ITP001 Axioms: ITP129+5.ax
%------------------------------------------------------------------------------
% File : ITP129+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : ratRing+2.ax [Gau20]
% : HL4129+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 40 ( 39 unt; 0 def)
% Number of atoms : 251 ( 75 equ)
% Maximal formula atoms : 212 ( 6 avg)
% Number of connectives : 211 ( 0 ~; 0 |; 56 &)
% ( 0 <=>; 155 =>; 0 <=; 0 <~>)
% Maximal formula depth : 62 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 83 ( 83 usr; 35 con; 0-2 aty)
% Number of variables : 155 ( 155 !; 0 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2EratRing_2Erat__interp__p,axiom,
mem(c_2EratRing_2Erat__interp__p,arr(ty_2Equote_2Evarmap(ty_2Erat_2Erat),arr(ty_2EringNorm_2Epolynom(ty_2Erat_2Erat),ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__polynom__normalize,axiom,
mem(c_2EratRing_2Erat__polynom__normalize,arr(ty_2EringNorm_2Epolynom(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__polynom__simplify,axiom,
mem(c_2EratRing_2Erat__polynom__simplify,arr(ty_2EringNorm_2Epolynom(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__r__canonical__sum__merge,axiom,
mem(c_2EratRing_2Erat__r__canonical__sum__merge,arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)))) ).
fof(mem_c_2EratRing_2Erat__r__canonical__sum__prod,axiom,
mem(c_2EratRing_2Erat__r__canonical__sum__prod,arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)))) ).
fof(mem_c_2EratRing_2Erat__r__canonical__sum__scalar,axiom,
mem(c_2EratRing_2Erat__r__canonical__sum__scalar,arr(ty_2Erat_2Erat,arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)))) ).
fof(mem_c_2EratRing_2Erat__r__canonical__sum__scalar2,axiom,
mem(c_2EratRing_2Erat__r__canonical__sum__scalar2,arr(ty_2Elist_2Elist(ty_2Equote_2Eindex),arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)))) ).
fof(mem_c_2EratRing_2Erat__r__canonical__sum__scalar3,axiom,
mem(c_2EratRing_2Erat__r__canonical__sum__scalar3,arr(ty_2Erat_2Erat,arr(ty_2Elist_2Elist(ty_2Equote_2Eindex),arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))))) ).
fof(mem_c_2EratRing_2Erat__r__canonical__sum__simplify,axiom,
mem(c_2EratRing_2Erat__r__canonical__sum__simplify,arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__r__ics__aux,axiom,
mem(c_2EratRing_2Erat__r__ics__aux,arr(ty_2Equote_2Evarmap(ty_2Erat_2Erat),arr(ty_2Erat_2Erat,arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Erat_2Erat)))) ).
fof(mem_c_2EratRing_2Erat__r__interp__cs,axiom,
mem(c_2EratRing_2Erat__r__interp__cs,arr(ty_2Equote_2Evarmap(ty_2Erat_2Erat),arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__r__interp__m,axiom,
mem(c_2EratRing_2Erat__r__interp__m,arr(ty_2Equote_2Evarmap(ty_2Erat_2Erat),arr(ty_2Erat_2Erat,arr(ty_2Elist_2Elist(ty_2Equote_2Eindex),ty_2Erat_2Erat)))) ).
fof(mem_c_2EratRing_2Erat__r__interp__sp,axiom,
mem(c_2EratRing_2Erat__r__interp__sp,arr(ty_2Equote_2Evarmap(ty_2Erat_2Erat),arr(ty_2Ecanonical_2Espolynom(ty_2Erat_2Erat),ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__r__interp__vl,axiom,
mem(c_2EratRing_2Erat__r__interp__vl,arr(ty_2Equote_2Evarmap(ty_2Erat_2Erat),arr(ty_2Elist_2Elist(ty_2Equote_2Eindex),ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__r__ivl__aux,axiom,
mem(c_2EratRing_2Erat__r__ivl__aux,arr(ty_2Equote_2Evarmap(ty_2Erat_2Erat),arr(ty_2Equote_2Eindex,arr(ty_2Elist_2Elist(ty_2Equote_2Eindex),ty_2Erat_2Erat)))) ).
