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 : 97 ( 30 unt; 38 typ; 0 def)
% Number of atoms : 2147 ( 90 equ; 0 cnn)
% Maximal formula atoms : 97 ( 22 avg)
% Number of connectives : 2807 ( 0 ~; 0 |; 56 &;2738 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 5 avg;2738 nst)
% Number of types : 5 ( 4 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 110 ( 109 usr; 94 con; 0-3 aty)
% Number of variables : 185 ( 1 ^ 184 !; 0 ?; 185 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(stp_c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,type,
tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat: $tType ).
thf(stp_inj_c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,type,
inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat > $i ).
thf(stp_surj_c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,type,
surj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat: $i > tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat ).
thf(stp_inj_surj_c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,axiom,
! [X: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,axiom,
! [X: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] : ( mem @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ X ) @ ( ty_2EringNorm_2Epolynom @ ty_2Erat_2Erat ) ) ).
thf(stp_iso_mem_c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2EringNorm_2Epolynom @ ty_2Erat_2Erat ) )
=> ( X
= ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ ( surj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ X ) ) ) ) ).
thf(stp_c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,type,
tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat: $tType ).
thf(stp_inj_c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,type,
inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat > $i ).
thf(stp_surj_c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,type,
surj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat: $i > tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat ).
thf(stp_inj_surj_c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,axiom,
! [X: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat] :
( ( surj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,axiom,
! [X: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat] : ( mem @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X ) @ ( ty_2Equote_2Evarmap @ ty_2Erat_2Erat ) ) ).
thf(stp_iso_mem_c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Equote_2Evarmap @ ty_2Erat_2Erat ) )
=> ( X
= ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ ( surj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X ) ) ) ) ).
thf(tp_c_2EratRing_2Erat__interp__p,type,
c_2EratRing_2Erat__interp__p: $i ).
thf(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 ) ) ).
thf(stp_fo_c_2EratRing_2Erat__interp__p,type,
fo__c_2EratRing_2Erat__interp__p: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat > tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat > tp__ty_2Erat_2Erat ).
thf(stp_eq_fo_c_2EratRing_2Erat__interp__p,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,X1: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( inj__ty_2Erat_2Erat @ ( fo__c_2EratRing_2Erat__interp__p @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X0 ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ X1 ) ) ) ).
thf(stp_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,type,
tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat: $tType ).
thf(stp_inj_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,type,
inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat > $i ).
thf(stp_surj_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,type,
surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat: $i > tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat ).
thf(stp_inj_surj_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,axiom,
! [X: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,axiom,
! [X: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] : ( mem @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ X ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Erat_2Erat ) ) ).
thf(stp_iso_mem_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Erat_2Erat ) )
=> ( X
= ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ X ) ) ) ) ).
thf(tp_c_2EratRing_2Erat__polynom__normalize,type,
c_2EratRing_2Erat__polynom__normalize: $i ).
thf(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 ) ) ).
thf(tp_c_2EratRing_2Erat__polynom__simplify,type,
c_2EratRing_2Erat__polynom__simplify: $i ).
thf(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 ) ) ).
thf(tp_c_2EratRing_2Erat__r__canonical__sum__merge,type,
c_2EratRing_2Erat__r__canonical__sum__merge: $i ).
thf(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 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__canonical__sum__prod,type,
c_2EratRing_2Erat__r__canonical__sum__prod: $i ).
thf(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 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__canonical__sum__scalar,type,
c_2EratRing_2Erat__r__canonical__sum__scalar: $i ).
thf(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 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__canonical__sum__scalar2,type,
c_2EratRing_2Erat__r__canonical__sum__scalar2: $i ).
thf(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 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__canonical__sum__scalar3,type,
c_2EratRing_2Erat__r__canonical__sum__scalar3: $i ).
thf(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 ) ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__canonical__sum__simplify,type,
c_2EratRing_2Erat__r__canonical__sum__simplify: $i ).
thf(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 ) ) ).
thf(tp_c_2EratRing_2Erat__r__ics__aux,type,
c_2EratRing_2Erat__r__ics__aux: $i ).
thf(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 ) ) ) ).
thf(stp_fo_c_2EratRing_2Erat__r__ics__aux,type,
fo__c_2EratRing_2Erat__r__ics__aux: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat > tp__ty_2Erat_2Erat > tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat > tp__ty_2Erat_2Erat ).
