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 : 119 ( 25 unt; 91 typ; 0 def)
% Number of atoms : 93 ( 76 equ; 1 cnn)
% Maximal formula atoms : 57 ( 0 avg)
% Number of connectives : 1391 ( 1 ~; 1 |; 57 &;1324 @)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 5 avg;1324 nst)
% Number of types : 6 ( 5 usr)
% Number of type conns : 181 ( 181 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 86 usr; 5 con; 0-6 aty)
% Number of variables : 215 ( 1 ^ 170 !; 1 ?; 215 :)
% ( 43 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Ecanonical_2Ecanonical__sum,type,
tyop_2Ecanonical_2Ecanonical__sum: $tType > $tType ).
thf(tyop_2Ecanonical_2Espolynom,type,
tyop_2Ecanonical_2Espolynom: $tType > $tType ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Equote_2Eindex,type,
tyop_2Equote_2Eindex: $tType ).
thf(tyop_2Equote_2Evarmap,type,
tyop_2Equote_2Evarmap: $tType > $tType ).
thf(tyop_2Erat_2Erat,type,
tyop_2Erat_2Erat: $tType ).
thf(tyop_2Ering_2Ering,type,
tyop_2Ering_2Ering: $tType > $tType ).
thf(tyop_2EringNorm_2Epolynom,type,
tyop_2EringNorm_2Epolynom: $tType > $tType ).
thf(tyop_2EternaryComparisons_2Eordering,type,
tyop_2EternaryComparisons_2Eordering: $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Emin_2E_40,type,
c_2Emin_2E_40:
!>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Elist_2ECONS,type,
c_2Elist_2ECONS:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ecanonical_2ECons__monom,type,
c_2Ecanonical_2ECons__monom:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2Ecanonical_2ECons__varlist,type,
c_2Ecanonical_2ECons__varlist:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2Equote_2EEmpty__vm,type,
c_2Equote_2EEmpty__vm:
!>[A_27a: $tType] : ( tyop_2Equote_2Evarmap @ A_27a ) ).
thf(c_2Equote_2EEnd__idx,type,
c_2Equote_2EEnd__idx: tyop_2Equote_2Eindex ).
thf(c_2Equote_2ELeft__idx,type,
c_2Equote_2ELeft__idx: tyop_2Equote_2Eindex > tyop_2Equote_2Eindex ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ecanonical_2ENil__monom,type,
c_2Ecanonical_2ENil__monom:
!>[A_27a: $tType] : ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ).
thf(c_2Equote_2ENode__vm,type,
c_2Equote_2ENode__vm:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Equote_2Evarmap @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) ) ).
thf(c_2EringNorm_2EPconst,type,
c_2EringNorm_2EPconst:
!>[A_27a: $tType] : ( A_27a > ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ).
thf(c_2EringNorm_2EPmult,type,
c_2EringNorm_2EPmult:
!>[A_27a: $tType] : ( ( tyop_2EringNorm_2Epolynom @ A_27a ) > ( tyop_2EringNorm_2Epolynom @ A_27a ) > ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ).
thf(c_2EringNorm_2EPopp,type,
c_2EringNorm_2EPopp:
!>[A_27a: $tType] : ( ( tyop_2EringNorm_2Epolynom @ A_27a ) > ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ).
thf(c_2EringNorm_2EPplus,type,
c_2EringNorm_2EPplus:
!>[A_27a: $tType] : ( ( tyop_2EringNorm_2Epolynom @ A_27a ) > ( tyop_2EringNorm_2Epolynom @ A_27a ) > ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ).
thf(c_2EringNorm_2EPvar,type,
c_2EringNorm_2EPvar:
!>[A_27a: $tType] : ( tyop_2Equote_2Eindex > ( tyop_2EringNorm_2Epolynom @ A_27a ) ) ).
thf(c_2Equote_2ERight__idx,type,
c_2Equote_2ERight__idx: tyop_2Equote_2Eindex > tyop_2Equote_2Eindex ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Equote_2Eindex__compare,type,
c_2Equote_2Eindex__compare: tyop_2Equote_2Eindex > tyop_2Equote_2Eindex > tyop_2EternaryComparisons_2Eordering ).
thf(c_2Equote_2Eindex__lt,type,
c_2Equote_2Eindex__lt: tyop_2Equote_2Eindex > tyop_2Equote_2Eindex > $o ).
thf(c_2EringNorm_2Einterp__p,type,
c_2EringNorm_2Einterp__p:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) > ( tyop_2EringNorm_2Epolynom @ A_27a ) > A_27a ) ).
thf(c_2Ering_2Eis__ring,type,
c_2Ering_2Eis__ring:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > $o ) ).