fof(mem_c_2EratRing_2Erat__r__monom__insert,axiom,
mem(c_2EratRing_2Erat__r__monom__insert,arr(ty_2Erat_2Erat,arr(ty_2Elist_2Elist(ty_2Equote_2Eindex),arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))))) ).
fof(mem_c_2EratRing_2Erat__r__spolynom__normalize,axiom,
mem(c_2EratRing_2Erat__r__spolynom__normalize,arr(ty_2Ecanonical_2Espolynom(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__r__spolynom__simplify,axiom,
mem(c_2EratRing_2Erat__r__spolynom__simplify,arr(ty_2Ecanonical_2Espolynom(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))) ).
fof(mem_c_2EratRing_2Erat__r__varlist__insert,axiom,
mem(c_2EratRing_2Erat__r__varlist__insert,arr(ty_2Elist_2Elist(ty_2Equote_2Eindex),arr(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat),ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)))) ).
fof(conj_thm_2EratRing_2ERAT__IS__RING,axiom,
p(ap(c_2Ering_2Eis__ring(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv))) ).
fof(ax_thm_2EratRing_2Erat__interp__p__def,axiom,
c_2EratRing_2Erat__interp__p = ap(c_2EringNorm_2Einterp__p(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__polynom__simplify__def,axiom,
c_2EratRing_2Erat__polynom__simplify = ap(c_2EringNorm_2Epolynom__simplify(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__polynom__normalize__def,axiom,
c_2EratRing_2Erat__polynom__normalize = ap(c_2EringNorm_2Epolynom__normalize(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__canonical__sum__merge__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__merge = ap(c_2EringNorm_2Er__canonical__sum__merge(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__monom__insert__def,axiom,
c_2EratRing_2Erat__r__monom__insert = ap(c_2EringNorm_2Er__monom__insert(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__varlist__insert__def,axiom,
c_2EratRing_2Erat__r__varlist__insert = ap(c_2EringNorm_2Er__varlist__insert(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__canonical__sum__scalar__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__scalar = ap(c_2EringNorm_2Er__canonical__sum__scalar(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__canonical__sum__scalar2__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__scalar2 = ap(c_2EringNorm_2Er__canonical__sum__scalar2(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__canonical__sum__scalar3__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__scalar3 = ap(c_2EringNorm_2Er__canonical__sum__scalar3(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__canonical__sum__prod__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__prod = ap(c_2EringNorm_2Er__canonical__sum__prod(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__canonical__sum__simplify__def,axiom,
c_2EratRing_2Erat__r__canonical__sum__simplify = ap(c_2EringNorm_2Er__canonical__sum__simplify(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__ivl__aux__def,axiom,
c_2EratRing_2Erat__r__ivl__aux = ap(c_2EringNorm_2Er__ivl__aux(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__interp__vl__def,axiom,
c_2EratRing_2Erat__r__interp__vl = ap(c_2EringNorm_2Er__interp__vl(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__interp__m__def,axiom,
c_2EratRing_2Erat__r__interp__m = ap(c_2EringNorm_2Er__interp__m(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__ics__aux__def,axiom,
c_2EratRing_2Erat__r__ics__aux = ap(c_2EringNorm_2Er__ics__aux(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__interp__cs__def,axiom,
c_2EratRing_2Erat__r__interp__cs = ap(c_2EringNorm_2Er__interp__cs(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__spolynom__normalize__def,axiom,
c_2EratRing_2Erat__r__spolynom__normalize = ap(c_2EringNorm_2Er__spolynom__normalize(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__spolynom__simplify__def,axiom,
c_2EratRing_2Erat__r__spolynom__simplify = ap(c_2EringNorm_2Er__spolynom__simplify(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(ax_thm_2EratRing_2Erat__r__interp__sp__def,axiom,
c_2EratRing_2Erat__r__interp__sp = ap(c_2EringNorm_2Er__interp__sp(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)) ).
