            & ! [V4vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V5i_2E0: tyop_2Equote_2Eindex] : ( c_2EnumRing_2Enum__interp__sp_2E2(V4vm_2E0,c_2Ecanonical_2ESPvar_2E1(tyop_2Enum_2Enum,V5i_2E0)) = c_2Equote_2Evarmap__find_2E2(tyop_2Enum_2Enum,V5i_2E0,V4vm_2E0) )
            & ! [V6vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V7p1_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V8p2_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__sp_2E2(V6vm_2E0,c_2Ecanonical_2ESPplus_2E2(tyop_2Enum_2Enum,V7p1_2E0,V8p2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2EnumRing_2Enum__interp__sp_2E2(V6vm_2E0,V7p1_2E0),c_2EnumRing_2Enum__interp__sp_2E2(V6vm_2E0,V8p2_2E0)) )
            & ! [V9vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V10p1_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V11p2_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__sp_2E2(V9vm_2E0,c_2Ecanonical_2ESPmult_2E2(tyop_2Enum_2Enum,V10p1_2E0,V11p2_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2EnumRing_2Enum__interp__sp_2E2(V9vm_2E0,V10p1_2E0),c_2EnumRing_2Enum__interp__sp_2E2(V9vm_2E0,V11p2_2E0)) )
            & ! [V12x_2E0: A_27a,V13v2_2E0: tyop_2Equote_2Evarmap(A_27a),V14v1_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( c_2Equote_2Evarmap__find_2E2(A_27a,c_2Equote_2EEnd__idx_2E0,c_2Equote_2ENode__vm_2E3(A_27a,V12x_2E0,V14v1_2E0,V13v2_2E0)) = V12x_2E0 )
            & ! [V15x_2E0: A_27a,V16v2_2E0: tyop_2Equote_2Evarmap(A_27a),V17v1_2E0: tyop_2Equote_2Evarmap(A_27a),V18i1_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,c_2Equote_2ERight__idx_2E1(V18i1_2E0),c_2Equote_2ENode__vm_2E3(A_27a,V15x_2E0,V17v1_2E0,V16v2_2E0)) = c_2Equote_2Evarmap__find_2E2(A_27a,V18i1_2E0,V16v2_2E0) )
            & ! [V19x_2E0: A_27a,V20v2_2E0: tyop_2Equote_2Evarmap(A_27a),V21v1_2E0: tyop_2Equote_2Evarmap(A_27a),V22i1_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,c_2Equote_2ELeft__idx_2E1(V22i1_2E0),c_2Equote_2ENode__vm_2E3(A_27a,V19x_2E0,V21v1_2E0,V20v2_2E0)) = c_2Equote_2Evarmap__find_2E2(A_27a,V22i1_2E0,V21v1_2E0) )
            & ! [V23i_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,V23i_2E0,c_2Equote_2EEmpty__vm_2E0(A_27a)) = c_2Emin_2E_40_2E1(A_27a,F0_2E0) )
            & ! [V25t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V26t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V27l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V28l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V29c2_2E0: tyop_2Enum_2Enum,V30c1_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V30c1_2E0,V28l1_2E0,V26t1_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V29c2_2E0,V27l2_2E0,V25t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V28l1_2E0,V27l2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V30c1_2E0,V28l1_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(V26t1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V29c2_2E0,V27l2_2E0,V25t2_2E0))),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V30c1_2E0,V29c2_2E0),V28l1_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(V26t1_2E0,V25t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V29c2_2E0,V27l2_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V30c1_2E0,V28l1_2E0,V26t1_2E0),V25t2_2E0))) )
            & ! [V31t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V32t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V33l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V34l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V35c1_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V35c1_2E0,V34l1_2E0,V32t1_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V33l2_2E0,V31t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V34l1_2E0,V33l2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V35c1_2E0,V34l1_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(V32t1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V33l2_2E0,V31t2_2E0))),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V35c1_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V34l1_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(V32t1_2E0,V31t2_2E0)),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V33l2_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V35c1_2E0,V34l1_2E0,V32t1_2E0),V31t2_2E0))) )
