ITP001 Axioms: ITP129_7.ax
%------------------------------------------------------------------------------
% File : ITP129_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : ratRing.ax [Gau19]
% : HL4129_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 268 ( 88 unt; 164 typ; 0 def)
% Number of atoms : 187 ( 151 equ)
% Maximal formula atoms : 62 ( 0 avg)
% Number of connectives : 86 ( 3 ~; 3 |; 58 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 124 ( 76 >; 48 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 158 ( 158 usr; 38 con; 0-6 aty)
% Number of variables : 409 ( 317 !; 1 ?; 409 :)
% ( 91 !>; 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_2Erat_2Erat,type,
tyop_2Erat_2Erat: $tType ).
tff(tyop_2Ering_2Ering,type,
tyop_2Ering_2Ering: $tType > $tType ).
tff(tyop_2EringNorm_2Epolynom,type,
tyop_2EringNorm_2Epolynom: $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_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_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_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_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_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_2EringNorm_2EPconst_2E0,type,
c_2EringNorm_2EPconst_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2EringNorm_2Epolynom(A_27a)) ).
tff(c_2EringNorm_2EPconst_2E1,type,
c_2EringNorm_2EPconst_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2EringNorm_2Epolynom(A_27a) ) ).
tff(c_2EringNorm_2EPmult_2E0,type,
c_2EringNorm_2EPmult_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2EringNorm_2Epolynom(A_27a))) ).
tff(c_2EringNorm_2EPmult_2E2,type,
c_2EringNorm_2EPmult_2E2:
!>[A_27a: $tType] : ( ( tyop_2EringNorm_2Epolynom(A_27a) * tyop_2EringNorm_2Epolynom(A_27a) ) > tyop_2EringNorm_2Epolynom(A_27a) ) ).
tff(c_2EringNorm_2EPopp_2E0,type,
c_2EringNorm_2EPopp_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2EringNorm_2Epolynom(A_27a)) ).
tff(c_2EringNorm_2EPopp_2E1,type,
c_2EringNorm_2EPopp_2E1:
!>[A_27a: $tType] : ( tyop_2EringNorm_2Epolynom(A_27a) > tyop_2EringNorm_2Epolynom(A_27a) ) ).
tff(c_2EringNorm_2EPplus_2E0,type,
c_2EringNorm_2EPplus_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2EringNorm_2Epolynom(A_27a))) ).
tff(c_2EringNorm_2EPplus_2E2,type,
c_2EringNorm_2EPplus_2E2:
!>[A_27a: $tType] : ( ( tyop_2EringNorm_2Epolynom(A_27a) * tyop_2EringNorm_2Epolynom(A_27a) ) > tyop_2EringNorm_2Epolynom(A_27a) ) ).
tff(c_2EringNorm_2EPvar_2E0,type,
c_2EringNorm_2EPvar_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EringNorm_2Epolynom(A_27a)) ).
tff(c_2EringNorm_2EPvar_2E1,type,
c_2EringNorm_2EPvar_2E1:
!>[A_27a: $tType] : ( tyop_2Equote_2Eindex > tyop_2EringNorm_2Epolynom(A_27a) ) ).
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_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_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_2EringNorm_2Einterp__p_2E0,type,
c_2EringNorm_2Einterp__p_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27a))) ).
tff(c_2EringNorm_2Einterp__p_2E1,type,
c_2EringNorm_2Einterp__p_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27a)) ) ).
tff(c_2Ering_2Eis__ring_2E0,type,
c_2Ering_2Eis__ring_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Ering_2Eis__ring_2E1,type,
c_2Ering_2Eis__ring_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Ebool ) ).
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_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_2EringNorm_2Epolynom__normalize_2E0,type,
c_2EringNorm_2Epolynom__normalize_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ).
tff(c_2EringNorm_2Epolynom__normalize_2E1,type,
c_2EringNorm_2Epolynom__normalize_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)) ) ).
tff(c_2EringNorm_2Epolynom__simplify_2E0,type,
c_2EringNorm_2Epolynom__simplify_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ).
tff(c_2EringNorm_2Epolynom__simplify_2E1,type,
c_2EringNorm_2Epolynom__simplify_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)) ) ).
tff(c_2EringNorm_2Er__canonical__sum__merge_2E0,type,
c_2EringNorm_2Er__canonical__sum__merge_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))) ).
tff(c_2EringNorm_2Er__canonical__sum__merge_2E1,type,
c_2EringNorm_2Er__canonical__sum__merge_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ) ).
tff(c_2EringNorm_2Er__canonical__sum__prod_2E0,type,
c_2EringNorm_2Er__canonical__sum__prod_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))) ).
tff(c_2EringNorm_2Er__canonical__sum__prod_2E1,type,
c_2EringNorm_2Er__canonical__sum__prod_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ) ).
tff(c_2EringNorm_2Er__canonical__sum__scalar_2E0,type,
c_2EringNorm_2Er__canonical__sum__scalar_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))) ).
tff(c_2EringNorm_2Er__canonical__sum__scalar_2E1,type,
c_2EringNorm_2Er__canonical__sum__scalar_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ) ).
tff(c_2EringNorm_2Er__canonical__sum__scalar2_2E0,type,
c_2EringNorm_2Er__canonical__sum__scalar2_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))) ).
tff(c_2EringNorm_2Er__canonical__sum__scalar2_2E1,type,
c_2EringNorm_2Er__canonical__sum__scalar2_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ) ).
tff(c_2EringNorm_2Er__canonical__sum__scalar3_2E0,type,
c_2EringNorm_2Er__canonical__sum__scalar3_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))))) ).
tff(c_2EringNorm_2Er__canonical__sum__scalar3_2E1,type,
c_2EringNorm_2Er__canonical__sum__scalar3_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))) ) ).