thf(c_2EternaryComparisons_2Elist__compare,type,
c_2EternaryComparisons_2Elist__compare:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > tyop_2EternaryComparisons_2Eordering ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27b ) > tyop_2EternaryComparisons_2Eordering ) ).
thf(c_2EternaryComparisons_2Elist__merge,type,
c_2EternaryComparisons_2Elist__merge:
!>[A_27a: $tType] : ( ( A_27a > A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2EternaryComparisons_2Eordering__CASE,type,
c_2EternaryComparisons_2Eordering__CASE:
!>[A_27a: $tType] : ( tyop_2EternaryComparisons_2Eordering > A_27a > A_27a > A_27a > A_27a ) ).
thf(c_2EringNorm_2Epolynom__normalize,type,
c_2EringNorm_2Epolynom__normalize:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2EringNorm_2Epolynom @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Epolynom__simplify,type,
c_2EringNorm_2Epolynom__simplify:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2EringNorm_2Epolynom @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__canonical__sum__merge,type,
c_2EringNorm_2Er__canonical__sum__merge:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__canonical__sum__prod,type,
c_2EringNorm_2Er__canonical__sum__prod:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__canonical__sum__scalar,type,
c_2EringNorm_2Er__canonical__sum__scalar:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > A_27a > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__canonical__sum__scalar2,type,
c_2EringNorm_2Er__canonical__sum__scalar2:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__canonical__sum__scalar3,type,
c_2EringNorm_2Er__canonical__sum__scalar3:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > A_27a > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__canonical__sum__simplify,type,
c_2EringNorm_2Er__canonical__sum__simplify:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__ics__aux,type,
c_2EringNorm_2Er__ics__aux:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) > A_27a > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > A_27a ) ).
thf(c_2EringNorm_2Er__interp__cs,type,
c_2EringNorm_2Er__interp__cs:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > A_27a ) ).
thf(c_2EringNorm_2Er__interp__m,type,
c_2EringNorm_2Er__interp__m:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) > A_27a > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > A_27a ) ).
thf(c_2EringNorm_2Er__interp__sp,type,
c_2EringNorm_2Er__interp__sp:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) > ( tyop_2Ecanonical_2Espolynom @ A_27a ) > A_27a ) ).
thf(c_2EringNorm_2Er__interp__vl,type,
c_2EringNorm_2Er__interp__vl:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > A_27a ) ).
thf(c_2EringNorm_2Er__ivl__aux,type,
c_2EringNorm_2Er__ivl__aux:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Equote_2Evarmap @ A_27a ) > tyop_2Equote_2Eindex > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > A_27a ) ).
thf(c_2EringNorm_2Er__monom__insert,type,
c_2EringNorm_2Er__monom__insert:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > A_27a > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__spolynom__normalize,type,
c_2EringNorm_2Er__spolynom__normalize:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Ecanonical_2Espolynom @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__spolynom__simplify,type,
c_2EringNorm_2Er__spolynom__simplify:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Ecanonical_2Espolynom @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2EringNorm_2Er__varlist__insert,type,
c_2EringNorm_2Er__varlist__insert:
!>[A_27a: $tType] : ( ( tyop_2Ering_2Ering @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) > ( tyop_2Ecanonical_2Ecanonical__sum @ A_27a ) ) ).
thf(c_2Erat_2Erat__add,type,
c_2Erat_2Erat__add: tyop_2Erat_2Erat > tyop_2Erat_2Erat > tyop_2Erat_2Erat ).
thf(c_2Erat_2Erat__ainv,type,
c_2Erat_2Erat__ainv: tyop_2Erat_2Erat > tyop_2Erat_2Erat ).
thf(c_2EratRing_2Erat__interp__p,type,
c_2EratRing_2Erat__interp__p: ( tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat ) > ( tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat ) > tyop_2Erat_2Erat ).
thf(c_2Erat_2Erat__mul,type,
c_2Erat_2Erat__mul: tyop_2Erat_2Erat > tyop_2Erat_2Erat > tyop_2Erat_2Erat ).
thf(c_2Erat_2Erat__of__num,type,
c_2Erat_2Erat__of__num: tyop_2Enum_2Enum > tyop_2Erat_2Erat ).