            & ! [V36t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V37t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V38l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V39l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V40c2_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V39l1_2E0,V37t1_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V40c2_2E0,V38l2_2E0,V36t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V39l1_2E0,V38l2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V39l1_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(V37t1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V40c2_2E0,V38l2_2E0,V36t2_2E0))),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V40c2_2E0),V39l1_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(V37t1_2E0,V36t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V40c2_2E0,V38l2_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V39l1_2E0,V37t1_2E0),V36t2_2E0))) )
            & ! [V41t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V42t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V43l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V44l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V44l1_2E0,V42t1_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V43l2_2E0,V41t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V44l1_2E0,V43l2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V44l1_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(V42t1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V43l2_2E0,V41t2_2E0))),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V44l1_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(V42t1_2E0,V41t2_2E0)),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V43l2_2E0,c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V44l1_2E0,V42t1_2E0),V41t2_2E0))) )
            & ! [V45s1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__merge_2E2(V45s1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = V45s1_2E0 )
            & ! [V46v6_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V47v5_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V48v4_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V48v4_2E0,V47v5_2E0,V46v6_2E0)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V48v4_2E0,V47v5_2E0,V46v6_2E0) )
            & ! [V49v8_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V50v7_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V50v7_2E0,V49v8_2E0)) = c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V50v7_2E0,V49v8_2E0) )
            & ! [V51t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V52l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V53l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V54c2_2E0: tyop_2Enum_2Enum,V55c1_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__monom__insert_2E3(V55c1_2E0,V53l1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V54c2_2E0,V52l2_2E0,V51t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V53l1_2E0,V52l2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V55c1_2E0,V53l1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V54c2_2E0,V52l2_2E0,V51t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V55c1_2E0,V54c2_2E0),V53l1_2E0,V51t2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V54c2_2E0,V52l2_2E0,c_2EnumRing_2Enum__monom__insert_2E3(V55c1_2E0,V53l1_2E0,V51t2_2E0))) )
            & ! [V56t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V57l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V58l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V59c1_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__monom__insert_2E3(V59c1_2E0,V58l1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V57l2_2E0,V56t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V58l1_2E0,V57l2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V59c1_2E0,V58l1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V57l2_2E0,V56t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V59c1_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V58l1_2E0,V56t2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V57l2_2E0,c_2EnumRing_2Enum__monom__insert_2E3(V59c1_2E0,V58l1_2E0,V56t2_2E0))) )
            & ! [V60l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V61c1_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__monom__insert_2E3(V61c1_2E0,V60l1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V61c1_2E0,V60l1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) )
            & ! [V62t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V63l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V64l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V65c2_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__varlist__insert_2E2(V64l1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V65c2_2E0,V63l2_2E0,V62t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V64l1_2E0,V63l2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V64l1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V65c2_2E0,V63l2_2E0,V62t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V65c2_2E0),V64l1_2E0,V62t2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V65c2_2E0,V63l2_2E0,c_2EnumRing_2Enum__varlist__insert_2E2(V64l1_2E0,V62t2_2E0))) )