tff(c_2EringNorm_2Er__canonical__sum__simplify_2E0,type,
c_2EringNorm_2Er__canonical__sum__simplify_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ).
tff(c_2EringNorm_2Er__canonical__sum__simplify_2E1,type,
c_2EringNorm_2Er__canonical__sum__simplify_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)) ) ).
tff(c_2EringNorm_2Er__ics__aux_2E0,type,
c_2EringNorm_2Er__ics__aux_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),A_27a)))) ).
tff(c_2EringNorm_2Er__ics__aux_2E1,type,
c_2EringNorm_2Er__ics__aux_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),A_27a))) ) ).
tff(c_2EringNorm_2Er__interp__cs_2E0,type,
c_2EringNorm_2Er__interp__cs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),A_27a))) ).
tff(c_2EringNorm_2Er__interp__cs_2E1,type,
c_2EringNorm_2Er__interp__cs_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),A_27a)) ) ).
tff(c_2EringNorm_2Er__interp__m_2E0,type,
c_2EringNorm_2Er__interp__m_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),A_27a)))) ).
tff(c_2EringNorm_2Er__interp__m_2E1,type,
c_2EringNorm_2Er__interp__m_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),A_27a))) ) ).
tff(c_2EringNorm_2Er__interp__sp_2E0,type,
c_2EringNorm_2Er__interp__sp_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27a))) ).
tff(c_2EringNorm_2Er__interp__sp_2E1,type,
c_2EringNorm_2Er__interp__sp_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27a)) ) ).
tff(c_2EringNorm_2Er__interp__vl_2E0,type,
c_2EringNorm_2Er__interp__vl_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),A_27a))) ).
tff(c_2EringNorm_2Er__interp__vl_2E1,type,
c_2EringNorm_2Er__interp__vl_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),A_27a)) ) ).
tff(c_2EringNorm_2Er__ivl__aux_2E0,type,
c_2EringNorm_2Er__ivl__aux_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),A_27a)))) ).
tff(c_2EringNorm_2Er__ivl__aux_2E1,type,
c_2EringNorm_2Er__ivl__aux_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),A_27a))) ) ).
tff(c_2EringNorm_2Er__monom__insert_2E0,type,
c_2EringNorm_2Er__monom__insert_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))))) ).
tff(c_2EringNorm_2Er__monom__insert_2E1,type,
c_2EringNorm_2Er__monom__insert_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))) ) ).
tff(c_2EringNorm_2Er__spolynom__normalize_2E0,type,
c_2EringNorm_2Er__spolynom__normalize_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ).
tff(c_2EringNorm_2Er__spolynom__normalize_2E1,type,
c_2EringNorm_2Er__spolynom__normalize_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)) ) ).
tff(c_2EringNorm_2Er__spolynom__simplify_2E0,type,
c_2EringNorm_2Er__spolynom__simplify_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ).
tff(c_2EringNorm_2Er__spolynom__simplify_2E1,type,
c_2EringNorm_2Er__spolynom__simplify_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)) ) ).
tff(c_2EringNorm_2Er__varlist__insert_2E0,type,
c_2EringNorm_2Er__varlist__insert_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))) ).
tff(c_2EringNorm_2Er__varlist__insert_2E1,type,
c_2EringNorm_2Er__varlist__insert_2E1:
!>[A_27a: $tType] : ( tyop_2Ering_2Ering(A_27a) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))) ) ).
tff(c_2Erat_2Erat__add_2E0,type,
c_2Erat_2Erat__add_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)) ).
tff(c_2Erat_2Erat__add_2E2,type,
c_2Erat_2Erat__add_2E2: ( tyop_2Erat_2Erat * tyop_2Erat_2Erat ) > tyop_2Erat_2Erat ).
tff(c_2Erat_2Erat__ainv_2E0,type,
c_2Erat_2Erat__ainv_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat) ).
tff(c_2Erat_2Erat__ainv_2E1,type,
c_2Erat_2Erat__ainv_2E1: tyop_2Erat_2Erat > tyop_2Erat_2Erat ).
tff(c_2EratRing_2Erat__interp__p_2E0,type,
c_2EratRing_2Erat__interp__p_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__interp__p_2E2,type,
c_2EratRing_2Erat__interp__p_2E2: ( tyop_2Equote_2Evarmap(tyop_2Erat_2Erat) * tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat) ) > tyop_2Erat_2Erat ).
tff(c_2Erat_2Erat__mul_2E0,type,
c_2Erat_2Erat__mul_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)) ).
tff(c_2Erat_2Erat__mul_2E2,type,
c_2Erat_2Erat__mul_2E2: ( tyop_2Erat_2Erat * tyop_2Erat_2Erat ) > tyop_2Erat_2Erat ).
tff(c_2Erat_2Erat__of__num_2E0,type,
c_2Erat_2Erat__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erat_2Erat) ).
tff(c_2Erat_2Erat__of__num_2E1,type,
c_2Erat_2Erat__of__num_2E1: tyop_2Enum_2Enum > tyop_2Erat_2Erat ).
tff(c_2EratRing_2Erat__polynom__normalize_2E0,type,
c_2EratRing_2Erat__polynom__normalize_2E0: tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__polynom__normalize_2E1,type,
c_2EratRing_2Erat__polynom__normalize_2E1: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__polynom__simplify_2E0,type,
c_2EratRing_2Erat__polynom__simplify_2E0: tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__polynom__simplify_2E1,type,
c_2EratRing_2Erat__polynom__simplify_2E1: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__r__canonical__sum__merge_2E0,type,
c_2EratRing_2Erat__r__canonical__sum__merge_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))) ).
tff(c_2EratRing_2Erat__r__canonical__sum__merge_2E2,type,
c_2EratRing_2Erat__r__canonical__sum__merge_2E2: ( tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__r__canonical__sum__prod_2E0,type,
c_2EratRing_2Erat__r__canonical__sum__prod_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))) ).
