ITP001 Axioms: ITP117^5.ax
%------------------------------------------------------------------------------
% File : ITP117^5 : 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 : numRing^2.ax [Gau20]
% : HL4117^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 81 ( 25 unt; 31 typ; 0 def)
% Number of atoms : 2892 ( 149 equ; 0 cnn)
% Maximal formula atoms : 256 ( 35 avg)
% Number of connectives : 3572 ( 1 ~; 0 |; 130 &;3402 @)
% ( 27 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 6 avg;3402 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 112 ( 109 usr; 99 con; 0-3 aty)
% Number of variables : 228 ( 1 ^ 227 !; 0 ?; 228 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(stp_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,type,
tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum: $tType ).
thf(stp_inj_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,type,
inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum > $i ).
thf(stp_surj_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,type,
surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum: $i > tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum ).
thf(stp_inj_surj_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ X ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ).
thf(stp_iso_mem_c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) )
=> ( X
= ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ X ) ) ) ) ).
thf(tp_c_2EnumRing_2Enum__canonical__sum__merge,type,
c_2EnumRing_2Enum__canonical__sum__merge: $i ).
thf(mem_c_2EnumRing_2Enum__canonical__sum__merge,axiom,
mem @ c_2EnumRing_2Enum__canonical__sum__merge @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2EnumRing_2Enum__canonical__sum__prod,type,
c_2EnumRing_2Enum__canonical__sum__prod: $i ).
thf(mem_c_2EnumRing_2Enum__canonical__sum__prod,axiom,
mem @ c_2EnumRing_2Enum__canonical__sum__prod @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2EnumRing_2Enum__canonical__sum__scalar,type,
c_2EnumRing_2Enum__canonical__sum__scalar: $i ).
thf(mem_c_2EnumRing_2Enum__canonical__sum__scalar,axiom,
mem @ c_2EnumRing_2Enum__canonical__sum__scalar @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2EnumRing_2Enum__canonical__sum__scalar2,type,
c_2EnumRing_2Enum__canonical__sum__scalar2: $i ).
thf(mem_c_2EnumRing_2Enum__canonical__sum__scalar2,axiom,
mem @ c_2EnumRing_2Enum__canonical__sum__scalar2 @ ( arr @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2EnumRing_2Enum__canonical__sum__scalar3,type,
c_2EnumRing_2Enum__canonical__sum__scalar3: $i ).
thf(mem_c_2EnumRing_2Enum__canonical__sum__scalar3,axiom,
mem @ c_2EnumRing_2Enum__canonical__sum__scalar3 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ) ) ).
thf(tp_c_2EnumRing_2Enum__canonical__sum__simplify,type,
c_2EnumRing_2Enum__canonical__sum__simplify: $i ).
thf(mem_c_2EnumRing_2Enum__canonical__sum__simplify,axiom,
mem @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ).
thf(stp_c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,type,
tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum: $tType ).
thf(stp_inj_c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,type,
inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum > $i ).
thf(stp_surj_c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,type,
surj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum: $i > tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum ).
thf(stp_inj_surj_c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum] :
( ( surj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X ) @ ( ty_2Equote_2Evarmap @ ty_2Enum_2Enum ) ) ).
thf(stp_iso_mem_c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Equote_2Evarmap @ ty_2Enum_2Enum ) )
=> ( X
= ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ ( surj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X ) ) ) ) ).
thf(tp_c_2EnumRing_2Enum__ics__aux,type,
c_2EnumRing_2Enum__ics__aux: $i ).
thf(mem_c_2EnumRing_2Enum__ics__aux,axiom,
mem @ c_2EnumRing_2Enum__ics__aux @ ( arr @ ( ty_2Equote_2Evarmap @ ty_2Enum_2Enum ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ) ) ).
thf(stp_fo_c_2EnumRing_2Enum__ics__aux,type,
fo__c_2EnumRing_2Enum__ics__aux: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2EnumRing_2Enum__ics__aux,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum,X2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2EnumRing_2Enum__ics__aux @ X0 @ X1 @ X2 ) )
= ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ X2 ) ) ) ).