fof(conj_thm_2EratRing_2Erat__ring__thms,axiom,
! [A_27a] :
( ne(A_27a)
=> ( p(ap(c_2Ering_2Eis__ring(ty_2Erat_2Erat),ap(ap(ap(ap(ap(c_2Ering_2Erecordtype_2Ering(ty_2Erat_2Erat),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0)),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Erat_2Erat__add),c_2Erat_2Erat__mul),c_2Erat_2Erat__ainv)))
& ! [V0vm] :
( mem(V0vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V1p] :
( mem(V1p,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__interp__p,V0vm),V1p) = ap(ap(c_2EratRing_2Erat__r__interp__cs,V0vm),ap(c_2EratRing_2Erat__polynom__simplify,V1p)) ) )
& ! [V2vm] :
( mem(V2vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V3c] :
( mem(V3c,ty_2Erat_2Erat)
=> ap(ap(c_2EratRing_2Erat__interp__p,V2vm),ap(c_2EringNorm_2EPconst(ty_2Erat_2Erat),V3c)) = V3c ) )
& ! [V4vm] :
( mem(V4vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V5i] :
( mem(V5i,ty_2Equote_2Eindex)
=> ap(ap(c_2EratRing_2Erat__interp__p,V4vm),ap(c_2EringNorm_2EPvar(ty_2Erat_2Erat),V5i)) = ap(ap(c_2Equote_2Evarmap__find(ty_2Erat_2Erat),V5i),V4vm) ) )
& ! [V6vm] :
( mem(V6vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V7p1] :
( mem(V7p1,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ! [V8p2] :
( mem(V8p2,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__interp__p,V6vm),ap(ap(c_2EringNorm_2EPplus(ty_2Erat_2Erat),V7p1),V8p2)) = ap(ap(c_2Erat_2Erat__add,ap(ap(c_2EratRing_2Erat__interp__p,V6vm),V7p1)),ap(ap(c_2EratRing_2Erat__interp__p,V6vm),V8p2)) ) ) )
& ! [V9vm] :
( mem(V9vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V10p1] :
( mem(V10p1,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ! [V11p2] :
( mem(V11p2,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__interp__p,V9vm),ap(ap(c_2EringNorm_2EPmult(ty_2Erat_2Erat),V10p1),V11p2)) = ap(ap(c_2Erat_2Erat__mul,ap(ap(c_2EratRing_2Erat__interp__p,V9vm),V10p1)),ap(ap(c_2EratRing_2Erat__interp__p,V9vm),V11p2)) ) ) )
& ! [V12vm] :
( mem(V12vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V13p1] :
( mem(V13p1,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__interp__p,V12vm),ap(c_2EringNorm_2EPopp(ty_2Erat_2Erat),V13p1)) = ap(c_2Erat_2Erat__ainv,ap(ap(c_2EratRing_2Erat__interp__p,V12vm),V13p1)) ) )
& ! [V14x] :
( mem(V14x,A_27a)
=> ! [V15v2] :
( mem(V15v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V16v1] :
( mem(V16v1,ty_2Equote_2Evarmap(A_27a))
=> ap(ap(c_2Equote_2Evarmap__find(A_27a),c_2Equote_2EEnd__idx),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V14x),V16v1),V15v2)) = V14x ) ) )
& ! [V17x] :
( mem(V17x,A_27a)
=> ! [V18v2] :
( mem(V18v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V19v1] :
( mem(V19v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V20i1] :
( mem(V20i1,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Evarmap__find(A_27a),ap(c_2Equote_2ERight__idx,V20i1)),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V17x),V19v1),V18v2)) = ap(ap(c_2Equote_2Evarmap__find(A_27a),V20i1),V18v2) ) ) ) )
& ! [V21x] :
( mem(V21x,A_27a)
=> ! [V22v2] :
( mem(V22v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V23v1] :
( mem(V23v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V24i1] :
( mem(V24i1,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Evarmap__find(A_27a),ap(c_2Equote_2ELeft__idx,V24i1)),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V21x),V23v1),V22v2)) = ap(ap(c_2Equote_2Evarmap__find(A_27a),V24i1),V23v1) ) ) ) )
& ! [V25i] :
( mem(V25i,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Evarmap__find(A_27a),V25i),c_2Equote_2EEmpty__vm(A_27a)) = ap(c_2Emin_2E_40(A_27a),k(A_27a,c_2Ebool_2ET)) )
& ! [V27t2] :
( mem(V27t2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V28t1] :
( mem(V28t1,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V29l2] :
( mem(V29l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V30l1] :
( mem(V30l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V31c2] :
( mem(V31c2,ty_2Erat_2Erat)
=> ! [V32c1] :
( mem(V32c1,ty_2Erat_2Erat)