tff(c_2EratRing_2Erat__r__canonical__sum__prod_2E2,type,
c_2EratRing_2Erat__r__canonical__sum__prod_2E2: ( tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__r__canonical__sum__scalar_2E0,type,
c_2EratRing_2Erat__r__canonical__sum__scalar_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))) ).
tff(c_2EratRing_2Erat__r__canonical__sum__scalar_2E2,type,
c_2EratRing_2Erat__r__canonical__sum__scalar_2E2: ( tyop_2Erat_2Erat * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__r__canonical__sum__scalar2_2E0,type,
c_2EratRing_2Erat__r__canonical__sum__scalar2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))) ).
tff(c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2,type,
c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2: ( tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__r__canonical__sum__scalar3_2E0,type,
c_2EratRing_2Erat__r__canonical__sum__scalar3_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))) ).
tff(c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3,type,
c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3: ( tyop_2Erat_2Erat * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__r__canonical__sum__simplify_2E0,type,
c_2EratRing_2Erat__r__canonical__sum__simplify_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__r__canonical__sum__simplify_2E1,type,
c_2EratRing_2Erat__r__canonical__sum__simplify_2E1: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__r__ics__aux_2E0,type,
c_2EratRing_2Erat__r__ics__aux_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat))) ).
tff(c_2EratRing_2Erat__r__ics__aux_2E3,type,
c_2EratRing_2Erat__r__ics__aux_2E3: ( tyop_2Equote_2Evarmap(tyop_2Erat_2Erat) * tyop_2Erat_2Erat * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Erat_2Erat ).
tff(c_2EratRing_2Erat__r__interp__cs_2E0,type,
c_2EratRing_2Erat__r__interp__cs_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__r__interp__cs_2E2,type,
c_2EratRing_2Erat__r__interp__cs_2E2: ( tyop_2Equote_2Evarmap(tyop_2Erat_2Erat) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Erat_2Erat ).
tff(c_2EratRing_2Erat__r__interp__m_2E0,type,
c_2EratRing_2Erat__r__interp__m_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))) ).
tff(c_2EratRing_2Erat__r__interp__m_2E3,type,
c_2EratRing_2Erat__r__interp__m_2E3: ( tyop_2Equote_2Evarmap(tyop_2Erat_2Erat) * tyop_2Erat_2Erat * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) ) > tyop_2Erat_2Erat ).
tff(c_2EratRing_2Erat__r__interp__sp_2E0,type,
c_2EratRing_2Erat__r__interp__sp_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__r__interp__vl_2E0,type,
c_2EratRing_2Erat__r__interp__vl_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__r__interp__vl_2E2,type,
c_2EratRing_2Erat__r__interp__vl_2E2: ( tyop_2Equote_2Evarmap(tyop_2Erat_2Erat) * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) ) > tyop_2Erat_2Erat ).
tff(c_2EratRing_2Erat__r__ivl__aux_2E0,type,
c_2EratRing_2Erat__r__ivl__aux_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))) ).
tff(c_2EratRing_2Erat__r__ivl__aux_2E3,type,
c_2EratRing_2Erat__r__ivl__aux_2E3: ( tyop_2Equote_2Evarmap(tyop_2Erat_2Erat) * tyop_2Equote_2Eindex * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) ) > tyop_2Erat_2Erat ).
tff(c_2EratRing_2Erat__r__monom__insert_2E0,type,
c_2EratRing_2Erat__r__monom__insert_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))) ).
tff(c_2EratRing_2Erat__r__monom__insert_2E3,type,
c_2EratRing_2Erat__r__monom__insert_2E3: ( tyop_2Erat_2Erat * tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2EratRing_2Erat__r__spolynom__normalize_2E0,type,
c_2EratRing_2Erat__r__spolynom__normalize_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__r__spolynom__simplify_2E0,type,
c_2EratRing_2Erat__r__spolynom__simplify_2E0: tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)) ).
tff(c_2EratRing_2Erat__r__varlist__insert_2E0,type,
c_2EratRing_2Erat__r__varlist__insert_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))) ).
tff(c_2EratRing_2Erat__r__varlist__insert_2E2,type,
c_2EratRing_2Erat__r__varlist__insert_2E2: ( tyop_2Elist_2Elist(tyop_2Equote_2Eindex) * tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ) > tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat) ).
tff(c_2Ering_2Erecordtype_2Ering_2E0,type,
c_2Ering_2Erecordtype_2Ering_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_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a)))))) ).