            & ! [V66t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V67l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V68l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__varlist__insert_2E2(V68l1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V67l2_2E0,V66t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V68l1_2E0,V67l2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V68l1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V67l2_2E0,V66t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V68l1_2E0,V66t2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V67l2_2E0,c_2EnumRing_2Enum__varlist__insert_2E2(V68l1_2E0,V66t2_2E0))) )
            & ! [V69l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__varlist__insert_2E2(V69l1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V69l1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) )
            & ! [V70c0_2E0: tyop_2Enum_2Enum,V71c_2E0: tyop_2Enum_2Enum,V72l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V73t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar_2E2(V70c0_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V71c_2E0,V72l_2E0,V73t_2E0)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(V70c0_2E0,V71c_2E0),V72l_2E0,c_2EnumRing_2Enum__canonical__sum__scalar_2E2(V70c0_2E0,V73t_2E0)) )
            & ! [V74c0_2E0: tyop_2Enum_2Enum,V75l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V76t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar_2E2(V74c0_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V75l_2E0,V76t_2E0)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V74c0_2E0,V75l_2E0,c_2EnumRing_2Enum__canonical__sum__scalar_2E2(V74c0_2E0,V76t_2E0)) )
            & ! [V77c0_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__canonical__sum__scalar_2E2(V77c0_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum) )
            & ! [V78l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V79c_2E0: tyop_2Enum_2Enum,V80l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V81t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(V78l0_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V79c_2E0,V80l_2E0,V81t_2E0)) = c_2EnumRing_2Enum__monom__insert_2E3(V79c_2E0,c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,c_2Equote_2Eindex__lt_2E0,V78l0_2E0,V80l_2E0),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(V78l0_2E0,V81t_2E0)) )
            & ! [V82l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V83l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V84t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(V82l0_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V83l_2E0,V84t_2E0)) = c_2EnumRing_2Enum__varlist__insert_2E2(c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,c_2Equote_2Eindex__lt_2E0,V82l0_2E0,V83l_2E0),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(V82l0_2E0,V84t_2E0)) )
            & ! [V85l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(V85l0_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum) )
            & ! [V86c0_2E0: tyop_2Enum_2Enum,V87l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V88c_2E0: tyop_2Enum_2Enum,V89l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V90t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(V86c0_2E0,V87l0_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V88c_2E0,V89l_2E0,V90t_2E0)) = c_2EnumRing_2Enum__monom__insert_2E3(c_2Earithmetic_2E_2A_2E2(V86c0_2E0,V88c_2E0),c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,c_2Equote_2Eindex__lt_2E0,V87l0_2E0,V89l_2E0),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(V86c0_2E0,V87l0_2E0,V90t_2E0)) )
            & ! [V91c0_2E0: tyop_2Enum_2Enum,V92l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V93l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V94t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(V91c0_2E0,V92l0_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V93l_2E0,V94t_2E0)) = c_2EnumRing_2Enum__monom__insert_2E3(V91c0_2E0,c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,c_2Equote_2Eindex__lt_2E0,V92l0_2E0,V93l_2E0),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(V91c0_2E0,V92l0_2E0,V94t_2E0)) )
            & ! [V95c0_2E0: tyop_2Enum_2Enum,V96l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(V95c0_2E0,V96l0_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum) )