thf(stp_eq_fo_c_2EratRing_2Erat__r__ics__aux,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,X1: tp__ty_2Erat_2Erat,X2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( inj__ty_2Erat_2Erat @ ( fo__c_2EratRing_2Erat__r__ics__aux @ X0 @ X1 @ X2 ) )
= ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X0 ) ) @ ( inj__ty_2Erat_2Erat @ X1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ X2 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__interp__cs,type,
c_2EratRing_2Erat__r__interp__cs: $i ).
thf(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 ) ) ).
thf(stp_fo_c_2EratRing_2Erat__r__interp__cs,type,
fo__c_2EratRing_2Erat__r__interp__cs: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat > tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat > tp__ty_2Erat_2Erat ).
thf(stp_eq_fo_c_2EratRing_2Erat__r__interp__cs,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,X1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( inj__ty_2Erat_2Erat @ ( fo__c_2EratRing_2Erat__r__interp__cs @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ X1 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__interp__m,type,
c_2EratRing_2Erat__r__interp__m: $i ).
thf(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 ) ) ) ).
thf(stp_fo_c_2EratRing_2Erat__r__interp__m,type,
fo__c_2EratRing_2Erat__r__interp__m: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat > tp__ty_2Erat_2Erat > tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex > tp__ty_2Erat_2Erat ).
thf(stp_eq_fo_c_2EratRing_2Erat__r__interp__m,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,X1: tp__ty_2Erat_2Erat,X2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( inj__ty_2Erat_2Erat @ ( fo__c_2EratRing_2Erat__r__interp__m @ X0 @ X1 @ X2 ) )
= ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X0 ) ) @ ( inj__ty_2Erat_2Erat @ X1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X2 ) ) ) ).
thf(stp_c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat,type,
tp__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat: $tType ).
thf(stp_inj_c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat,type,
inj__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat: tp__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat > $i ).
thf(stp_surj_c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat,type,
surj__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat: $i > tp__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat ).
thf(stp_inj_surj_c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat,axiom,
! [X: tp__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat,axiom,
! [X: tp__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat] : ( mem @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat @ X ) @ ( ty_2Ecanonical_2Espolynom @ ty_2Erat_2Erat ) ) ).
thf(stp_iso_mem_c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Ecanonical_2Espolynom @ ty_2Erat_2Erat ) )
=> ( X
= ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat @ ( surj__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat @ X ) ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__interp__sp,type,
c_2EratRing_2Erat__r__interp__sp: $i ).
thf(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 ) ) ).
thf(stp_fo_c_2EratRing_2Erat__r__interp__sp,type,
fo__c_2EratRing_2Erat__r__interp__sp: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat > tp__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat > tp__ty_2Erat_2Erat ).
thf(stp_eq_fo_c_2EratRing_2Erat__r__interp__sp,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,X1: tp__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat] :
( ( inj__ty_2Erat_2Erat @ ( fo__c_2EratRing_2Erat__r__interp__sp @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X0 ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Erat_2Erat @ X1 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__interp__vl,type,
c_2EratRing_2Erat__r__interp__vl: $i ).
thf(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 ) ) ).
thf(stp_fo_c_2EratRing_2Erat__r__interp__vl,type,
fo__c_2EratRing_2Erat__r__interp__vl: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat > tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex > tp__ty_2Erat_2Erat ).
thf(stp_eq_fo_c_2EratRing_2Erat__r__interp__vl,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,X1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( inj__ty_2Erat_2Erat @ ( fo__c_2EratRing_2Erat__r__interp__vl @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X1 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__ivl__aux,type,
c_2EratRing_2Erat__r__ivl__aux: $i ).
thf(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 ) ) ) ).
thf(stp_fo_c_2EratRing_2Erat__r__ivl__aux,type,
fo__c_2EratRing_2Erat__r__ivl__aux: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat > tp__ty_2Equote_2Eindex > tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex > tp__ty_2Erat_2Erat ).
thf(stp_eq_fo_c_2EratRing_2Erat__r__ivl__aux,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,X1: tp__ty_2Equote_2Eindex,X2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( inj__ty_2Erat_2Erat @ ( fo__c_2EratRing_2Erat__r__ivl__aux @ X0 @ X1 @ X2 ) )
= ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ X0 ) ) @ ( inj__ty_2Equote_2Eindex @ X1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X2 ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__monom__insert,type,
c_2EratRing_2Erat__r__monom__insert: $i ).