tff(c_2Ering_2Erecordtype_2Ering_2E5,type,
c_2Ering_2Erecordtype_2Ering_2E5:
!>[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_2Emin_2Efun(A_27a,A_27a) ) > tyop_2Ering_2Ering(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_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_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Emin_2E_40_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Erat_2Erat_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2Ebool_2ECOND_2E3(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2Ebool_2ECOND_2E0(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),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_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Erat_2Erat,X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2Ecanonical_2ECons__monom_2E0(tyop_2Erat_2Erat),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ecanonical_2ECons__varlist_2E2_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2Ecanonical_2ECons__varlist_2E0(tyop_2Erat_2Erat),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_2EringNorm_2EPconst_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Erat_2Erat] : ( c_2EringNorm_2EPconst_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Erat_2Erat,tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPconst_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq2_2Ec_2EringNorm_2EPmult_2E2_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X1_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EringNorm_2EPmult_2E2(tyop_2Erat_2Erat,X0_2E0,X1_2E0) = app_2E2(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),app_2E2(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)),c_2EringNorm_2EPmult_2E0(tyop_2Erat_2Erat),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2EPopp_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EringNorm_2EPopp_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPopp_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq2_2Ec_2EringNorm_2EPplus_2E2_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X1_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EringNorm_2EPplus_2E2(tyop_2Erat_2Erat,X0_2E0,X1_2E0) = app_2E2(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),app_2E2(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)),c_2EringNorm_2EPplus_2E0(tyop_2Erat_2Erat),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2EPvar_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Equote_2Eindex] : ( c_2EringNorm_2EPvar_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPvar_2E0(tyop_2Erat_2Erat),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(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_2EringNorm_2Einterp__p_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Einterp__p_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Einterp__p_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ering_2Eis__ring_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2Ering_2Eis__ring_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E0(tyop_2Erat_2Erat),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(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Erat_2Erat_29,axiom,
! [X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X3_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Epolynom__normalize_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Epolynom__normalize_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Epolynom__normalize_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Epolynom__simplify_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Epolynom__simplify_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Epolynom__simplify_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__merge_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__canonical__sum__merge_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__merge_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__prod_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__canonical__sum__prod_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__prod_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__canonical__sum__scalar_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__scalar_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar2_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__canonical__sum__scalar2_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__scalar2_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar3_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__canonical__sum__scalar3_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__canonical__sum__scalar3_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__simplify_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__canonical__sum__simplify_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__canonical__sum__simplify_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__ics__aux_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__ics__aux_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),c_2EringNorm_2Er__ics__aux_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__interp__cs_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__interp__cs_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__cs_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__interp__m_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__interp__m_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EringNorm_2Er__interp__m_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__interp__sp_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__interp__sp_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__sp_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__interp__vl_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__interp__vl_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__vl_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__ivl__aux_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__ivl__aux_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EringNorm_2Er__ivl__aux_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__monom__insert_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__monom__insert_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__monom__insert_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__spolynom__normalize_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__spolynom__normalize_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__spolynom__normalize_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__spolynom__simplify_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__spolynom__simplify_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__spolynom__simplify_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq1_2Ec_2EringNorm_2Er__varlist__insert_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Ering_2Ering(tyop_2Erat_2Erat)] : ( c_2EringNorm_2Er__varlist__insert_2E1(tyop_2Erat_2Erat,X0_2E0) = app_2E2(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__varlist__insert_2E0(tyop_2Erat_2Erat),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erat_2Erat__add_2E2,axiom,
! [X0_2E0: tyop_2Erat_2Erat,X1_2E0: tyop_2Erat_2Erat] : ( c_2Erat_2Erat__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erat_2Erat,tyop_2Erat_2Erat,app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erat_2Erat__ainv_2E1,axiom,
! [X0_2E0: tyop_2Erat_2Erat] : ( c_2Erat_2Erat__ainv_2E1(X0_2E0) = app_2E2(tyop_2Erat_2Erat,tyop_2Erat_2Erat,c_2Erat_2Erat__ainv_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2EratRing_2Erat__interp__p_2E2,axiom,
! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X1_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__interp__p_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat,app_2E2(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat),c_2EratRing_2Erat__interp__p_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erat_2Erat__mul_2E2,axiom,