thf(c_2EratRing_2Erat__polynom__normalize,type,
c_2EratRing_2Erat__polynom__normalize: ( tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__polynom__simplify,type,
c_2EratRing_2Erat__polynom__simplify: ( tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__canonical__sum__merge,type,
c_2EratRing_2Erat__r__canonical__sum__merge: ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__canonical__sum__prod,type,
c_2EratRing_2Erat__r__canonical__sum__prod: ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__canonical__sum__scalar,type,
c_2EratRing_2Erat__r__canonical__sum__scalar: tyop_2Erat_2Erat > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__canonical__sum__scalar2,type,
c_2EratRing_2Erat__r__canonical__sum__scalar2: ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__canonical__sum__scalar3,type,
c_2EratRing_2Erat__r__canonical__sum__scalar3: tyop_2Erat_2Erat > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__canonical__sum__simplify,type,
c_2EratRing_2Erat__r__canonical__sum__simplify: ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__ics__aux,type,
c_2EratRing_2Erat__r__ics__aux: ( tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat ) > tyop_2Erat_2Erat > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > tyop_2Erat_2Erat ).
thf(c_2EratRing_2Erat__r__interp__cs,type,
c_2EratRing_2Erat__r__interp__cs: ( tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > tyop_2Erat_2Erat ).
thf(c_2EratRing_2Erat__r__interp__m,type,
c_2EratRing_2Erat__r__interp__m: ( tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat ) > tyop_2Erat_2Erat > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > tyop_2Erat_2Erat ).
thf(c_2EratRing_2Erat__r__interp__sp,type,
c_2EratRing_2Erat__r__interp__sp: ( tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Espolynom @ tyop_2Erat_2Erat ) > tyop_2Erat_2Erat ).
thf(c_2EratRing_2Erat__r__interp__vl,type,
c_2EratRing_2Erat__r__interp__vl: ( tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat ) > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > tyop_2Erat_2Erat ).
thf(c_2EratRing_2Erat__r__ivl__aux,type,
c_2EratRing_2Erat__r__ivl__aux: ( tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat ) > tyop_2Equote_2Eindex > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > tyop_2Erat_2Erat ).
thf(c_2EratRing_2Erat__r__monom__insert,type,
c_2EratRing_2Erat__r__monom__insert: tyop_2Erat_2Erat > ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__spolynom__normalize,type,
c_2EratRing_2Erat__r__spolynom__normalize: ( tyop_2Ecanonical_2Espolynom @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__spolynom__simplify,type,
c_2EratRing_2Erat__r__spolynom__simplify: ( tyop_2Ecanonical_2Espolynom @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2EratRing_2Erat__r__varlist__insert,type,
c_2EratRing_2Erat__r__varlist__insert: ( tyop_2Elist_2Elist @ tyop_2Equote_2Eindex ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) > ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) ).
thf(c_2Ering_2Erecordtype_2Ering,type,
c_2Ering_2Erecordtype_2Ering:
!>[A_27a: $tType] : ( A_27a > A_27a > ( A_27a > A_27a > A_27a ) > ( A_27a > A_27a > A_27a ) > ( A_27a > A_27a ) > ( tyop_2Ering_2Ering @ A_27a ) ) ).
thf(c_2Equote_2Evarmap__find,type,
c_2Equote_2Evarmap__find:
!>[A_27a: $tType] : ( tyop_2Equote_2Eindex > ( tyop_2Equote_2Evarmap @ A_27a ) > A_27a ) ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2EratRing_2Erat__interp__p__def,axiom,
( c_2EratRing_2Erat__interp__p
= ( c_2EringNorm_2Einterp__p @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__polynom__simplify__def,axiom,
( c_2EratRing_2Erat__polynom__simplify
= ( c_2EringNorm_2Epolynom__simplify @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__polynom__normalize__def,axiom,
( c_2EratRing_2Erat__polynom__normalize
= ( c_2EringNorm_2Epolynom__normalize @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__canonical__sum__merge__def,axiom,
( c_2EratRing_2Erat__r__canonical__sum__merge
= ( c_2EringNorm_2Er__canonical__sum__merge @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__monom__insert__def,axiom,
( c_2EratRing_2Erat__r__monom__insert
= ( c_2EringNorm_2Er__monom__insert @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__varlist__insert__def,axiom,
( c_2EratRing_2Erat__r__varlist__insert
= ( c_2EringNorm_2Er__varlist__insert @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__canonical__sum__scalar__def,axiom,
( c_2EratRing_2Erat__r__canonical__sum__scalar
= ( c_2EringNorm_2Er__canonical__sum__scalar @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__canonical__sum__scalar2__def,axiom,
( c_2EratRing_2Erat__r__canonical__sum__scalar2
= ( c_2EringNorm_2Er__canonical__sum__scalar2 @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__canonical__sum__scalar3__def,axiom,
( c_2EratRing_2Erat__r__canonical__sum__scalar3
= ( c_2EringNorm_2Er__canonical__sum__scalar3 @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__canonical__sum__prod__def,axiom,
( c_2EratRing_2Erat__r__canonical__sum__prod
= ( c_2EringNorm_2Er__canonical__sum__prod @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__canonical__sum__simplify__def,axiom,