            & ! [V97c1_2E0: tyop_2Enum_2Enum,V98l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V99t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V100s2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__prod_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V97c1_2E0,V98l1_2E0,V99t1_2E0),V100s2_2E0) = c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(V97c1_2E0,V98l1_2E0,V100s2_2E0),c_2EnumRing_2Enum__canonical__sum__prod_2E2(V99t1_2E0,V100s2_2E0)) )
            & ! [V101l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V102t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V103s2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__prod_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V101l1_2E0,V102t1_2E0),V103s2_2E0) = c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(V101l1_2E0,V103s2_2E0),c_2EnumRing_2Enum__canonical__sum__prod_2E2(V102t1_2E0,V103s2_2E0)) )
            & ! [V104s2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__prod_2E2(c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum),V104s2_2E0) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum) )
            & ! [V105c_2E0: tyop_2Enum_2Enum,V106l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V107t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__simplify_2E1(c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V105c_2E0,V106l_2E0,V107t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V105c_2E0),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(V107t_2E0),c_2Ebool_2ECOND_2E3(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V105c_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V106l_2E0,c_2EnumRing_2Enum__canonical__sum__simplify_2E1(V107t_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V105c_2E0,V106l_2E0,c_2EnumRing_2Enum__canonical__sum__simplify_2E1(V107t_2E0)))) )
            & ! [V108l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V109t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__canonical__sum__simplify_2E1(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V108l_2E0,V109t_2E0)) = c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V108l_2E0,c_2EnumRing_2Enum__canonical__sum__simplify_2E1(V109t_2E0)) )
            & ( c_2EnumRing_2Enum__canonical__sum__simplify_2E1(c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum) )
            & ! [V110vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V111x_2E0: tyop_2Equote_2Eindex] : ( c_2EnumRing_2Enum__ivl__aux_2E3(V110vm_2E0,V111x_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex)) = c_2Equote_2Evarmap__find_2E2(tyop_2Enum_2Enum,V111x_2E0,V110vm_2E0) )
            & ! [V112vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V113x_2E0: tyop_2Equote_2Eindex,V114x_27_2E0: tyop_2Equote_2Eindex,V115t_27_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__ivl__aux_2E3(V112vm_2E0,V113x_2E0,c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,V114x_27_2E0,V115t_27_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Equote_2Evarmap__find_2E2(tyop_2Enum_2Enum,V113x_2E0,V112vm_2E0),c_2EnumRing_2Enum__ivl__aux_2E3(V112vm_2E0,V114x_27_2E0,V115t_27_2E0)) )
            & ! [V116vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__vl_2E2(V116vm_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
            & ! [V117vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V118x_2E0: tyop_2Equote_2Eindex,V119t_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__interp__vl_2E2(V117vm_2E0,c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,V118x_2E0,V119t_2E0)) = c_2EnumRing_2Enum__ivl__aux_2E3(V117vm_2E0,V118x_2E0,V119t_2E0) )
            & ! [V120vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V121c_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__interp__m_2E3(V120vm_2E0,V121c_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex)) = V121c_2E0 )
            & ! [V122vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V123c_2E0: tyop_2Enum_2Enum,V124x_2E0: tyop_2Equote_2Eindex,V125t_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EnumRing_2Enum__interp__m_2E3(V122vm_2E0,V123c_2E0,c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,V124x_2E0,V125t_2E0)) = c_2Earithmetic_2E_2A_2E2(V123c_2E0,c_2EnumRing_2Enum__ivl__aux_2E3(V122vm_2E0,V124x_2E0,V125t_2E0)) )
            & ! [V126vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V127a_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__ics__aux_2E3(V126vm_2E0,V127a_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = V127a_2E0 )