thf(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 ) ) ) ) ).
thf(tp_c_2EratRing_2Erat__r__spolynom__normalize,type,
c_2EratRing_2Erat__r__spolynom__normalize: $i ).
thf(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 ) ) ).
thf(tp_c_2EratRing_2Erat__r__spolynom__simplify,type,
c_2EratRing_2Erat__r__spolynom__simplify: $i ).
thf(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 ) ) ).
thf(tp_c_2EratRing_2Erat__r__varlist__insert,type,
c_2EratRing_2Erat__r__varlist__insert: $i ).
thf(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 ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) ) ).
thf(conj_thm_2EratRing_2Erat__ring__thms,axiom,
! [A_27a: del] :
( ( 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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Erat_2Erat__add ) @ c_2Erat_2Erat__mul ) @ c_2Erat_2Erat__ainv ) ) )
& ! [V0vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V1p: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V0vm ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V1p ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V0vm ) ) @ ( ap @ c_2EratRing_2Erat__polynom__simplify @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V1p ) ) ) ) )
& ! [V2vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V3c: tp__ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V2vm ) ) @ ( ap @ ( c_2EringNorm_2EPconst @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V3c ) ) ) )
= V3c )
& ! [V4vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V5i: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V4vm ) ) @ ( ap @ ( c_2EringNorm_2EPvar @ ty_2Erat_2Erat ) @ ( inj__ty_2Equote_2Eindex @ V5i ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ ty_2Erat_2Erat ) @ ( inj__ty_2Equote_2Eindex @ V5i ) ) @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V4vm ) ) ) )
& ! [V6vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V7p1: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,V8p2: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V6vm ) ) @ ( ap @ ( ap @ ( c_2EringNorm_2EPplus @ ty_2Erat_2Erat ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V7p1 ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V8p2 ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2Erat_2Erat__add @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V6vm ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V7p1 ) ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V6vm ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V8p2 ) ) ) ) )
& ! [V9vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V10p1: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,V11p2: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V9vm ) ) @ ( ap @ ( ap @ ( c_2EringNorm_2EPmult @ ty_2Erat_2Erat ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V10p1 ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V11p2 ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2Erat_2Erat__mul @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V9vm ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V10p1 ) ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V9vm ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V11p2 ) ) ) ) )
& ! [V12vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V13p1: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V12vm ) ) @ ( ap @ ( c_2EringNorm_2EPopp @ ty_2Erat_2Erat ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V13p1 ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ c_2Erat_2Erat__ainv @ ( ap @ ( ap @ c_2EratRing_2Erat__interp__p @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V12vm ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V13p1 ) ) ) ) )
& ! [V14x: $i] :
( ( mem @ V14x @ A_27a )
=> ! [V15v2: $i] :
( ( mem @ V15v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V16v1: $i] :
( ( mem @ V16v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V14x ) @ V16v1 ) @ V15v2 ) )
= V14x ) ) ) )
& ! [V17x: $i] :
( ( mem @ V17x @ A_27a )
=> ! [V18v2: $i] :
( ( mem @ V18v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V19v1: $i] :
( ( mem @ V19v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V20i1: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V20i1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V17x ) @ V19v1 ) @ V18v2 ) )
= ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V20i1 ) ) @ V18v2 ) ) ) ) )
& ! [V21x: $i] :
( ( mem @ V21x @ A_27a )
=> ! [V22v2: $i] :
( ( mem @ V22v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V23v1: $i] :
( ( mem @ V23v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V24i1: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V24i1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V21x ) @ V23v1 ) @ V22v2 ) )
= ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V24i1 ) ) @ V23v1 ) ) ) ) )
& ! [V25i: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V25i ) ) @ ( c_2Equote_2EEmpty__vm @ A_27a ) )
= ( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V26x: $i] : c_2Ebool_2ET ) ) )
& ! [V27t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V28t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V29l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V30l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V31c2: tp__ty_2Erat_2Erat,V32c1: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V32c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V30l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V28t1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V31c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V29l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V27t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V30l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V29l2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V32c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V30l1 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V28t1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V31c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V29l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V27t2 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( ap @ ( ap @ c_2Erat_2Erat__add @ ( inj__ty_2Erat_2Erat @ V32c1 ) ) @ ( inj__ty_2Erat_2Erat @ V31c2 ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V30l1 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V28t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V27t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V31c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V29l2 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V32c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V30l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V28t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V27t2 ) ) ) ) ) )
& ! [V33t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V34t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V35l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V36l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V37c1: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V37c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V36l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V34t1 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V35l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V33t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V36l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V35l2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V37c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V36l1 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V34t1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V35l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V33t2 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( ap @ ( ap @ c_2Erat_2Erat__add @ ( inj__ty_2Erat_2Erat @ V37c1 ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V36l1 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V34t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V33t2 ) ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V35l2 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V37c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V36l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V34t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V33t2 ) ) ) ) ) )