( c_2EratRing_2Erat__r__canonical__sum__simplify
= ( c_2EringNorm_2Er__canonical__sum__simplify @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__ivl__aux__def,axiom,
( c_2EratRing_2Erat__r__ivl__aux
= ( c_2EringNorm_2Er__ivl__aux @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__interp__vl__def,axiom,
( c_2EratRing_2Erat__r__interp__vl
= ( c_2EringNorm_2Er__interp__vl @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__interp__m__def,axiom,
( c_2EratRing_2Erat__r__interp__m
= ( c_2EringNorm_2Er__interp__m @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__ics__aux__def,axiom,
( c_2EratRing_2Erat__r__ics__aux
= ( c_2EringNorm_2Er__ics__aux @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__interp__cs__def,axiom,
( c_2EratRing_2Erat__r__interp__cs
= ( c_2EringNorm_2Er__interp__cs @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__spolynom__normalize__def,axiom,
( c_2EratRing_2Erat__r__spolynom__normalize
= ( c_2EringNorm_2Er__spolynom__normalize @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__spolynom__simplify__def,axiom,
( c_2EratRing_2Erat__r__spolynom__simplify
= ( c_2EringNorm_2Er__spolynom__simplify @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2Erat__r__interp__sp__def,axiom,
( c_2EratRing_2Erat__r__interp__sp
= ( c_2EringNorm_2Er__interp__sp @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ) ) ).
thf(thm_2EratRing_2ERAT__IS__RING,axiom,
c_2Ering_2Eis__ring @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) ).
thf(thm_2EratRing_2Erat__ring__thms,axiom,
! [A_27a: $tType] :
( ( c_2Ering_2Eis__ring @ tyop_2Erat_2Erat @ ( c_2Ering_2Erecordtype_2Ering @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Erat_2Erat__add @ c_2Erat_2Erat__mul @ c_2Erat_2Erat__ainv ) )
& ! [V0vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V1p: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__interp__p @ V0vm @ V1p )
= ( c_2EratRing_2Erat__r__interp__cs @ V0vm @ ( c_2EratRing_2Erat__polynom__simplify @ V1p ) ) )
& ! [V2vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V3c: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__interp__p @ V2vm @ ( c_2EringNorm_2EPconst @ tyop_2Erat_2Erat @ V3c ) )
= V3c )
& ! [V4vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V5i: tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__interp__p @ V4vm @ ( c_2EringNorm_2EPvar @ tyop_2Erat_2Erat @ V5i ) )
= ( c_2Equote_2Evarmap__find @ tyop_2Erat_2Erat @ V5i @ V4vm ) )
& ! [V6vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V7p1: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat,V8p2: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__interp__p @ V6vm @ ( c_2EringNorm_2EPplus @ tyop_2Erat_2Erat @ V7p1 @ V8p2 ) )
= ( c_2Erat_2Erat__add @ ( c_2EratRing_2Erat__interp__p @ V6vm @ V7p1 ) @ ( c_2EratRing_2Erat__interp__p @ V6vm @ V8p2 ) ) )
& ! [V9vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V10p1: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat,V11p2: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__interp__p @ V9vm @ ( c_2EringNorm_2EPmult @ tyop_2Erat_2Erat @ V10p1 @ V11p2 ) )
= ( c_2Erat_2Erat__mul @ ( c_2EratRing_2Erat__interp__p @ V9vm @ V10p1 ) @ ( c_2EratRing_2Erat__interp__p @ V9vm @ V11p2 ) ) )
& ! [V12vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V13p1: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__interp__p @ V12vm @ ( c_2EringNorm_2EPopp @ tyop_2Erat_2Erat @ V13p1 ) )
= ( c_2Erat_2Erat__ainv @ ( c_2EratRing_2Erat__interp__p @ V12vm @ V13p1 ) ) )
& ! [V14x: A_27a,V15v2: tyop_2Equote_2Evarmap @ A_27a,V16v1: tyop_2Equote_2Evarmap @ A_27a] :
( ( c_2Equote_2Evarmap__find @ A_27a @ c_2Equote_2EEnd__idx @ ( c_2Equote_2ENode__vm @ A_27a @ V14x @ V16v1 @ V15v2 ) )
= V14x )
& ! [V17x: A_27a,V18v2: tyop_2Equote_2Evarmap @ A_27a,V19v1: tyop_2Equote_2Evarmap @ A_27a,V20i1: tyop_2Equote_2Eindex] :
( ( c_2Equote_2Evarmap__find @ A_27a @ ( c_2Equote_2ERight__idx @ V20i1 ) @ ( c_2Equote_2ENode__vm @ A_27a @ V17x @ V19v1 @ V18v2 ) )
= ( c_2Equote_2Evarmap__find @ A_27a @ V20i1 @ V18v2 ) )
& ! [V21x: A_27a,V22v2: tyop_2Equote_2Evarmap @ A_27a,V23v1: tyop_2Equote_2Evarmap @ A_27a,V24i1: tyop_2Equote_2Eindex] :
( ( c_2Equote_2Evarmap__find @ A_27a @ ( c_2Equote_2ELeft__idx @ V24i1 ) @ ( c_2Equote_2ENode__vm @ A_27a @ V21x @ V23v1 @ V22v2 ) )
= ( c_2Equote_2Evarmap__find @ A_27a @ V24i1 @ V23v1 ) )
& ! [V25i: tyop_2Equote_2Eindex] :
( ( c_2Equote_2Evarmap__find @ A_27a @ V25i @ ( c_2Equote_2EEmpty__vm @ A_27a ) )
= ( c_2Emin_2E_40 @ A_27a
@ ^ [V26x: A_27a] : c_2Ebool_2ET ) )
& ! [V27t2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V28t1: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V29l2: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V30l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V31c2: tyop_2Erat_2Erat,V32c1: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V32c1 @ V30l1 @ V28t1 ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V31c2 @ V29l2 @ V27t2 ) )