thf(tp_c_2EnumRing_2Enum__interp__cs,type,
c_2EnumRing_2Enum__interp__cs: $i ).
thf(mem_c_2EnumRing_2Enum__interp__cs,axiom,
mem @ c_2EnumRing_2Enum__interp__cs @ ( arr @ ( ty_2Equote_2Evarmap @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ) ).
thf(stp_fo_c_2EnumRing_2Enum__interp__cs,type,
fo__c_2EnumRing_2Enum__interp__cs: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum > tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2EnumRing_2Enum__interp__cs,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,X1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2EnumRing_2Enum__interp__cs @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EnumRing_2Enum__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ X1 ) ) ) ).
thf(tp_c_2EnumRing_2Enum__interp__m,type,
c_2EnumRing_2Enum__interp__m: $i ).
thf(mem_c_2EnumRing_2Enum__interp__m,axiom,
mem @ c_2EnumRing_2Enum__interp__m @ ( arr @ ( ty_2Equote_2Evarmap @ ty_2Enum_2Enum ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) @ ty_2Enum_2Enum ) ) ) ).
thf(stp_fo_c_2EnumRing_2Enum__interp__m,type,
fo__c_2EnumRing_2Enum__interp__m: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2EnumRing_2Enum__interp__m,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum,X2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2EnumRing_2Enum__interp__m @ X0 @ X1 @ X2 ) )
= ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X2 ) ) ) ).
thf(stp_c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,type,
tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum: $tType ).
thf(stp_inj_c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,type,
inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum > $i ).
thf(stp_surj_c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,type,
surj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum: $i > tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum ).
thf(stp_inj_surj_c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ X ) @ ( ty_2Ecanonical_2Espolynom @ ty_2Enum_2Enum ) ) ).
thf(stp_iso_mem_c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Ecanonical_2Espolynom @ ty_2Enum_2Enum ) )
=> ( X
= ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ ( surj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ X ) ) ) ) ).
thf(tp_c_2EnumRing_2Enum__interp__sp,type,
c_2EnumRing_2Enum__interp__sp: $i ).
thf(mem_c_2EnumRing_2Enum__interp__sp,axiom,
mem @ c_2EnumRing_2Enum__interp__sp @ ( arr @ ( ty_2Equote_2Evarmap @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Ecanonical_2Espolynom @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ) ).
thf(stp_fo_c_2EnumRing_2Enum__interp__sp,type,
fo__c_2EnumRing_2Enum__interp__sp: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum > tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2EnumRing_2Enum__interp__sp,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,X1: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2EnumRing_2Enum__interp__sp @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X0 ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ X1 ) ) ) ).
thf(tp_c_2EnumRing_2Enum__interp__vl,type,
c_2EnumRing_2Enum__interp__vl: $i ).
thf(mem_c_2EnumRing_2Enum__interp__vl,axiom,
mem @ c_2EnumRing_2Enum__interp__vl @ ( arr @ ( ty_2Equote_2Evarmap @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) @ ty_2Enum_2Enum ) ) ).
thf(stp_fo_c_2EnumRing_2Enum__interp__vl,type,
fo__c_2EnumRing_2Enum__interp__vl: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum > tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2EnumRing_2Enum__interp__vl,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,X1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2EnumRing_2Enum__interp__vl @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EnumRing_2Enum__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X1 ) ) ) ).
thf(tp_c_2EnumRing_2Enum__ivl__aux,type,
c_2EnumRing_2Enum__ivl__aux: $i ).
thf(mem_c_2EnumRing_2Enum__ivl__aux,axiom,
mem @ c_2EnumRing_2Enum__ivl__aux @ ( arr @ ( ty_2Equote_2Evarmap @ ty_2Enum_2Enum ) @ ( arr @ ty_2Equote_2Eindex @ ( arr @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) @ ty_2Enum_2Enum ) ) ) ).