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V32c1),V30l1),V28t1)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V31c2),V29l2),V27t2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V30l1),V29l2)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V32c1),V30l1),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V28t1),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V31c2),V29l2),V27t2)))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__add,V32c1),V31c2)),V30l1),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V28t1),V27t2))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V31c2),V29l2),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V32c1),V30l1),V28t1)),V27t2))) ) ) ) ) ) )
& ! [V33t2] :
( mem(V33t2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V34t1] :
( mem(V34t1,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V35l2] :
( mem(V35l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V36l1] :
( mem(V36l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V37c1] :
( mem(V37c1,ty_2Erat_2Erat)
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V37c1),V36l1),V34t1)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V35l2),V33t2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V36l1),V35l2)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V37c1),V36l1),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V34t1),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V35l2),V33t2)))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__add,V37c1),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V36l1),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V34t1),V33t2))),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V35l2),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V37c1),V36l1),V34t1)),V33t2))) ) ) ) ) )
& ! [V38t2] :
( mem(V38t2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V39t1] :
( mem(V39t1,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V40l2] :
( mem(V40l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V41l1] :
( mem(V41l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V42c2] :
( mem(V42c2,ty_2Erat_2Erat)
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V41l1),V39t1)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V42c2),V40l2),V38t2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V41l1),V40l2)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V41l1),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V39t1),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V42c2),V40l2),V38t2)))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__add,ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V42c2)),V41l1),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V39t1),V38t2))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V42c2),V40l2),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V41l1),V39t1)),V38t2))) ) ) ) ) )
& ! [V43t2] :
( mem(V43t2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V44t1] :
( mem(V44t1,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V45l2] :
( mem(V45l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V46l1] :
( mem(V46l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V46l1),V44t1)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V45l2),V43t2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V46l1),V45l2)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V46l1),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V44t1),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V45l2),V43t2)))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__add,ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V46l1),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V44t1),V43t2))),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V45l2),ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V46l1),V44t1)),V43t2))) ) ) ) )
& ! [V47s1] :
( mem(V47s1,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,V47s1),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = V47s1 )
& ! [V48v6] :
( mem(V48v6,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V49v5] :
( mem(V49v5,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V50v4] :
( mem(V50v4,ty_2Erat_2Erat)
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V50v4),V49v5),V48v6)) = ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V50v4),V49v5),V48v6) ) ) )
& ! [V51v8] :
( mem(V51v8,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V52v7] :
( mem(V52v7,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V52v7),V51v8)) = ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V52v7),V51v8) ) )