! [X0_2E0: tyop_2Erat_2Erat,X1_2E0: tyop_2Erat_2Erat] : ( c_2Erat_2Erat__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erat_2Erat,tyop_2Erat_2Erat,app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erat_2Erat__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Erat_2Erat__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2EratRing_2Erat__polynom__normalize_2E1,axiom,
! [X0_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__polynom__normalize_2E1(X0_2E0) = app_2E2(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2EratRing_2Erat__polynom__simplify_2E1,axiom,
! [X0_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__polynom__simplify_2E1(X0_2E0) = app_2E2(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__simplify_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2EratRing_2Erat__r__canonical__sum__merge_2E2,axiom,
! [X0_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__merge_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__canonical__sum__merge_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EratRing_2Erat__r__canonical__sum__prod_2E2,axiom,
! [X0_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__prod_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__canonical__sum__prod_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EratRing_2Erat__r__canonical__sum__scalar_2E2,axiom,
! [X0_2E0: tyop_2Erat_2Erat,X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__canonical__sum__scalar_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EratRing_2Erat__r__canonical__sum__scalar2_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EratRing_2Erat__r__canonical__sum__scalar3_2E3,axiom,
! [X0_2E0: tyop_2Erat_2Erat,X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2EratRing_2Erat__r__canonical__sum__simplify_2E1,axiom,
! [X0_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(X0_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2EratRing_2Erat__r__ics__aux_2E3,axiom,
! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X1_2E0: tyop_2Erat_2Erat,X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__ics__aux_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat,app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat),app_2E2(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__ics__aux_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EratRing_2Erat__r__interp__cs_2E2,axiom,
! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__interp__cs_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat,app_2E2(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat),c_2EratRing_2Erat__r__interp__cs_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EratRing_2Erat__r__interp__m_2E3,axiom,
! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X1_2E0: tyop_2Erat_2Erat,X2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__interp__m_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat,app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat),app_2E2(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__interp__m_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EratRing_2Erat__r__interp__vl_2E2,axiom,
! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__interp__vl_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat,app_2E2(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat),c_2EratRing_2Erat__r__interp__vl_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EratRing_2Erat__r__ivl__aux_2E3,axiom,
! [X0_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X1_2E0: tyop_2Equote_2Eindex,X2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__ivl__aux_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat),app_2E2(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__ivl__aux_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2EratRing_2Erat__r__monom__insert_2E3,axiom,
! [X0_2E0: tyop_2Erat_2Erat,X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__monom__insert_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__monom__insert_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EratRing_2Erat__r__varlist__insert_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__varlist__insert_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__varlist__insert_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq5_2Ec_2Ering_2Erecordtype_2Ering_2E5_2Emono_2Etyop_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Erat_2Erat,X1_2E0: tyop_2Erat_2Erat,X2_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),X3_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),X4_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)] : ( c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat),app_2E2(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat)),app_2E2(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat))),app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat)))),app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat))))),c_2Ering_2Erecordtype_2Ering_2E0(tyop_2Erat_2Erat),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_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_2Erat_2Erat,axiom,
! [X0_2E0: tyop_2Equote_2Eindex,X1_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat)] : ( c_2Equote_2Evarmap__find_2E2(tyop_2Erat_2Erat,X0_2E0,X1_2E0) = app_2E2(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Erat_2Erat,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Erat_2Erat),c_2Equote_2Evarmap__find_2E0(tyop_2Erat_2Erat),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_2EratRing_2Erat__interp__p__def,axiom,
c_2EratRing_2Erat__interp__p_2E0 = c_2EringNorm_2Einterp__p_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__polynom__simplify__def,axiom,
c_2EratRing_2Erat__polynom__simplify_2E0 = c_2EringNorm_2Epolynom__simplify_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__polynom__normalize__def,axiom,
c_2EratRing_2Erat__polynom__normalize_2E0 = c_2EringNorm_2Epolynom__normalize_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__canonical__sum__merge__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__merge_2E0 = c_2EringNorm_2Er__canonical__sum__merge_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__monom__insert__def,axiom,
c_2EratRing_2Erat__r__monom__insert_2E0 = c_2EringNorm_2Er__monom__insert_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__varlist__insert__def,axiom,
c_2EratRing_2Erat__r__varlist__insert_2E0 = c_2EringNorm_2Er__varlist__insert_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__canonical__sum__scalar__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__scalar_2E0 = c_2EringNorm_2Er__canonical__sum__scalar_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__canonical__sum__scalar2__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__scalar2_2E0 = c_2EringNorm_2Er__canonical__sum__scalar2_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__canonical__sum__scalar3__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__scalar3_2E0 = c_2EringNorm_2Er__canonical__sum__scalar3_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__canonical__sum__prod__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__prod_2E0 = c_2EringNorm_2Er__canonical__sum__prod_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__canonical__sum__simplify__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__simplify_2E0 = c_2EringNorm_2Er__canonical__sum__simplify_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__ivl__aux__def,axiom,
c_2EratRing_2Erat__r__ivl__aux_2E0 = c_2EringNorm_2Er__ivl__aux_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__interp__vl__def,axiom,
c_2EratRing_2Erat__r__interp__vl_2E0 = c_2EringNorm_2Er__interp__vl_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__interp__m__def,axiom,
c_2EratRing_2Erat__r__interp__m_2E0 = c_2EringNorm_2Er__interp__m_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__ics__aux__def,axiom,
c_2EratRing_2Erat__r__ics__aux_2E0 = c_2EringNorm_2Er__ics__aux_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__interp__cs__def,axiom,
c_2EratRing_2Erat__r__interp__cs_2E0 = c_2EringNorm_2Er__interp__cs_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__spolynom__normalize__def,axiom,