            & ! [V128vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V129a_2E0: tyop_2Enum_2Enum,V130l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V131t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__ics__aux_2E3(V128vm_2E0,V129a_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V130l_2E0,V131t_2E0)) = c_2Earithmetic_2E_2B_2E2(V129a_2E0,c_2EnumRing_2Enum__ics__aux_2E3(V128vm_2E0,c_2EnumRing_2Enum__interp__vl_2E2(V128vm_2E0,V130l_2E0),V131t_2E0)) )
            & ! [V132vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V133a_2E0: tyop_2Enum_2Enum,V134c_2E0: tyop_2Enum_2Enum,V135l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V136t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__ics__aux_2E3(V132vm_2E0,V133a_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V134c_2E0,V135l_2E0,V136t_2E0)) = c_2Earithmetic_2E_2B_2E2(V133a_2E0,c_2EnumRing_2Enum__ics__aux_2E3(V132vm_2E0,c_2EnumRing_2Enum__interp__m_2E3(V132vm_2E0,V134c_2E0,V135l_2E0),V136t_2E0)) )
            & ! [V137vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__cs_2E2(V137vm_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) = c_2Enum_2E0_2E0 )
            & ! [V138vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V139l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V140t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__cs_2E2(V138vm_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,V139l_2E0,V140t_2E0)) = c_2EnumRing_2Enum__ics__aux_2E3(V138vm_2E0,c_2EnumRing_2Enum__interp__vl_2E2(V138vm_2E0,V139l_2E0),V140t_2E0) )
            & ! [V141vm_2E0: tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V142c_2E0: tyop_2Enum_2Enum,V143l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V144t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__interp__cs_2E2(V141vm_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V142c_2E0,V143l_2E0,V144t_2E0)) = c_2EnumRing_2Enum__ics__aux_2E3(V141vm_2E0,c_2EnumRing_2Enum__interp__m_2E3(V141vm_2E0,V142c_2E0,V143l_2E0),V144t_2E0) )
            & ! [V145i_2E0: tyop_2Equote_2Eindex] : ( c_2EnumRing_2Enum__spolynom__normalize_2E1(c_2Ecanonical_2ESPvar_2E1(tyop_2Enum_2Enum,V145i_2E0)) = c_2Ecanonical_2ECons__varlist_2E2(tyop_2Enum_2Enum,c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,V145i_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex)),c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) )
            & ! [V146c_2E0: tyop_2Enum_2Enum] : ( c_2EnumRing_2Enum__spolynom__normalize_2E1(c_2Ecanonical_2ESPconst_2E1(tyop_2Enum_2Enum,V146c_2E0)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Enum_2Enum,V146c_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex),c_2Ecanonical_2ENil__monom_2E0(tyop_2Enum_2Enum)) )
            & ! [V147l_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V148r_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__spolynom__normalize_2E1(c_2Ecanonical_2ESPplus_2E2(tyop_2Enum_2Enum,V147l_2E0,V148r_2E0)) = c_2EnumRing_2Enum__canonical__sum__merge_2E2(c_2EnumRing_2Enum__spolynom__normalize_2E1(V147l_2E0),c_2EnumRing_2Enum__spolynom__normalize_2E1(V148r_2E0)) )
            & ! [V149l_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V150r_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__spolynom__normalize_2E1(c_2Ecanonical_2ESPmult_2E2(tyop_2Enum_2Enum,V149l_2E0,V150r_2E0)) = c_2EnumRing_2Enum__canonical__sum__prod_2E2(c_2EnumRing_2Enum__spolynom__normalize_2E1(V149l_2E0),c_2EnumRing_2Enum__spolynom__normalize_2E1(V150r_2E0)) )
            & ! [V151x_2E0: tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)] : ( c_2EnumRing_2Enum__spolynom__simplify_2E1(V151x_2E0) = c_2EnumRing_2Enum__canonical__sum__simplify_2E1(c_2EnumRing_2Enum__spolynom__normalize_2E1(V151x_2E0)) ) ) ) ) ) ).

tff(thm_2EnumRing_2Enum__rewrites,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(c_2Enum_2E0_2E0,V1n_2E0) = V1n_2E0 )
      & ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Enum_2E0_2E0) = V2n_2E0 )
      & ! [V3n_2E0: tyop_2Enum_2Enum,V4m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(V3n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V4m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V3n_2E0,V4m_2E0))) )
      & ! [V5n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(c_2Enum_2E0_2E0,V5n_2E0) = c_2Enum_2E0_2E0 )
      & ! [V6n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(V6n_2E0,c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
      & ! [V7n_2E0: tyop_2Enum_2Enum,V8m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(V7n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V8m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2A_2E2(V7n_2E0,V8m_2E0)) )
      & ! [V9n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(c_2Enum_2E0_2E0,V9n_2E0) = c_2Enum_2E0_2E0 )