& ! [V53t2] :
( mem(V53t2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V54l2] :
( mem(V54l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V55l1] :
( mem(V55l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V56c2] :
( mem(V56c2,ty_2Erat_2Erat)
=> ! [V57c1] :
( mem(V57c1,ty_2Erat_2Erat)
=> ap(ap(ap(c_2EratRing_2Erat__r__monom__insert,V57c1),V55l1),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V56c2),V54l2),V53t2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V55l1),V54l2)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V57c1),V55l1),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V56c2),V54l2),V53t2))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__add,V57c1),V56c2)),V55l1),V53t2)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V56c2),V54l2),ap(ap(ap(c_2EratRing_2Erat__r__monom__insert,V57c1),V55l1),V53t2))) ) ) ) ) )
& ! [V58t2] :
( mem(V58t2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V59l2] :
( mem(V59l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V60l1] :
( mem(V60l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V61c1] :
( mem(V61c1,ty_2Erat_2Erat)
=> ap(ap(ap(c_2EratRing_2Erat__r__monom__insert,V61c1),V60l1),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V59l2),V58t2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V60l1),V59l2)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V61c1),V60l1),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V59l2),V58t2))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__add,V61c1),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V60l1),V58t2)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V59l2),ap(ap(ap(c_2EratRing_2Erat__r__monom__insert,V61c1),V60l1),V58t2))) ) ) ) )
& ! [V62l1] :
( mem(V62l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V63c1] :
( mem(V63c1,ty_2Erat_2Erat)
=> ap(ap(ap(c_2EratRing_2Erat__r__monom__insert,V63c1),V62l1),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V63c1),V62l1),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) ) )
& ! [V64t2] :
( mem(V64t2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V65l2] :
( mem(V65l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V66l1] :
( mem(V66l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V67c2] :
( mem(V67c2,ty_2Erat_2Erat)
=> ap(ap(c_2EratRing_2Erat__r__varlist__insert,V66l1),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V67c2),V65l2),V64t2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V66l1),V65l2)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V66l1),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V67c2),V65l2),V64t2))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__add,ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V67c2)),V66l1),V64t2)),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V67c2),V65l2),ap(ap(c_2EratRing_2Erat__r__varlist__insert,V66l1),V64t2))) ) ) ) )
& ! [V68t2] :
( mem(V68t2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V69l2] :
( mem(V69l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V70l1] :
( mem(V70l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(c_2EratRing_2Erat__r__varlist__insert,V70l1),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V69l2),V68t2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V70l1),V69l2)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V70l1),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V69l2),V68t2))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__add,ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V70l1),V68t2)),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V69l2),ap(ap(c_2EratRing_2Erat__r__varlist__insert,V70l1),V68t2))) ) ) )
& ! [V71l1] :
( mem(V71l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(c_2EratRing_2Erat__r__varlist__insert,V71l1),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V71l1),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) )
& ! [V72c0] :
( mem(V72c0,ty_2Erat_2Erat)
=> ! [V73c] :
( mem(V73c,ty_2Erat_2Erat)
=> ! [V74l] :
( mem(V74l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V75t] :