c_2EratRing_2Erat__r__spolynom__normalize_2E0 = c_2EringNorm_2Er__spolynom__normalize_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__spolynom__simplify__def,axiom,
c_2EratRing_2Erat__r__spolynom__simplify_2E0 = c_2EringNorm_2Er__spolynom__simplify_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2Erat__r__interp__sp__def,axiom,
c_2EratRing_2Erat__r__interp__sp_2E0 = c_2EringNorm_2Er__interp__sp_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)) ).
tff(thm_2EratRing_2ERAT__IS__RING,axiom,
p(c_2Ering_2Eis__ring_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0))) ).
tff(thm_2EratRing_2Erat__ring__thms,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V107c_2E0: tyop_2Erat_2Erat] :
( p(app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Ebool,F2_2E0,V107c_2E0))
<=> ( V107c_2E0 = c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
=> ( ! [V107c_2E0: tyop_2Erat_2Erat] :
( p(app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Ebool,F1_2E0,V107c_2E0))
<=> ( V107c_2E0 = c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0) ) )
=> ( ! [V26x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,F0_2E0,V26x_2E0) = c_2Ebool_2ET_2E0 )
=> ( p(c_2Ering_2Eis__ring_2E1(tyop_2Erat_2Erat,c_2Ering_2Erecordtype_2Ering_2E5(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__add_2E0,c_2Erat_2Erat__mul_2E0,c_2Erat_2Erat__ainv_2E0)))
& ! [V0vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V1p_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__interp__p_2E2(V0vm_2E0,V1p_2E0) = c_2EratRing_2Erat__r__interp__cs_2E2(V0vm_2E0,c_2EratRing_2Erat__polynom__simplify_2E1(V1p_2E0)) )
& ! [V2vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V3c_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__interp__p_2E2(V2vm_2E0,c_2EringNorm_2EPconst_2E1(tyop_2Erat_2Erat,V3c_2E0)) = V3c_2E0 )
& ! [V4vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V5i_2E0: tyop_2Equote_2Eindex] : ( c_2EratRing_2Erat__interp__p_2E2(V4vm_2E0,c_2EringNorm_2EPvar_2E1(tyop_2Erat_2Erat,V5i_2E0)) = c_2Equote_2Evarmap__find_2E2(tyop_2Erat_2Erat,V5i_2E0,V4vm_2E0) )
& ! [V6vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V7p1_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V8p2_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__interp__p_2E2(V6vm_2E0,c_2EringNorm_2EPplus_2E2(tyop_2Erat_2Erat,V7p1_2E0,V8p2_2E0)) = c_2Erat_2Erat__add_2E2(c_2EratRing_2Erat__interp__p_2E2(V6vm_2E0,V7p1_2E0),c_2EratRing_2Erat__interp__p_2E2(V6vm_2E0,V8p2_2E0)) )
& ! [V9vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V10p1_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V11p2_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__interp__p_2E2(V9vm_2E0,c_2EringNorm_2EPmult_2E2(tyop_2Erat_2Erat,V10p1_2E0,V11p2_2E0)) = c_2Erat_2Erat__mul_2E2(c_2EratRing_2Erat__interp__p_2E2(V9vm_2E0,V10p1_2E0),c_2EratRing_2Erat__interp__p_2E2(V9vm_2E0,V11p2_2E0)) )
& ! [V12vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V13p1_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__interp__p_2E2(V12vm_2E0,c_2EringNorm_2EPopp_2E1(tyop_2Erat_2Erat,V13p1_2E0)) = c_2Erat_2Erat__ainv_2E1(c_2EratRing_2Erat__interp__p_2E2(V12vm_2E0,V13p1_2E0)) )
& ! [V14x_2E0: A_27a,V15v2_2E0: tyop_2Equote_2Evarmap(A_27a),V16v1_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,V14x_2E0,V16v1_2E0,V15v2_2E0)) = V14x_2E0 )
& ! [V17x_2E0: A_27a,V18v2_2E0: tyop_2Equote_2Evarmap(A_27a),V19v1_2E0: tyop_2Equote_2Evarmap(A_27a),V20i1_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,c_2Equote_2ERight__idx_2E1(V20i1_2E0),c_2Equote_2ENode__vm_2E3(A_27a,V17x_2E0,V19v1_2E0,V18v2_2E0)) = c_2Equote_2Evarmap__find_2E2(A_27a,V20i1_2E0,V18v2_2E0) )
& ! [V21x_2E0: A_27a,V22v2_2E0: tyop_2Equote_2Evarmap(A_27a),V23v1_2E0: tyop_2Equote_2Evarmap(A_27a),V24i1_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,c_2Equote_2ELeft__idx_2E1(V24i1_2E0),c_2Equote_2ENode__vm_2E3(A_27a,V21x_2E0,V23v1_2E0,V22v2_2E0)) = c_2Equote_2Evarmap__find_2E2(A_27a,V24i1_2E0,V23v1_2E0) )
& ! [V25i_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,V25i_2E0,c_2Equote_2EEmpty__vm_2E0(A_27a)) = c_2Emin_2E_40_2E1(A_27a,F0_2E0) )
& ! [V27t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V28t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V29l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V30l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V31c2_2E0: tyop_2Erat_2Erat,V32c1_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V32c1_2E0,V30l1_2E0,V28t1_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V31c2_2E0,V29l2_2E0,V27t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V30l1_2E0,V29l2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V32c1_2E0,V30l1_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V28t1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V31c2_2E0,V29l2_2E0,V27t2_2E0))),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(V32c1_2E0,V31c2_2E0),V30l1_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V28t1_2E0,V27t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V31c2_2E0,V29l2_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V32c1_2E0,V30l1_2E0,V28t1_2E0),V27t2_2E0))) )
& ! [V33t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V34t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V35l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V36l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V37c1_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V37c1_2E0,V36l1_2E0,V34t1_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V35l2_2E0,V33t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V36l1_2E0,V35l2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V37c1_2E0,V36l1_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V34t1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V35l2_2E0,V33t2_2E0))),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(V37c1_2E0,c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V36l1_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V34t1_2E0,V33t2_2E0)),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V35l2_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V37c1_2E0,V36l1_2E0,V34t1_2E0),V33t2_2E0))) )
& ! [V38t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V39t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V40l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V41l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V42c2_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V41l1_2E0,V39t1_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V42c2_2E0,V40l2_2E0,V38t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V41l1_2E0,V40l2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V41l1_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V39t1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V42c2_2E0,V40l2_2E0,V38t2_2E0))),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V42c2_2E0),V41l1_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V39t1_2E0,V38t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V42c2_2E0,V40l2_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V41l1_2E0,V39t1_2E0),V38t2_2E0))) )
& ! [V43t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V44t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V45l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V46l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V46l1_2E0,V44t1_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V45l2_2E0,V43t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V46l1_2E0,V45l2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V46l1_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V44t1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V45l2_2E0,V43t2_2E0))),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V46l1_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V44t1_2E0,V43t2_2E0)),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V45l2_2E0,c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V46l1_2E0,V44t1_2E0),V43t2_2E0))) )