thf(stp_fo_c_2EnumRing_2Enum__ivl__aux,type,
fo__c_2EnumRing_2Enum__ivl__aux: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum > tp__ty_2Equote_2Eindex > tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2EnumRing_2Enum__ivl__aux,axiom,
! [X0: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,X1: tp__ty_2Equote_2Eindex,X2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2EnumRing_2Enum__ivl__aux @ X0 @ X1 @ X2 ) )
= ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Equote_2Eindex @ X1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X2 ) ) ) ).
thf(tp_c_2EnumRing_2Enum__monom__insert,type,
c_2EnumRing_2Enum__monom__insert: $i ).
thf(mem_c_2EnumRing_2Enum__monom__insert,axiom,
mem @ c_2EnumRing_2Enum__monom__insert @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ) ) ).
thf(tp_c_2EnumRing_2Enum__spolynom__normalize,type,
c_2EnumRing_2Enum__spolynom__normalize: $i ).
thf(mem_c_2EnumRing_2Enum__spolynom__normalize,axiom,
mem @ c_2EnumRing_2Enum__spolynom__normalize @ ( arr @ ( ty_2Ecanonical_2Espolynom @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2EnumRing_2Enum__spolynom__simplify,type,
c_2EnumRing_2Enum__spolynom__simplify: $i ).
thf(mem_c_2EnumRing_2Enum__spolynom__simplify,axiom,
mem @ c_2EnumRing_2Enum__spolynom__simplify @ ( arr @ ( ty_2Ecanonical_2Espolynom @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2EnumRing_2Enum__varlist__insert,type,
c_2EnumRing_2Enum__varlist__insert: $i ).
thf(mem_c_2EnumRing_2Enum__varlist__insert,axiom,
mem @ c_2EnumRing_2Enum__varlist__insert @ ( arr @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) @ ( arr @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) ) ).
thf(conj_thm_2EnumRing_2Enum__semi__ring,axiom,
p @ ( ap @ ( c_2Esemi__ring_2Eis__semi__ring @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ).
thf(ax_thm_2EnumRing_2Enum__interp__sp__def,axiom,
( c_2EnumRing_2Enum__interp__sp
= ( ap @ ( c_2Ecanonical_2Einterp__sp @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__spolynom__simplify__def,axiom,
( c_2EnumRing_2Enum__spolynom__simplify
= ( ap @ ( c_2Ecanonical_2Espolynom__simplify @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__spolynom__normalize__def,axiom,
( c_2EnumRing_2Enum__spolynom__normalize
= ( ap @ ( c_2Ecanonical_2Espolynom__normalize @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__interp__cs__def,axiom,
( c_2EnumRing_2Enum__interp__cs
= ( ap @ ( c_2Ecanonical_2Einterp__cs @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__ics__aux__def,axiom,
( c_2EnumRing_2Enum__ics__aux
= ( ap @ ( c_2Ecanonical_2Eics__aux @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__interp__m__def,axiom,
( c_2EnumRing_2Enum__interp__m
= ( ap @ ( c_2Ecanonical_2Einterp__m @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__interp__vl__def,axiom,
( c_2EnumRing_2Enum__interp__vl
= ( ap @ ( c_2Ecanonical_2Einterp__vl @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__ivl__aux__def,axiom,
( c_2EnumRing_2Enum__ivl__aux
= ( ap @ ( c_2Ecanonical_2Eivl__aux @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__canonical__sum__simplify__def,axiom,
( c_2EnumRing_2Enum__canonical__sum__simplify
= ( ap @ ( c_2Ecanonical_2Ecanonical__sum__simplify @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__canonical__sum__prod__def,axiom,
( c_2EnumRing_2Enum__canonical__sum__prod
= ( ap @ ( c_2Ecanonical_2Ecanonical__sum__prod @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__canonical__sum__scalar3__def,axiom,
( c_2EnumRing_2Enum__canonical__sum__scalar3
= ( ap @ ( c_2Ecanonical_2Ecanonical__sum__scalar3 @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__canonical__sum__scalar2__def,axiom,
( c_2EnumRing_2Enum__canonical__sum__scalar2
= ( ap @ ( c_2Ecanonical_2Ecanonical__sum__scalar2 @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__canonical__sum__scalar__def,axiom,
( c_2EnumRing_2Enum__canonical__sum__scalar
= ( ap @ ( c_2Ecanonical_2Ecanonical__sum__scalar @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__varlist__insert__def,axiom,
( c_2EnumRing_2Enum__varlist__insert
= ( ap @ ( c_2Ecanonical_2Evarlist__insert @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__monom__insert__def,axiom,
( c_2EnumRing_2Enum__monom__insert
= ( ap @ ( c_2Ecanonical_2Emonom__insert @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(ax_thm_2EnumRing_2Enum__canonical__sum__merge__def,axiom,
( c_2EnumRing_2Enum__canonical__sum__merge
= ( ap @ ( c_2Ecanonical_2Ecanonical__sum__merge @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) ) ).