      & ! [V10n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(V10n_2E0,c_2Enum_2E0_2E0) = V10n_2E0 )
      & ! [V11n_2E0: tyop_2Enum_2Enum,V12m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V11n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V12m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2D_2E2(V11n_2E0,V12m_2E0)) )
      & ! [V13n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V13n_2E0))) = c_2Enum_2E0_2E0 )
      & ! [V14n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V14n_2E0))) = c_2Enum_2E0_2E0 )
      & ! [V15n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(V15n_2E0,c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
      & ! [V16n_2E0: tyop_2Enum_2Enum,V17m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(V16n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V17m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EEXP_2E2(V16n_2E0,V17m_2E0)) )
      & ( c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
      & ! [V18n_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2ENUMERAL_2E1(V18n_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enum_2ESUC_2E1(V18n_2E0)) )
      & ( c_2Eprim__rec_2EPRE_2E1(c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
      & ! [V19n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2ENUMERAL_2E1(V19n_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Eprim__rec_2EPRE_2E1(V19n_2E0)) )
      & ! [V20n_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2ENUMERAL_2E1(V20n_2E0) = c_2Enum_2E0_2E0 )
        <=> ( V20n_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
      & ! [V21n_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Enum_2E0_2E0 = c_2Earithmetic_2ENUMERAL_2E1(V21n_2E0) )
        <=> ( V21n_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
      & ! [V22n_2E0: tyop_2Enum_2Enum,V23m_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2ENUMERAL_2E1(V22n_2E0) = c_2Earithmetic_2ENUMERAL_2E1(V23m_2E0) )
        <=> ( V22n_2E0 = V23m_2E0 ) )
      & ! [V24n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(V24n_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0 )
      & ! [V25n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(V25n_2E0)) = c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,V25n_2E0) )
      & ! [V26n_2E0: tyop_2Enum_2Enum,V27m_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(V26n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V27m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V26n_2E0,V27m_2E0) )
      & ! [V28n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E2(c_2Enum_2E0_2E0,V28n_2E0) = c_2Ebool_2EF_2E0 )
      & ! [V29n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E2(c_2Earithmetic_2ENUMERAL_2E1(V29n_2E0),c_2Enum_2E0_2E0) = c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,V29n_2E0) )
      & ! [V30n_2E0: tyop_2Enum_2Enum,V31m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E2(c_2Earithmetic_2ENUMERAL_2E1(V30n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V31m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V31m_2E0,V30n_2E0) )
      & ! [V32n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2E0_2E0,V32n_2E0) = c_2Ebool_2ET_2E0 )
      & ! [V33n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V33n_2E0),c_2Enum_2E0_2E0) = c_2Earithmetic_2E_3C_3D_2E2(V33n_2E0,c_2Earithmetic_2EZERO_2E0) )
      & ! [V34n_2E0: tyop_2Enum_2Enum,V35m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V34n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V35m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V34n_2E0,V35m_2E0) )
      & ! [V36n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(V36n_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0 )
      & ! [V37n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Earithmetic_2E_3E_3D_2E2(c_2Enum_2E0_2E0,V37n_2E0))
        <=> ( V37n_2E0 = c_2Enum_2E0_2E0 ) )
      & ! [V38n_2E0: tyop_2Enum_2Enum,V39m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V38n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V39m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V39m_2E0,V38n_2E0) )
      & ! [V40n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EODD_2E1(c_2Earithmetic_2ENUMERAL_2E1(V40n_2E0)) = c_2Earithmetic_2EODD_2E1(V40n_2E0) )
      & ! [V41n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2ENUMERAL_2E1(V41n_2E0)) = c_2Earithmetic_2EEVEN_2E1(V41n_2E0) )
      & ~ p(c_2Earithmetic_2EODD_2E1(c_2Enum_2E0_2E0))
      & p(c_2Earithmetic_2EEVEN_2E1(c_2Enum_2E0_2E0))
      & ! [V42n_2E0: tyop_2Enum_2Enum,V43m_2E0: tyop_2Enum_2Enum] :