& ! [V38t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V39t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V40l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V41l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V42c2: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V41l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V39t1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V42c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V40l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V38t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V41l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V40l2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V41l1 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V39t1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V42c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V40l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ 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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erat_2Erat @ V42c2 ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V41l1 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V39t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V38t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V42c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V40l2 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V41l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V39t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V38t2 ) ) ) ) ) )
& ! [V43t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V44t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V45l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V46l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V46l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V44t1 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V45l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V43t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V46l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V45l2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V46l1 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V44t1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V45l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ 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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V46l1 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V44t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V43t2 ) ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V45l2 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V46l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V44t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V43t2 ) ) ) ) ) )
& ! [V47s1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V47s1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= V47s1 )
& ! [V48v6: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V49v5: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V50v4: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_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 ) @ ( inj__ty_2Erat_2Erat @ V50v4 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V49v5 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V48v6 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V50v4 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V49v5 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V48v6 ) ) ) )
& ! [V51v8: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V52v7: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V52v7 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V51v8 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V52v7 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V51v8 ) ) ) )
& ! [V53t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V54l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V55l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V56c2: tp__ty_2Erat_2Erat,V57c1: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__monom__insert @ ( inj__ty_2Erat_2Erat @ V57c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V55l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V56c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V54l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V53t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V55l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V54l2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V57c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V55l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V56c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V54l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V53t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( ap @ ( ap @ c_2Erat_2Erat__add @ ( inj__ty_2Erat_2Erat @ V57c1 ) ) @ ( inj__ty_2Erat_2Erat @ V56c2 ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V55l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V53t2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V56c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V54l2 ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__monom__insert @ ( inj__ty_2Erat_2Erat @ V57c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V55l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V53t2 ) ) ) ) ) )
& ! [V58t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V59l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V60l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V61c1: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__monom__insert @ ( inj__ty_2Erat_2Erat @ V61c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V60l1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V59l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V58t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V60l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V59l2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V61c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V60l1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V59l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V58t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( ap @ ( ap @ c_2Erat_2Erat__add @ ( inj__ty_2Erat_2Erat @ V61c1 ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V60l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V58t2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V59l2 ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__monom__insert @ ( inj__ty_2Erat_2Erat @ V61c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V60l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V58t2 ) ) ) ) ) )
& ! [V62l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V63c1: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__monom__insert @ ( inj__ty_2Erat_2Erat @ V63c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V62l1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V63c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V62l1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) ) )
& ! [V64t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V65l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V66l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V67c2: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V66l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V67c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V65l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V64t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V66l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V65l2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V66l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V67c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V65l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ 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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erat_2Erat @ V67c2 ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V66l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V64t2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V67c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V65l2 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V66l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V64t2 ) ) ) ) ) )
& ! [V68t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V69l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V70l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V70l1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V69l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V68t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V70l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V69l2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V70l1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V69l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ 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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V70l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V68t2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V69l2 ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V70l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V68t2 ) ) ) ) ) )
& ! [V71l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V71l1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V71l1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) ) )