& ! [V47s1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__merge_2E2(V47s1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = V47s1_2E0 )
& ! [V48v6_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V49v5_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V50v4_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V50v4_2E0,V49v5_2E0,V48v6_2E0)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V50v4_2E0,V49v5_2E0,V48v6_2E0) )
& ! [V51v8_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V52v7_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V52v7_2E0,V51v8_2E0)) = c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V52v7_2E0,V51v8_2E0) )
& ! [V53t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V54l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V55l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V56c2_2E0: tyop_2Erat_2Erat,V57c1_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__monom__insert_2E3(V57c1_2E0,V55l1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V56c2_2E0,V54l2_2E0,V53t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V55l1_2E0,V54l2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V57c1_2E0,V55l1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V56c2_2E0,V54l2_2E0,V53t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(V57c1_2E0,V56c2_2E0),V55l1_2E0,V53t2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V56c2_2E0,V54l2_2E0,c_2EratRing_2Erat__r__monom__insert_2E3(V57c1_2E0,V55l1_2E0,V53t2_2E0))) )
& ! [V58t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V59l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V60l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V61c1_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__monom__insert_2E3(V61c1_2E0,V60l1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V59l2_2E0,V58t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V60l1_2E0,V59l2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V61c1_2E0,V60l1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V59l2_2E0,V58t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(V61c1_2E0,c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V60l1_2E0,V58t2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V59l2_2E0,c_2EratRing_2Erat__r__monom__insert_2E3(V61c1_2E0,V60l1_2E0,V58t2_2E0))) )
& ! [V62l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V63c1_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__monom__insert_2E3(V63c1_2E0,V62l1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V63c1_2E0,V62l1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) )
& ! [V64t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V65l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V66l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V67c2_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__varlist__insert_2E2(V66l1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V67c2_2E0,V65l2_2E0,V64t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V66l1_2E0,V65l2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V66l1_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V67c2_2E0,V65l2_2E0,V64t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V67c2_2E0),V66l1_2E0,V64t2_2E0),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V67c2_2E0,V65l2_2E0,c_2EratRing_2Erat__r__varlist__insert_2E2(V66l1_2E0,V64t2_2E0))) )
& ! [V68t2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V69l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V70l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__varlist__insert_2E2(V70l1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V69l2_2E0,V68t2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V70l1_2E0,V69l2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V70l1_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V69l2_2E0,V68t2_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V70l1_2E0,V68t2_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V69l2_2E0,c_2EratRing_2Erat__r__varlist__insert_2E2(V70l1_2E0,V68t2_2E0))) )
& ! [V71l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__varlist__insert_2E2(V71l1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V71l1_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) )
& ! [V72c0_2E0: tyop_2Erat_2Erat,V73c_2E0: tyop_2Erat_2Erat,V74l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V75t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(V72c0_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V73c_2E0,V74l_2E0,V75t_2E0)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,c_2Erat_2Erat__mul_2E2(V72c0_2E0,V73c_2E0),V74l_2E0,c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(V72c0_2E0,V75t_2E0)) )
& ! [V76c0_2E0: tyop_2Erat_2Erat,V77l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V78t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(V76c0_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V77l_2E0,V78t_2E0)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V76c0_2E0,V77l_2E0,c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(V76c0_2E0,V78t_2E0)) )
& ! [V79c0_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(V79c0_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat) )
& ! [V80l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V81c_2E0: tyop_2Erat_2Erat,V82l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V83t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(V80l0_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V81c_2E0,V82l_2E0,V83t_2E0)) = c_2EratRing_2Erat__r__monom__insert_2E3(V81c_2E0,c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,c_2Equote_2Eindex__lt_2E0,V80l0_2E0,V82l_2E0),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(V80l0_2E0,V83t_2E0)) )
& ! [V84l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V85l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V86t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(V84l0_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V85l_2E0,V86t_2E0)) = c_2EratRing_2Erat__r__varlist__insert_2E2(c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,c_2Equote_2Eindex__lt_2E0,V84l0_2E0,V85l_2E0),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(V84l0_2E0,V86t_2E0)) )
& ! [V87l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(V87l0_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat) )
& ! [V88c0_2E0: tyop_2Erat_2Erat,V89l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V90c_2E0: tyop_2Erat_2Erat,V91l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V92t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(V88c0_2E0,V89l0_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V90c_2E0,V91l_2E0,V92t_2E0)) = c_2EratRing_2Erat__r__monom__insert_2E3(c_2Erat_2Erat__mul_2E2(V88c0_2E0,V90c_2E0),c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,c_2Equote_2Eindex__lt_2E0,V89l0_2E0,V91l_2E0),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(V88c0_2E0,V89l0_2E0,V92t_2E0)) )
& ! [V93c0_2E0: tyop_2Erat_2Erat,V94l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V95l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V96t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(V93c0_2E0,V94l0_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V95l_2E0,V96t_2E0)) = c_2EratRing_2Erat__r__monom__insert_2E3(V93c0_2E0,c_2EternaryComparisons_2Elist__merge_2E3(tyop_2Equote_2Eindex,c_2Equote_2Eindex__lt_2E0,V94l0_2E0,V95l_2E0),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(V93c0_2E0,V94l0_2E0,V96t_2E0)) )
& ! [V97c0_2E0: tyop_2Erat_2Erat,V98l0_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(V97c0_2E0,V98l0_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat) )
& ! [V99c1_2E0: tyop_2Erat_2Erat,V100l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V101t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V102s2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__prod_2E2(c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V99c1_2E0,V100l1_2E0,V101t1_2E0),V102s2_2E0) = c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(V99c1_2E0,V100l1_2E0,V102s2_2E0),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(V101t1_2E0,V102s2_2E0)) )