          ( ( ( c_2Earithmetic_2EZERO_2E0 = c_2Earithmetic_2EBIT1_2E1(V42n_2E0) )
          <=> p(c_2Ebool_2EF_2E0) )
          & ( ( c_2Earithmetic_2EBIT1_2E1(V42n_2E0) = c_2Earithmetic_2EZERO_2E0 )
          <=> p(c_2Ebool_2EF_2E0) )
          & ( ( c_2Earithmetic_2EZERO_2E0 = c_2Earithmetic_2EBIT2_2E1(V42n_2E0) )
          <=> p(c_2Ebool_2EF_2E0) )
          & ( ( c_2Earithmetic_2EBIT2_2E1(V42n_2E0) = c_2Earithmetic_2EZERO_2E0 )
          <=> p(c_2Ebool_2EF_2E0) )
          & ( ( c_2Earithmetic_2EBIT1_2E1(V42n_2E0) = c_2Earithmetic_2EBIT2_2E1(V43m_2E0) )
          <=> p(c_2Ebool_2EF_2E0) )
          & ( ( c_2Earithmetic_2EBIT2_2E1(V42n_2E0) = c_2Earithmetic_2EBIT1_2E1(V43m_2E0) )
          <=> p(c_2Ebool_2EF_2E0) )
          & ( ( c_2Earithmetic_2EBIT1_2E1(V42n_2E0) = c_2Earithmetic_2EBIT1_2E1(V43m_2E0) )
          <=> ( V42n_2E0 = V43m_2E0 ) )
          & ( ( c_2Earithmetic_2EBIT2_2E1(V42n_2E0) = c_2Earithmetic_2EBIT2_2E1(V43m_2E0) )
          <=> ( V42n_2E0 = V43m_2E0 ) ) )
      & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0) )
      & ! [V44n_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2EBIT1_2E1(V44n_2E0)) = c_2Earithmetic_2EBIT2_2E1(V44n_2E0) )
      & ! [V45n_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2EBIT2_2E1(V45n_2E0)) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(V45n_2E0)) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)) )
      & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)) )
      & ! [V46n_2E0: tyop_2Enum_2Enum,V47m_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V46n_2E0)) = V46n_2E0 )
          & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,c_2Earithmetic_2EZERO_2E0)) = V46n_2E0 )
          & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V46n_2E0),c_2Earithmetic_2EBIT1_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V46n_2E0),c_2Earithmetic_2EBIT2_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V46n_2E0),c_2Earithmetic_2EBIT1_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V46n_2E0),c_2Earithmetic_2EBIT2_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V46n_2E0)) = c_2Enum_2ESUC_2E1(V46n_2E0) )
          & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,c_2Earithmetic_2EZERO_2E0)) = c_2Enum_2ESUC_2E1(V46n_2E0) )
          & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V46n_2E0),c_2Earithmetic_2EBIT1_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V46n_2E0),c_2Earithmetic_2EBIT2_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V46n_2E0),c_2Earithmetic_2EBIT1_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V46n_2E0),c_2Earithmetic_2EBIT2_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V46n_2E0)) = c_2Enumeral_2EiiSUC_2E1(V46n_2E0) )
          & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,c_2Earithmetic_2EZERO_2E0)) = c_2Enumeral_2EiiSUC_2E1(V46n_2E0) )
          & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V46n_2E0),c_2Earithmetic_2EBIT1_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V46n_2E0),c_2Earithmetic_2EBIT2_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V46n_2E0),c_2Earithmetic_2EBIT1_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) )
          & ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V46n_2E0),c_2Earithmetic_2EBIT2_2E1(V47m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V46n_2E0,V47m_2E0))) ) )
      & ! [V48n_2E0: tyop_2Enum_2Enum,V49m_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EZERO_2E0,V48n_2E0) = c_2Earithmetic_2EZERO_2E0 )
          & ( c_2Earithmetic_2E_2A_2E2(V48n_2E0,c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 )
          & ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT1_2E1(V48n_2E0),V49m_2E0) = c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2E_2A_2E2(V48n_2E0,V49m_2E0)),V49m_2E0)) )
          & ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT2_2E1(V48n_2E0),V49m_2E0) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(V48n_2E0,V49m_2E0),V49m_2E0))) ) )
      & ! [V50n_2E0: tyop_2Enum_2Enum] :
          ( ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EBIT1_2E1(V50n_2E0)) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiDUB_2E1(V50n_2E0)) )
          & ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EBIT2_2E1(V50n_2E0)) = c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(V50n_2E0)) )
          & ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 ) )
      & ( ( c_2Earithmetic_2EZERO_2E0 = c_2Earithmetic_2EZERO_2E0 )
      <=> p(c_2Ebool_2ET_2E0) )
      & ( ( c_2Enum_2E0_2E0 = c_2Enum_2E0_2E0 )
      <=> p(c_2Ebool_2ET_2E0) ) ) ).

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