= ( c_2EternaryComparisons_2Eordering__CASE @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2EternaryComparisons_2Elist__compare @ tyop_2Equote_2Eindex @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__compare @ V30l1 @ V29l2 ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V32c1 @ V30l1 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ V28t1 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V31c2 @ V29l2 @ V27t2 ) ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__add @ V32c1 @ V31c2 ) @ V30l1 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ V28t1 @ V27t2 ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V31c2 @ V29l2 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V32c1 @ V30l1 @ V28t1 ) @ V27t2 ) ) ) )
& ! [V33t2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V34t1: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V35l2: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V36l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V37c1: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V37c1 @ V36l1 @ V34t1 ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V35l2 @ V33t2 ) )
= ( c_2EternaryComparisons_2Eordering__CASE @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2EternaryComparisons_2Elist__compare @ tyop_2Equote_2Eindex @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__compare @ V36l1 @ V35l2 ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V37c1 @ V36l1 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ V34t1 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V35l2 @ V33t2 ) ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__add @ V37c1 @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V36l1 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ V34t1 @ V33t2 ) ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V35l2 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V37c1 @ V36l1 @ V34t1 ) @ V33t2 ) ) ) )
& ! [V38t2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V39t1: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V40l2: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V41l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V42c2: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V41l1 @ V39t1 ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V42c2 @ V40l2 @ V38t2 ) )
= ( c_2EternaryComparisons_2Eordering__CASE @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2EternaryComparisons_2Elist__compare @ tyop_2Equote_2Eindex @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__compare @ V41l1 @ V40l2 ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V41l1 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ V39t1 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V42c2 @ V40l2 @ V38t2 ) ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__add @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V42c2 ) @ V41l1 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ V39t1 @ V38t2 ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V42c2 @ V40l2 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V41l1 @ V39t1 ) @ V38t2 ) ) ) )
& ! [V43t2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V44t1: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V45l2: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V46l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V46l1 @ V44t1 ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V45l2 @ V43t2 ) )
= ( c_2EternaryComparisons_2Eordering__CASE @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2EternaryComparisons_2Elist__compare @ tyop_2Equote_2Eindex @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__compare @ V46l1 @ V45l2 ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V46l1 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ V44t1 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V45l2 @ V43t2 ) ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__add @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V46l1 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ V44t1 @ V43t2 ) ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V45l2 @ ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V46l1 @ V44t1 ) @ V43t2 ) ) ) )
& ! [V47s1: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__merge @ V47s1 @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= V47s1 )
& ! [V48v6: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V49v5: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V50v4: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V50v4 @ V49v5 @ V48v6 ) )
= ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V50v4 @ V49v5 @ V48v6 ) )
& ! [V51v8: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V52v7: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V52v7 @ V51v8 ) )
= ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V52v7 @ V51v8 ) )
& ! [V53t2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V54l2: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V55l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V56c2: tyop_2Erat_2Erat,V57c1: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__monom__insert @ V57c1 @ V55l1 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V56c2 @ V54l2 @ V53t2 ) )