( mem(V75t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar,V72c0),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V73c),V74l),V75t)) = ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),ap(ap(c_2Erat_2Erat__mul,V72c0),V73c)),V74l),ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar,V72c0),V75t)) ) ) ) )
& ! [V76c0] :
( mem(V76c0,ty_2Erat_2Erat)
=> ! [V77l] :
( mem(V77l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V78t] :
( mem(V78t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar,V76c0),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V77l),V78t)) = ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V76c0),V77l),ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar,V76c0),V78t)) ) ) )
& ! [V79c0] :
( mem(V79c0,ty_2Erat_2Erat)
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar,V79c0),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat) )
& ! [V80l0] :
( mem(V80l0,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V81c] :
( mem(V81c,ty_2Erat_2Erat)
=> ! [V82l] :
( mem(V82l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V83t] :
( mem(V83t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar2,V80l0),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V81c),V82l),V83t)) = ap(ap(ap(c_2EratRing_2Erat__r__monom__insert,V81c),ap(ap(ap(c_2EternaryComparisons_2Elist__merge(ty_2Equote_2Eindex),c_2Equote_2Eindex__lt),V80l0),V82l)),ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar2,V80l0),V83t)) ) ) ) )
& ! [V84l0] :
( mem(V84l0,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V85l] :
( mem(V85l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V86t] :
( mem(V86t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar2,V84l0),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V85l),V86t)) = ap(ap(c_2EratRing_2Erat__r__varlist__insert,ap(ap(ap(c_2EternaryComparisons_2Elist__merge(ty_2Equote_2Eindex),c_2Equote_2Eindex__lt),V84l0),V85l)),ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar2,V84l0),V86t)) ) ) )
& ! [V87l0] :
( mem(V87l0,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar2,V87l0),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat) )
& ! [V88c0] :
( mem(V88c0,ty_2Erat_2Erat)
=> ! [V89l0] :
( mem(V89l0,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V90c] :
( mem(V90c,ty_2Erat_2Erat)
=> ! [V91l] :
( mem(V91l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V92t] :
( mem(V92t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar3,V88c0),V89l0),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V90c),V91l),V92t)) = ap(ap(ap(c_2EratRing_2Erat__r__monom__insert,ap(ap(c_2Erat_2Erat__mul,V88c0),V90c)),ap(ap(ap(c_2EternaryComparisons_2Elist__merge(ty_2Equote_2Eindex),c_2Equote_2Eindex__lt),V89l0),V91l)),ap(ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar3,V88c0),V89l0),V92t)) ) ) ) ) )
& ! [V93c0] :
( mem(V93c0,ty_2Erat_2Erat)
=> ! [V94l0] :
( mem(V94l0,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V95l] :
( mem(V95l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V96t] :
( mem(V96t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar3,V93c0),V94l0),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V95l),V96t)) = ap(ap(ap(c_2EratRing_2Erat__r__monom__insert,V93c0),ap(ap(ap(c_2EternaryComparisons_2Elist__merge(ty_2Equote_2Eindex),c_2Equote_2Eindex__lt),V94l0),V95l)),ap(ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar3,V93c0),V94l0),V96t)) ) ) ) )
& ! [V97c0] :
( mem(V97c0,ty_2Erat_2Erat)
=> ! [V98l0] :
( mem(V98l0,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar3,V97c0),V98l0),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat) ) )
& ! [V99c1] :
( mem(V99c1,ty_2Erat_2Erat)
=> ! [V100l1] :
( mem(V100l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V101t1] :
( mem(V101t1,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V102s2] :
( mem(V102s2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__prod,ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V99c1),V100l1),V101t1)),V102s2) = ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar3,V99c1),V100l1),V102s2)),ap(ap(c_2EratRing_2Erat__r__canonical__sum__prod,V101t1),V102s2)) ) ) ) )
& ! [V103l1] :
( mem(V103l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V104t1] :
( mem(V104t1,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ! [V105s2] :