thf(conj_thm_2EnumRing_2Enum__ring__thms,axiom,
! [A_27a: del] :
( ( p @ ( ap @ ( c_2Esemi__ring_2Eis__semi__ring @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2Earithmetic_2E_2B ) @ c_2Earithmetic_2E_2A ) ) )
& ! [V0vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V1p: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V0vm ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V1p ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V0vm ) ) @ ( ap @ c_2EnumRing_2Enum__spolynom__simplify @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V1p ) ) ) ) )
& ! [V2vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V3c: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V2vm ) ) @ ( ap @ ( c_2Ecanonical_2ESPconst @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3c ) ) ) )
= V3c )
& ! [V4vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V5i: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V4vm ) ) @ ( ap @ ( c_2Ecanonical_2ESPvar @ ty_2Enum_2Enum ) @ ( inj__ty_2Equote_2Eindex @ V5i ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ ty_2Enum_2Enum ) @ ( inj__ty_2Equote_2Eindex @ V5i ) ) @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V4vm ) ) ) )
& ! [V6vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V7p1: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,V8p2: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V6vm ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ESPplus @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V7p1 ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V8p2 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V6vm ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V7p1 ) ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V6vm ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V8p2 ) ) ) ) )
& ! [V9vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V10p1: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,V11p2: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V9vm ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ESPmult @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V10p1 ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V11p2 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V9vm ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V10p1 ) ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__sp @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V9vm ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V11p2 ) ) ) ) )
& ! [V12x: $i] :
( ( mem @ V12x @ A_27a )
=> ! [V13v2: $i] :
( ( mem @ V13v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V14v1: $i] :
( ( mem @ V14v1 @ ( 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 ) @ V12x ) @ V14v1 ) @ V13v2 ) )
= V12x ) ) ) )
& ! [V15x: $i] :
( ( mem @ V15x @ A_27a )
=> ! [V16v2: $i] :
( ( mem @ V16v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V17v1: $i] :
( ( mem @ V17v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V18i1: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V18i1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V15x ) @ V17v1 ) @ V16v2 ) )
= ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V18i1 ) ) @ V16v2 ) ) ) ) )
& ! [V19x: $i] :
( ( mem @ V19x @ A_27a )
=> ! [V20v2: $i] :
( ( mem @ V20v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V21v1: $i] :
( ( mem @ V21v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V22i1: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V22i1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V19x ) @ V21v1 ) @ V20v2 ) )
= ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V22i1 ) ) @ V21v1 ) ) ) ) )
& ! [V23i: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V23i ) ) @ ( c_2Equote_2EEmpty__vm @ A_27a ) )
= ( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V24x: $i] : c_2Ebool_2ET ) ) )
& ! [V25t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V26t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V27l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V28l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V29c2: tp__ty_2Enum_2Enum,V30c1: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V30c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V28l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V26t1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V29c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V27l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V25t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( 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 @ V28l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V27l2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V30c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V28l1 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V26t1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V29c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V27l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V25t2 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V30c1 ) ) @ ( inj__ty_2Enum_2Enum @ V29c2 ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V28l1 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V26t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V25t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V29c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V27l2 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V30c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V28l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V26t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V25t2 ) ) ) ) ) )
& ! [V31t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V32t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V33l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V34l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V35c1: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V35c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V34l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V32t1 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V33l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V31t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( 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 @ V34l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V33l2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V35c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V34l1 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V32t1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V33l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V31t2 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V35c1 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V34l1 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V32t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V31t2 ) ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V33l2 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V35c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V34l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V32t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V31t2 ) ) ) ) ) )
& ! [V36t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V37t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V38l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V39l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V40c2: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V39l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V37t1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V40c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V38l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V36t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( 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 @ V39l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V38l2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V39l1 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V37t1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V40c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V38l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V36t2 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V40c2 ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V39l1 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V37t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V36t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V40c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V38l2 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V39l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V37t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V36t2 ) ) ) ) ) )