= ( c_2EternaryComparisons_2Eordering__CASE @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2EternaryComparisons_2Elist__compare @ tyop_2Equote_2Eindex @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__compare @ V55l1 @ V54l2 ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V57c1 @ V55l1 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V56c2 @ V54l2 @ V53t2 ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__add @ V57c1 @ V56c2 ) @ V55l1 @ V53t2 ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V56c2 @ V54l2 @ ( c_2EratRing_2Erat__r__monom__insert @ V57c1 @ V55l1 @ V53t2 ) ) ) )
& ! [V58t2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V59l2: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V60l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V61c1: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__monom__insert @ V61c1 @ V60l1 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V59l2 @ V58t2 ) )
= ( c_2EternaryComparisons_2Eordering__CASE @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2EternaryComparisons_2Elist__compare @ tyop_2Equote_2Eindex @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__compare @ V60l1 @ V59l2 ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V61c1 @ V60l1 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V59l2 @ V58t2 ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__add @ V61c1 @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V60l1 @ V58t2 ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V59l2 @ ( c_2EratRing_2Erat__r__monom__insert @ V61c1 @ V60l1 @ V58t2 ) ) ) )
& ! [V62l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V63c1: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__monom__insert @ V63c1 @ V62l1 @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V63c1 @ V62l1 @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) ) )
& ! [V64t2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V65l2: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V66l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V67c2: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__varlist__insert @ V66l1 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V67c2 @ V65l2 @ V64t2 ) )
= ( c_2EternaryComparisons_2Eordering__CASE @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2EternaryComparisons_2Elist__compare @ tyop_2Equote_2Eindex @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__compare @ V66l1 @ V65l2 ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V66l1 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V67c2 @ V65l2 @ V64t2 ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__add @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V67c2 ) @ V66l1 @ V64t2 ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V67c2 @ V65l2 @ ( c_2EratRing_2Erat__r__varlist__insert @ V66l1 @ V64t2 ) ) ) )
& ! [V68t2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V69l2: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V70l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__varlist__insert @ V70l1 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V69l2 @ V68t2 ) )
= ( c_2EternaryComparisons_2Eordering__CASE @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2EternaryComparisons_2Elist__compare @ tyop_2Equote_2Eindex @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__compare @ V70l1 @ V69l2 ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V70l1 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V69l2 @ V68t2 ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__add @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V70l1 @ V68t2 ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V69l2 @ ( c_2EratRing_2Erat__r__varlist__insert @ V70l1 @ V68t2 ) ) ) )
& ! [V71l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__varlist__insert @ V71l1 @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V71l1 @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) ) )
& ! [V72c0: tyop_2Erat_2Erat,V73c: tyop_2Erat_2Erat,V74l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V75t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar @ V72c0 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V73c @ V74l @ V75t ) )
= ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ ( c_2Erat_2Erat__mul @ V72c0 @ V73c ) @ V74l @ ( c_2EratRing_2Erat__r__canonical__sum__scalar @ V72c0 @ V75t ) ) )
& ! [V76c0: tyop_2Erat_2Erat,V77l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V78t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar @ V76c0 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V77l @ V78t ) )
= ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V76c0 @ V77l @ ( c_2EratRing_2Erat__r__canonical__sum__scalar @ V76c0 @ V78t ) ) )
& ! [V79c0: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar @ V79c0 @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
& ! [V80l0: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V81c: tyop_2Erat_2Erat,V82l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V83t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar2 @ V80l0 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V81c @ V82l @ V83t ) )
= ( c_2EratRing_2Erat__r__monom__insert @ V81c @ ( c_2EternaryComparisons_2Elist__merge @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__lt @ V80l0 @ V82l ) @ ( c_2EratRing_2Erat__r__canonical__sum__scalar2 @ V80l0 @ V83t ) ) )