( mem(V105s2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__prod,ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V103l1),V104t1)),V105s2) = ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar2,V103l1),V105s2)),ap(ap(c_2EratRing_2Erat__r__canonical__sum__prod,V104t1),V105s2)) ) ) )
& ! [V106s2] :
( mem(V106s2,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__canonical__sum__prod,c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)),V106s2) = c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat) )
& ! [V107c] :
( mem(V107c,ty_2Erat_2Erat)
=> ! [V108l] :
( mem(V108l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V109t] :
( mem(V109t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(c_2EratRing_2Erat__r__canonical__sum__simplify,ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V107c),V108l),V109t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(c_2Emin_2E_3D(ty_2Erat_2Erat),V107c),ap(c_2Erat_2Erat__of__num,c_2Enum_2E0))),ap(c_2EratRing_2Erat__r__canonical__sum__simplify,V109t)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat)),ap(ap(c_2Emin_2E_3D(ty_2Erat_2Erat),V107c),ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V108l),ap(c_2EratRing_2Erat__r__canonical__sum__simplify,V109t))),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V107c),V108l),ap(c_2EratRing_2Erat__r__canonical__sum__simplify,V109t)))) ) ) )
& ! [V110l] :
( mem(V110l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V111t] :
( mem(V111t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(c_2EratRing_2Erat__r__canonical__sum__simplify,ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V110l),V111t)) = ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V110l),ap(c_2EratRing_2Erat__r__canonical__sum__simplify,V111t)) ) )
& ap(c_2EratRing_2Erat__r__canonical__sum__simplify,c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)
& ! [V112vm] :
( mem(V112vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V113x] :
( mem(V113x,ty_2Equote_2Eindex)
=> ap(ap(ap(c_2EratRing_2Erat__r__ivl__aux,V112vm),V113x),c_2Elist_2ENIL(ty_2Equote_2Eindex)) = ap(ap(c_2Equote_2Evarmap__find(ty_2Erat_2Erat),V113x),V112vm) ) )
& ! [V114vm] :
( mem(V114vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V115x] :
( mem(V115x,ty_2Equote_2Eindex)
=> ! [V116x_27] :
( mem(V116x_27,ty_2Equote_2Eindex)
=> ! [V117t_27] :
( mem(V117t_27,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(ap(c_2EratRing_2Erat__r__ivl__aux,V114vm),V115x),ap(ap(c_2Elist_2ECONS(ty_2Equote_2Eindex),V116x_27),V117t_27)) = ap(ap(c_2Erat_2Erat__mul,ap(ap(c_2Equote_2Evarmap__find(ty_2Erat_2Erat),V115x),V114vm)),ap(ap(ap(c_2EratRing_2Erat__r__ivl__aux,V114vm),V116x_27),V117t_27)) ) ) ) )
& ! [V118vm] :
( mem(V118vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__interp__vl,V118vm),c_2Elist_2ENIL(ty_2Equote_2Eindex)) = ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) )
& ! [V119vm] :
( mem(V119vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V120x] :
( mem(V120x,ty_2Equote_2Eindex)
=> ! [V121t] :
( mem(V121t,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(c_2EratRing_2Erat__r__interp__vl,V119vm),ap(ap(c_2Elist_2ECONS(ty_2Equote_2Eindex),V120x),V121t)) = ap(ap(ap(c_2EratRing_2Erat__r__ivl__aux,V119vm),V120x),V121t) ) ) )
& ! [V122vm] :
( mem(V122vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V123c] :
( mem(V123c,ty_2Erat_2Erat)
=> ap(ap(ap(c_2EratRing_2Erat__r__interp__m,V122vm),V123c),c_2Elist_2ENIL(ty_2Equote_2Eindex)) = V123c ) )
& ! [V124vm] :
( mem(V124vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V125c] :
( mem(V125c,ty_2Erat_2Erat)
=> ! [V126x] :
( mem(V126x,ty_2Equote_2Eindex)
=> ! [V127t] :
( mem(V127t,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ap(ap(ap(c_2EratRing_2Erat__r__interp__m,V124vm),V125c),ap(ap(c_2Elist_2ECONS(ty_2Equote_2Eindex),V126x),V127t)) = ap(ap(c_2Erat_2Erat__mul,V125c),ap(ap(ap(c_2EratRing_2Erat__r__ivl__aux,V124vm),V126x),V127t)) ) ) ) )
& ! [V128vm] :
( mem(V128vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V129a] :
( mem(V129a,ty_2Erat_2Erat)
=> ap(ap(ap(c_2EratRing_2Erat__r__ics__aux,V128vm),V129a),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = V129a ) )
& ! [V130vm] :
( mem(V130vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V131a] :
( mem(V131a,ty_2Erat_2Erat)
=> ! [V132l] :
( mem(V132l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V133t] :