& ! [V41t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V42t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V43l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V44l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V44l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V42t1 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V43l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V41t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( 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 @ V44l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V43l2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V44l1 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V42t1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V43l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V41t2 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V44l1 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V42t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V41t2 ) ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V43l2 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V44l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V42t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V41t2 ) ) ) ) ) )
& ! [V45s1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V45s1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= V45s1 )
& ! [V46v6: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V47v5: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V48v4: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V48v4 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V47v5 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V46v6 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V48v4 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V47v5 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V46v6 ) ) ) )
& ! [V49v8: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V50v7: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V50v7 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V49v8 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V50v7 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V49v8 ) ) ) )
& ! [V51t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V52l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V53l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V54c2: tp__ty_2Enum_2Enum,V55c1: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__monom__insert @ ( inj__ty_2Enum_2Enum @ V55c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V53l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V54c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V52l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V51t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( 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 @ V53l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V52l2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V55c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V53l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V54c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V52l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V51t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V55c1 ) ) @ ( inj__ty_2Enum_2Enum @ V54c2 ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V53l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V51t2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V54c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V52l2 ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__monom__insert @ ( inj__ty_2Enum_2Enum @ V55c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V53l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V51t2 ) ) ) ) ) )
& ! [V56t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V57l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V58l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V59c1: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__monom__insert @ ( inj__ty_2Enum_2Enum @ V59c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V58l1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V57l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V56t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( 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 @ V58l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V57l2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V59c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V58l1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V57l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V56t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V59c1 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V58l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V56t2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V57l2 ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__monom__insert @ ( inj__ty_2Enum_2Enum @ V59c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V58l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V56t2 ) ) ) ) ) )
& ! [V60l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V61c1: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__monom__insert @ ( inj__ty_2Enum_2Enum @ V61c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V60l1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V61c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V60l1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) ) )
& ! [V62t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V63l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V64l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V65c2: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V64l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V65c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V63l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V62t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( 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 @ V64l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V63l2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V64l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V65c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V63l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V62t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V65c2 ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V64l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V62t2 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V65c2 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V63l2 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V64l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V62t2 ) ) ) ) ) )
& ! [V66t2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V67l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V68l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V68l1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V67l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V66t2 ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Eordering__CASE @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( 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 @ V68l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V67l2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V68l1 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V67l2 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V66t2 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V68l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V66t2 ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V67l2 ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V68l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V66t2 ) ) ) ) ) )
& ! [V69l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__varlist__insert @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V69l1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V69l1 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) ) )
& ! [V70c0: tp__ty_2Enum_2Enum,V71c: tp__ty_2Enum_2Enum,V72l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V73t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar @ ( inj__ty_2Enum_2Enum @ V70c0 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V71c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V72l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V73t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V70c0 ) ) @ ( inj__ty_2Enum_2Enum @ V71c ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V72l ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar @ ( inj__ty_2Enum_2Enum @ V70c0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V73t ) ) ) ) )