& ! [V72c0: tp__ty_2Erat_2Erat,V73c: tp__ty_2Erat_2Erat,V74l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V75t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar @ ( inj__ty_2Erat_2Erat @ V72c0 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V73c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V74l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V75t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( ap @ ( ap @ c_2Erat_2Erat__mul @ ( inj__ty_2Erat_2Erat @ V72c0 ) ) @ ( inj__ty_2Erat_2Erat @ V73c ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V74l ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar @ ( inj__ty_2Erat_2Erat @ V72c0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V75t ) ) ) ) )
& ! [V76c0: tp__ty_2Erat_2Erat,V77l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V78t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar @ ( inj__ty_2Erat_2Erat @ V76c0 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V77l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V78t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V76c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V77l ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar @ ( inj__ty_2Erat_2Erat @ V76c0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V78t ) ) ) ) )
& ! [V79c0: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar @ ( inj__ty_2Erat_2Erat @ V79c0 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
& ! [V80l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V81c: tp__ty_2Erat_2Erat,V82l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V83t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V80l0 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V81c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V82l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V83t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__monom__insert @ ( inj__ty_2Erat_2Erat @ V81c ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__merge @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__lt ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V80l0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V82l ) ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V80l0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V83t ) ) ) ) )
& ! [V84l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V85l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V86t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V84l0 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V85l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V86t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__varlist__insert @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__merge @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__lt ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V84l0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V85l ) ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V84l0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V86t ) ) ) ) )
& ! [V87l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V87l0 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
& ! [V88c0: tp__ty_2Erat_2Erat,V89l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V90c: tp__ty_2Erat_2Erat,V91l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V92t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar3 @ ( inj__ty_2Erat_2Erat @ V88c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V89l0 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V90c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V91l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V92t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__monom__insert @ ( ap @ ( ap @ c_2Erat_2Erat__mul @ ( inj__ty_2Erat_2Erat @ V88c0 ) ) @ ( inj__ty_2Erat_2Erat @ V90c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__merge @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__lt ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V89l0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V91l ) ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar3 @ ( inj__ty_2Erat_2Erat @ V88c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V89l0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V92t ) ) ) ) )
& ! [V93c0: tp__ty_2Erat_2Erat,V94l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V95l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V96t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar3 @ ( inj__ty_2Erat_2Erat @ V93c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V94l0 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V95l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V96t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__monom__insert @ ( inj__ty_2Erat_2Erat @ V93c0 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__merge @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__lt ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V94l0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V95l ) ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar3 @ ( inj__ty_2Erat_2Erat @ V93c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V94l0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V96t ) ) ) ) )
& ! [V97c0: tp__ty_2Erat_2Erat,V98l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar3 @ ( inj__ty_2Erat_2Erat @ V97c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V98l0 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
& ! [V99c1: tp__ty_2Erat_2Erat,V100l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V101t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V102s2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_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 ) @ ( inj__ty_2Erat_2Erat @ V99c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V100l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V101t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V102s2 ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar3 @ ( inj__ty_2Erat_2Erat @ V99c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V100l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V102s2 ) ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__prod @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V101t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V102s2 ) ) ) ) )
& ! [V103l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V104t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat,V105s2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_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 ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V103l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V104t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V105s2 ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V103l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V105s2 ) ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__prod @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V104t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V105s2 ) ) ) ) )
& ! [V106s2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__prod @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V106s2 ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
& ! [V107c: tp__ty_2Erat_2Erat,V108l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V109t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_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 ) @ ( inj__ty_2Erat_2Erat @ V107c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V108l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V109t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Erat_2Erat ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V107c ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__simplify @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V109t ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Erat_2Erat ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V107c ) ) @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V108l ) ) @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__simplify @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V109t ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V107c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V108l ) ) @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__simplify @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V109t ) ) ) ) ) ) )
& ! [V110l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V111t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__simplify @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V110l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V111t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V110l ) ) @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__simplify @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V111t ) ) ) ) )
& ( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__simplify @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
& ! [V112vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V113x: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V112vm ) ) @ ( inj__ty_2Equote_2Eindex @ V113x ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ ty_2Erat_2Erat ) @ ( inj__ty_2Equote_2Eindex @ V113x ) ) @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V112vm ) ) ) )
& ! [V114vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V115x: tp__ty_2Equote_2Eindex,V116x_27: tp__ty_2Equote_2Eindex,V117t_27: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V114vm ) ) @ ( inj__ty_2Equote_2Eindex @ V115x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Equote_2Eindex ) @ ( inj__ty_2Equote_2Eindex @ V116x_27 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V117t_27 ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2Erat_2Erat__mul @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ ty_2Erat_2Erat ) @ ( inj__ty_2Equote_2Eindex @ V115x ) ) @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V114vm ) ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V114vm ) ) @ ( inj__ty_2Equote_2Eindex @ V116x_27 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V117t_27 ) ) ) ) )
& ! [V118vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V118vm ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ c_2Erat_2Erat__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V119vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V120x: tp__ty_2Equote_2Eindex,V121t: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V119vm ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Equote_2Eindex ) @ ( inj__ty_2Equote_2Eindex @ V120x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V121t ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V119vm ) ) @ ( inj__ty_2Equote_2Eindex @ V120x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V121t ) ) ) )
& ! [V122vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V123c: tp__ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V122vm ) ) @ ( inj__ty_2Erat_2Erat @ V123c ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) )
= V123c )
& ! [V124vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V125c: tp__ty_2Erat_2Erat,V126x: tp__ty_2Equote_2Eindex,V127t: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V124vm ) ) @ ( inj__ty_2Erat_2Erat @ V125c ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Equote_2Eindex ) @ ( inj__ty_2Equote_2Eindex @ V126x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V127t ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2Erat_2Erat__mul @ ( inj__ty_2Erat_2Erat @ V125c ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V124vm ) ) @ ( inj__ty_2Equote_2Eindex @ V126x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V127t ) ) ) ) )
& ! [V128vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V129a: tp__ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V128vm ) ) @ ( inj__ty_2Erat_2Erat @ V129a ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= V129a )
& ! [V130vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V131a: tp__ty_2Erat_2Erat,V132l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V133t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V130vm ) ) @ ( inj__ty_2Erat_2Erat @ V131a ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V132l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V133t ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2Erat_2Erat__add @ ( inj__ty_2Erat_2Erat @ V131a ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V130vm ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V130vm ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V132l ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V133t ) ) ) ) )
& ! [V134vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V135a: tp__ty_2Erat_2Erat,V136c: tp__ty_2Erat_2Erat,V137l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V138t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V134vm ) ) @ ( inj__ty_2Erat_2Erat @ V135a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V136c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V137l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V138t ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2Erat_2Erat__add @ ( inj__ty_2Erat_2Erat @ V135a ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V134vm ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V134vm ) ) @ ( inj__ty_2Erat_2Erat @ V136c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V137l ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V138t ) ) ) ) )
& ! [V139vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V139vm ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ c_2Erat_2Erat__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V140vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V141l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V142t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V140vm ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V141l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V142t ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V140vm ) ) @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V140vm ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V141l ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V142t ) ) ) )
& ! [V143vm: tp__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat,V144c: tp__ty_2Erat_2Erat,V145l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V146t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat] :
( ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V143vm ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V144c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V145l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V146t ) ) ) )
= ( surj__ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V143vm ) ) @ ( ap @ ( ap @ ( ap @ c_2EratRing_2Erat__r__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Erat_2Erat @ V143vm ) ) @ ( inj__ty_2Erat_2Erat @ V144c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V145l ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ V146t ) ) ) )
& ! [V147i: tp__ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( ap @ ( c_2EringNorm_2EPvar @ ty_2Erat_2Erat ) @ ( inj__ty_2Equote_2Eindex @ V147i ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Erat_2Erat ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Equote_2Eindex ) @ ( inj__ty_2Equote_2Eindex @ V147i ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) ) )
& ! [V148c: tp__ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( ap @ ( c_2EringNorm_2EPconst @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V148c ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Erat_2Erat ) @ ( inj__ty_2Erat_2Erat @ V148c ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Erat_2Erat ) ) ) )
& ! [V149pl: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,V150pr: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( ap @ ( ap @ ( c_2EringNorm_2EPplus @ ty_2Erat_2Erat ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V149pl ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V150pr ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__merge @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V149pl ) ) ) @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V150pr ) ) ) ) )
& ! [V151pl: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat,V152pr: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( ap @ ( ap @ ( c_2EringNorm_2EPmult @ ty_2Erat_2Erat ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V151pl ) ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V152pr ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__prod @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V151pl ) ) ) @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V152pr ) ) ) ) )
& ! [V153p: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( ap @ ( c_2EringNorm_2EPopp @ ty_2Erat_2Erat ) @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V153p ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( 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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V153p ) ) ) ) )
& ! [V154x: tp__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__polynom__simplify @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V154x ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Erat_2Erat @ ( ap @ c_2EratRing_2Erat__r__canonical__sum__simplify @ ( ap @ c_2EratRing_2Erat__polynom__normalize @ ( inj__c_ty_2EringNorm_2Epolynom_ty_2Erat_2Erat @ V154x ) ) ) ) ) ) ).
%------------------------------------------------------------------------------