( mem(V133t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(ap(c_2EratRing_2Erat__r__ics__aux,V130vm),V131a),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V132l),V133t)) = ap(ap(c_2Erat_2Erat__add,V131a),ap(ap(ap(c_2EratRing_2Erat__r__ics__aux,V130vm),ap(ap(c_2EratRing_2Erat__r__interp__vl,V130vm),V132l)),V133t)) ) ) ) )
& ! [V134vm] :
( mem(V134vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V135a] :
( mem(V135a,ty_2Erat_2Erat)
=> ! [V136c] :
( mem(V136c,ty_2Erat_2Erat)
=> ! [V137l] :
( mem(V137l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V138t] :
( mem(V138t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(ap(c_2EratRing_2Erat__r__ics__aux,V134vm),V135a),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V136c),V137l),V138t)) = ap(ap(c_2Erat_2Erat__add,V135a),ap(ap(ap(c_2EratRing_2Erat__r__ics__aux,V134vm),ap(ap(ap(c_2EratRing_2Erat__r__interp__m,V134vm),V136c),V137l)),V138t)) ) ) ) ) )
& ! [V139vm] :
( mem(V139vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__interp__cs,V139vm),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) = ap(c_2Erat_2Erat__of__num,c_2Enum_2E0) )
& ! [V140vm] :
( mem(V140vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V141l] :
( mem(V141l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V142t] :
( mem(V142t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__interp__cs,V140vm),ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),V141l),V142t)) = ap(ap(ap(c_2EratRing_2Erat__r__ics__aux,V140vm),ap(ap(c_2EratRing_2Erat__r__interp__vl,V140vm),V141l)),V142t) ) ) )
& ! [V143vm] :
( mem(V143vm,ty_2Equote_2Evarmap(ty_2Erat_2Erat))
=> ! [V144c] :
( mem(V144c,ty_2Erat_2Erat)
=> ! [V145l] :
( mem(V145l,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V146t] :
( mem(V146t,ty_2Ecanonical_2Ecanonical__sum(ty_2Erat_2Erat))
=> ap(ap(c_2EratRing_2Erat__r__interp__cs,V143vm),ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V144c),V145l),V146t)) = ap(ap(ap(c_2EratRing_2Erat__r__ics__aux,V143vm),ap(ap(ap(c_2EratRing_2Erat__r__interp__m,V143vm),V144c),V145l)),V146t) ) ) ) )
& ! [V147i] :
( mem(V147i,ty_2Equote_2Eindex)
=> ap(c_2EratRing_2Erat__polynom__normalize,ap(c_2EringNorm_2EPvar(ty_2Erat_2Erat),V147i)) = ap(ap(c_2Ecanonical_2ECons__varlist(ty_2Erat_2Erat),ap(ap(c_2Elist_2ECONS(ty_2Equote_2Eindex),V147i),c_2Elist_2ENIL(ty_2Equote_2Eindex))),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) )
& ! [V148c] :
( mem(V148c,ty_2Erat_2Erat)
=> ap(c_2EratRing_2Erat__polynom__normalize,ap(c_2EringNorm_2EPconst(ty_2Erat_2Erat),V148c)) = ap(ap(ap(c_2Ecanonical_2ECons__monom(ty_2Erat_2Erat),V148c),c_2Elist_2ENIL(ty_2Equote_2Eindex)),c_2Ecanonical_2ENil__monom(ty_2Erat_2Erat)) )
& ! [V149pl] :
( mem(V149pl,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ! [V150pr] :
( mem(V150pr,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ap(c_2EratRing_2Erat__polynom__normalize,ap(ap(c_2EringNorm_2EPplus(ty_2Erat_2Erat),V149pl),V150pr)) = ap(ap(c_2EratRing_2Erat__r__canonical__sum__merge,ap(c_2EratRing_2Erat__polynom__normalize,V149pl)),ap(c_2EratRing_2Erat__polynom__normalize,V150pr)) ) )
& ! [V151pl] :
( mem(V151pl,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ! [V152pr] :
( mem(V152pr,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ap(c_2EratRing_2Erat__polynom__normalize,ap(ap(c_2EringNorm_2EPmult(ty_2Erat_2Erat),V151pl),V152pr)) = ap(ap(c_2EratRing_2Erat__r__canonical__sum__prod,ap(c_2EratRing_2Erat__polynom__normalize,V151pl)),ap(c_2EratRing_2Erat__polynom__normalize,V152pr)) ) )
& ! [V153p] :
( mem(V153p,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ap(c_2EratRing_2Erat__polynom__normalize,ap(c_2EringNorm_2EPopp(ty_2Erat_2Erat),V153p)) = ap(ap(ap(c_2EratRing_2Erat__r__canonical__sum__scalar3,ap(c_2Erat_2Erat__ainv,ap(c_2Erat_2Erat__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),c_2Elist_2ENIL(ty_2Equote_2Eindex)),ap(c_2EratRing_2Erat__polynom__normalize,V153p)) )
& ! [V154x] :
( mem(V154x,ty_2EringNorm_2Epolynom(ty_2Erat_2Erat))
=> ap(c_2EratRing_2Erat__polynom__simplify,V154x) = ap(c_2EratRing_2Erat__r__canonical__sum__simplify,ap(c_2EratRing_2Erat__polynom__normalize,V154x)) ) ) ) ).
%------------------------------------------------------------------------------