& ! [V84l0: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V85l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V86t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar2 @ V84l0 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V85l @ V86t ) )
= ( c_2EratRing_2Erat__r__varlist__insert @ ( c_2EternaryComparisons_2Elist__merge @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__lt @ V84l0 @ V85l ) @ ( c_2EratRing_2Erat__r__canonical__sum__scalar2 @ V84l0 @ V86t ) ) )
& ! [V87l0: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar2 @ V87l0 @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
& ! [V88c0: tyop_2Erat_2Erat,V89l0: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V90c: tyop_2Erat_2Erat,V91l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V92t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar3 @ V88c0 @ V89l0 @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V90c @ V91l @ V92t ) )
= ( c_2EratRing_2Erat__r__monom__insert @ ( c_2Erat_2Erat__mul @ V88c0 @ V90c ) @ ( c_2EternaryComparisons_2Elist__merge @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__lt @ V89l0 @ V91l ) @ ( c_2EratRing_2Erat__r__canonical__sum__scalar3 @ V88c0 @ V89l0 @ V92t ) ) )
& ! [V93c0: tyop_2Erat_2Erat,V94l0: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V95l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V96t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar3 @ V93c0 @ V94l0 @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V95l @ V96t ) )
= ( c_2EratRing_2Erat__r__monom__insert @ V93c0 @ ( c_2EternaryComparisons_2Elist__merge @ tyop_2Equote_2Eindex @ c_2Equote_2Eindex__lt @ V94l0 @ V95l ) @ ( c_2EratRing_2Erat__r__canonical__sum__scalar3 @ V93c0 @ V94l0 @ V96t ) ) )
& ! [V97c0: tyop_2Erat_2Erat,V98l0: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__canonical__sum__scalar3 @ V97c0 @ V98l0 @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
& ! [V99c1: tyop_2Erat_2Erat,V100l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V101t1: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V102s2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__prod @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V99c1 @ V100l1 @ V101t1 ) @ V102s2 )
= ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2EratRing_2Erat__r__canonical__sum__scalar3 @ V99c1 @ V100l1 @ V102s2 ) @ ( c_2EratRing_2Erat__r__canonical__sum__prod @ V101t1 @ V102s2 ) ) )
& ! [V103l1: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V104t1: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat,V105s2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__prod @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V103l1 @ V104t1 ) @ V105s2 )
= ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2EratRing_2Erat__r__canonical__sum__scalar2 @ V103l1 @ V105s2 ) @ ( c_2EratRing_2Erat__r__canonical__sum__prod @ V104t1 @ V105s2 ) ) )
& ! [V106s2: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__prod @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) @ V106s2 )
= ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
& ! [V107c: tyop_2Erat_2Erat,V108l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V109t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__simplify @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V107c @ V108l @ V109t ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2Emin_2E_3D @ tyop_2Erat_2Erat @ V107c @ ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) ) @ ( c_2EratRing_2Erat__r__canonical__sum__simplify @ V109t ) @ ( c_2Ebool_2ECOND @ ( tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat ) @ ( c_2Emin_2E_3D @ tyop_2Erat_2Erat @ V107c @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V108l @ ( c_2EratRing_2Erat__r__canonical__sum__simplify @ V109t ) ) @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V107c @ V108l @ ( c_2EratRing_2Erat__r__canonical__sum__simplify @ V109t ) ) ) ) )
& ! [V110l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V111t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__canonical__sum__simplify @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V110l @ V111t ) )
= ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V110l @ ( c_2EratRing_2Erat__r__canonical__sum__simplify @ V111t ) ) )
& ( ( c_2EratRing_2Erat__r__canonical__sum__simplify @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
& ! [V112vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V113x: tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__ivl__aux @ V112vm @ V113x @ ( c_2Elist_2ENIL @ tyop_2Equote_2Eindex ) )
= ( c_2Equote_2Evarmap__find @ tyop_2Erat_2Erat @ V113x @ V112vm ) )
& ! [V114vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V115x: tyop_2Equote_2Eindex,V116x_27: tyop_2Equote_2Eindex,V117t_27: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__ivl__aux @ V114vm @ V115x @ ( c_2Elist_2ECONS @ tyop_2Equote_2Eindex @ V116x_27 @ V117t_27 ) )
= ( c_2Erat_2Erat__mul @ ( c_2Equote_2Evarmap__find @ tyop_2Erat_2Erat @ V115x @ V114vm ) @ ( c_2EratRing_2Erat__r__ivl__aux @ V114vm @ V116x_27 @ V117t_27 ) ) )
& ! [V118vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__interp__vl @ V118vm @ ( c_2Elist_2ENIL @ tyop_2Equote_2Eindex ) )
= ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
& ! [V119vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V120x: tyop_2Equote_2Eindex,V121t: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__interp__vl @ V119vm @ ( c_2Elist_2ECONS @ tyop_2Equote_2Eindex @ V120x @ V121t ) )
= ( c_2EratRing_2Erat__r__ivl__aux @ V119vm @ V120x @ V121t ) )
& ! [V122vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V123c: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__interp__m @ V122vm @ V123c @ ( c_2Elist_2ENIL @ tyop_2Equote_2Eindex ) )
= V123c )
& ! [V124vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V125c: tyop_2Erat_2Erat,V126x: tyop_2Equote_2Eindex,V127t: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__r__interp__m @ V124vm @ V125c @ ( c_2Elist_2ECONS @ tyop_2Equote_2Eindex @ V126x @ V127t ) )
= ( c_2Erat_2Erat__mul @ V125c @ ( c_2EratRing_2Erat__r__ivl__aux @ V124vm @ V126x @ V127t ) ) )
& ! [V128vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V129a: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__ics__aux @ V128vm @ V129a @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= V129a )
& ! [V130vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V131a: tyop_2Erat_2Erat,V132l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V133t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__ics__aux @ V130vm @ V131a @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V132l @ V133t ) )
= ( c_2Erat_2Erat__add @ V131a @ ( c_2EratRing_2Erat__r__ics__aux @ V130vm @ ( c_2EratRing_2Erat__r__interp__vl @ V130vm @ V132l ) @ V133t ) ) )
& ! [V134vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V135a: tyop_2Erat_2Erat,V136c: tyop_2Erat_2Erat,V137l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V138t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__ics__aux @ V134vm @ V135a @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V136c @ V137l @ V138t ) )
= ( c_2Erat_2Erat__add @ V135a @ ( c_2EratRing_2Erat__r__ics__aux @ V134vm @ ( c_2EratRing_2Erat__r__interp__m @ V134vm @ V136c @ V137l ) @ V138t ) ) )
& ! [V139vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__interp__cs @ V139vm @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) )
= ( c_2Erat_2Erat__of__num @ c_2Enum_2E0 ) )
& ! [V140vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V141l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V142t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__interp__cs @ V140vm @ ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ V141l @ V142t ) )
= ( c_2EratRing_2Erat__r__ics__aux @ V140vm @ ( c_2EratRing_2Erat__r__interp__vl @ V140vm @ V141l ) @ V142t ) )
& ! [V143vm: tyop_2Equote_2Evarmap @ tyop_2Erat_2Erat,V144c: tyop_2Erat_2Erat,V145l: tyop_2Elist_2Elist @ tyop_2Equote_2Eindex,V146t: tyop_2Ecanonical_2Ecanonical__sum @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__r__interp__cs @ V143vm @ ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V144c @ V145l @ V146t ) )
= ( c_2EratRing_2Erat__r__ics__aux @ V143vm @ ( c_2EratRing_2Erat__r__interp__m @ V143vm @ V144c @ V145l ) @ V146t ) )
& ! [V147i: tyop_2Equote_2Eindex] :
( ( c_2EratRing_2Erat__polynom__normalize @ ( c_2EringNorm_2EPvar @ tyop_2Erat_2Erat @ V147i ) )
= ( c_2Ecanonical_2ECons__varlist @ tyop_2Erat_2Erat @ ( c_2Elist_2ECONS @ tyop_2Equote_2Eindex @ V147i @ ( c_2Elist_2ENIL @ tyop_2Equote_2Eindex ) ) @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) ) )
& ! [V148c: tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__polynom__normalize @ ( c_2EringNorm_2EPconst @ tyop_2Erat_2Erat @ V148c ) )
= ( c_2Ecanonical_2ECons__monom @ tyop_2Erat_2Erat @ V148c @ ( c_2Elist_2ENIL @ tyop_2Equote_2Eindex ) @ ( c_2Ecanonical_2ENil__monom @ tyop_2Erat_2Erat ) ) )
& ! [V149pl: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat,V150pr: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__polynom__normalize @ ( c_2EringNorm_2EPplus @ tyop_2Erat_2Erat @ V149pl @ V150pr ) )
= ( c_2EratRing_2Erat__r__canonical__sum__merge @ ( c_2EratRing_2Erat__polynom__normalize @ V149pl ) @ ( c_2EratRing_2Erat__polynom__normalize @ V150pr ) ) )
& ! [V151pl: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat,V152pr: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__polynom__normalize @ ( c_2EringNorm_2EPmult @ tyop_2Erat_2Erat @ V151pl @ V152pr ) )
= ( c_2EratRing_2Erat__r__canonical__sum__prod @ ( c_2EratRing_2Erat__polynom__normalize @ V151pl ) @ ( c_2EratRing_2Erat__polynom__normalize @ V152pr ) ) )
& ! [V153p: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__polynom__normalize @ ( c_2EringNorm_2EPopp @ tyop_2Erat_2Erat @ V153p ) )
= ( c_2EratRing_2Erat__r__canonical__sum__scalar3 @ ( c_2Erat_2Erat__ainv @ ( c_2Erat_2Erat__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Elist_2ENIL @ tyop_2Equote_2Eindex ) @ ( c_2EratRing_2Erat__polynom__normalize @ V153p ) ) )
& ! [V154x: tyop_2EringNorm_2Epolynom @ tyop_2Erat_2Erat] :
( ( c_2EratRing_2Erat__polynom__simplify @ V154x )
= ( c_2EratRing_2Erat__r__canonical__sum__simplify @ ( c_2EratRing_2Erat__polynom__normalize @ V154x ) ) ) ) ).
%------------------------------------------------------------------------------