& ! [V103l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V104t1_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V105s2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__prod_2E2(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V103l1_2E0,V104t1_2E0),V105s2_2E0) = c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(V103l1_2E0,V105s2_2E0),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(V104t1_2E0,V105s2_2E0)) )
& ! [V106s2_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__prod_2E2(c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat),V106s2_2E0) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat) )
& ! [V107c_2E0: tyop_2Erat_2Erat,V108l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V109t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V107c_2E0,V108l_2E0,V109t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Ebool,F1_2E0,V107c_2E0),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(V109t_2E0),c_2Ebool_2ECOND_2E3(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(tyop_2Erat_2Erat,tyop_2Emin_2Ebool,F2_2E0,V107c_2E0),c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V108l_2E0,c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(V109t_2E0)),c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V107c_2E0,V108l_2E0,c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(V109t_2E0)))) )
& ! [V110l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V111t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V110l_2E0,V111t_2E0)) = c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V110l_2E0,c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(V111t_2E0)) )
& ( c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat) )
& ! [V112vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V113x_2E0: tyop_2Equote_2Eindex] : ( c_2EratRing_2Erat__r__ivl__aux_2E3(V112vm_2E0,V113x_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex)) = c_2Equote_2Evarmap__find_2E2(tyop_2Erat_2Erat,V113x_2E0,V112vm_2E0) )
& ! [V114vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V115x_2E0: tyop_2Equote_2Eindex,V116x_27_2E0: tyop_2Equote_2Eindex,V117t_27_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__ivl__aux_2E3(V114vm_2E0,V115x_2E0,c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,V116x_27_2E0,V117t_27_2E0)) = c_2Erat_2Erat__mul_2E2(c_2Equote_2Evarmap__find_2E2(tyop_2Erat_2Erat,V115x_2E0,V114vm_2E0),c_2EratRing_2Erat__r__ivl__aux_2E3(V114vm_2E0,V116x_27_2E0,V117t_27_2E0)) )
& ! [V118vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__interp__vl_2E2(V118vm_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex)) = c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
& ! [V119vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V120x_2E0: tyop_2Equote_2Eindex,V121t_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__interp__vl_2E2(V119vm_2E0,c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,V120x_2E0,V121t_2E0)) = c_2EratRing_2Erat__r__ivl__aux_2E3(V119vm_2E0,V120x_2E0,V121t_2E0) )
& ! [V122vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V123c_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__interp__m_2E3(V122vm_2E0,V123c_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex)) = V123c_2E0 )
& ! [V124vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V125c_2E0: tyop_2Erat_2Erat,V126x_2E0: tyop_2Equote_2Eindex,V127t_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EratRing_2Erat__r__interp__m_2E3(V124vm_2E0,V125c_2E0,c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,V126x_2E0,V127t_2E0)) = c_2Erat_2Erat__mul_2E2(V125c_2E0,c_2EratRing_2Erat__r__ivl__aux_2E3(V124vm_2E0,V126x_2E0,V127t_2E0)) )
& ! [V128vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V129a_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__r__ics__aux_2E3(V128vm_2E0,V129a_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = V129a_2E0 )
& ! [V130vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V131a_2E0: tyop_2Erat_2Erat,V132l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V133t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__ics__aux_2E3(V130vm_2E0,V131a_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V132l_2E0,V133t_2E0)) = c_2Erat_2Erat__add_2E2(V131a_2E0,c_2EratRing_2Erat__r__ics__aux_2E3(V130vm_2E0,c_2EratRing_2Erat__r__interp__vl_2E2(V130vm_2E0,V132l_2E0),V133t_2E0)) )
& ! [V134vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V135a_2E0: tyop_2Erat_2Erat,V136c_2E0: tyop_2Erat_2Erat,V137l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V138t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__ics__aux_2E3(V134vm_2E0,V135a_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V136c_2E0,V137l_2E0,V138t_2E0)) = c_2Erat_2Erat__add_2E2(V135a_2E0,c_2EratRing_2Erat__r__ics__aux_2E3(V134vm_2E0,c_2EratRing_2Erat__r__interp__m_2E3(V134vm_2E0,V136c_2E0,V137l_2E0),V138t_2E0)) )
& ! [V139vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__interp__cs_2E2(V139vm_2E0,c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) = c_2Erat_2Erat__of__num_2E1(c_2Enum_2E0_2E0) )
& ! [V140vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V141l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V142t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__interp__cs_2E2(V140vm_2E0,c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,V141l_2E0,V142t_2E0)) = c_2EratRing_2Erat__r__ics__aux_2E3(V140vm_2E0,c_2EratRing_2Erat__r__interp__vl_2E2(V140vm_2E0,V141l_2E0),V142t_2E0) )
& ! [V143vm_2E0: tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V144c_2E0: tyop_2Erat_2Erat,V145l_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V146t_2E0: tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__r__interp__cs_2E2(V143vm_2E0,c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V144c_2E0,V145l_2E0,V146t_2E0)) = c_2EratRing_2Erat__r__ics__aux_2E3(V143vm_2E0,c_2EratRing_2Erat__r__interp__m_2E3(V143vm_2E0,V144c_2E0,V145l_2E0),V146t_2E0) )
& ! [V147i_2E0: tyop_2Equote_2Eindex] : ( c_2EratRing_2Erat__polynom__normalize_2E1(c_2EringNorm_2EPvar_2E1(tyop_2Erat_2Erat,V147i_2E0)) = c_2Ecanonical_2ECons__varlist_2E2(tyop_2Erat_2Erat,c_2Elist_2ECONS_2E2(tyop_2Equote_2Eindex,V147i_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex)),c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) )
& ! [V148c_2E0: tyop_2Erat_2Erat] : ( c_2EratRing_2Erat__polynom__normalize_2E1(c_2EringNorm_2EPconst_2E1(tyop_2Erat_2Erat,V148c_2E0)) = c_2Ecanonical_2ECons__monom_2E3(tyop_2Erat_2Erat,V148c_2E0,c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex),c_2Ecanonical_2ENil__monom_2E0(tyop_2Erat_2Erat)) )
& ! [V149pl_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V150pr_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__polynom__normalize_2E1(c_2EringNorm_2EPplus_2E2(tyop_2Erat_2Erat,V149pl_2E0,V150pr_2E0)) = c_2EratRing_2Erat__r__canonical__sum__merge_2E2(c_2EratRing_2Erat__polynom__normalize_2E1(V149pl_2E0),c_2EratRing_2Erat__polynom__normalize_2E1(V150pr_2E0)) )
& ! [V151pl_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V152pr_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__polynom__normalize_2E1(c_2EringNorm_2EPmult_2E2(tyop_2Erat_2Erat,V151pl_2E0,V152pr_2E0)) = c_2EratRing_2Erat__r__canonical__sum__prod_2E2(c_2EratRing_2Erat__polynom__normalize_2E1(V151pl_2E0),c_2EratRing_2Erat__polynom__normalize_2E1(V152pr_2E0)) )
& ! [V153p_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__polynom__normalize_2E1(c_2EringNorm_2EPopp_2E1(tyop_2Erat_2Erat,V153p_2E0)) = c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(c_2Erat_2Erat__ainv_2E1(c_2Erat_2Erat__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Elist_2ENIL_2E0(tyop_2Equote_2Eindex),c_2EratRing_2Erat__polynom__normalize_2E1(V153p_2E0)) )
& ! [V154x_2E0: tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)] : ( c_2EratRing_2Erat__polynom__simplify_2E1(V154x_2E0) = c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(c_2EratRing_2Erat__polynom__normalize_2E1(V154x_2E0)) ) ) ) ) ) ).
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