& ! [V74c0: tp__ty_2Enum_2Enum,V75l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V76t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar @ ( inj__ty_2Enum_2Enum @ V74c0 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V75l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V76t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V74c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V75l ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar @ ( inj__ty_2Enum_2Enum @ V74c0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V76t ) ) ) ) )
& ! [V77c0: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar @ ( inj__ty_2Enum_2Enum @ V77c0 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
& ! [V78l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V79c: tp__ty_2Enum_2Enum,V80l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V81t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V78l0 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V79c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V80l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V81t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__monom__insert @ ( inj__ty_2Enum_2Enum @ V79c ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__merge @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__lt ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V78l0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V80l ) ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V78l0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V81t ) ) ) ) )
& ! [V82l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V83l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V84t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V82l0 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V83l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V84t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__varlist__insert @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__merge @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__lt ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V82l0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V83l ) ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V82l0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V84t ) ) ) ) )
& ! [V85l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V85l0 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
& ! [V86c0: tp__ty_2Enum_2Enum,V87l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V88c: tp__ty_2Enum_2Enum,V89l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V90t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar3 @ ( inj__ty_2Enum_2Enum @ V86c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V87l0 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V88c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V89l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V90t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__monom__insert @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V86c0 ) ) @ ( inj__ty_2Enum_2Enum @ V88c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__merge @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__lt ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V87l0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V89l ) ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar3 @ ( inj__ty_2Enum_2Enum @ V86c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V87l0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V90t ) ) ) ) )
& ! [V91c0: tp__ty_2Enum_2Enum,V92l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V93l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V94t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar3 @ ( inj__ty_2Enum_2Enum @ V91c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V92l0 ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V93l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V94t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__monom__insert @ ( inj__ty_2Enum_2Enum @ V91c0 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__merge @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__lt ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V92l0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V93l ) ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar3 @ ( inj__ty_2Enum_2Enum @ V91c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V92l0 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V94t ) ) ) ) )
& ! [V95c0: tp__ty_2Enum_2Enum,V96l0: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar3 @ ( inj__ty_2Enum_2Enum @ V95c0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V96l0 ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
& ! [V97c1: tp__ty_2Enum_2Enum,V98l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V99t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V100s2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__prod @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V97c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V98l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V99t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V100s2 ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar3 @ ( inj__ty_2Enum_2Enum @ V97c1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V98l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V100s2 ) ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__prod @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V99t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V100s2 ) ) ) ) )
& ! [V101l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V102t1: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum,V103s2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__prod @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V101l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V102t1 ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V103s2 ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__scalar2 @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V101l1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V103s2 ) ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__prod @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V102t1 ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V103s2 ) ) ) ) )
& ! [V104s2: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__prod @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V104s2 ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
& ! [V105c: tp__ty_2Enum_2Enum,V106l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V107t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V105c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V106l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V107t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V105c ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V107t ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ecanonical_2Ecanonical__sum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V105c ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V106l ) ) @ ( ap @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V107t ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V105c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V106l ) ) @ ( ap @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V107t ) ) ) ) ) ) )
& ! [V108l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V109t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V108l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V109t ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V108l ) ) @ ( ap @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V109t ) ) ) ) )
& ( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
& ! [V110vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V111x: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V110vm ) ) @ ( inj__ty_2Equote_2Eindex @ V111x ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ ty_2Enum_2Enum ) @ ( inj__ty_2Equote_2Eindex @ V111x ) ) @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V110vm ) ) ) )
& ! [V112vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V113x: tp__ty_2Equote_2Eindex,V114x_27: tp__ty_2Equote_2Eindex,V115t_27: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V112vm ) ) @ ( inj__ty_2Equote_2Eindex @ V113x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Equote_2Eindex ) @ ( inj__ty_2Equote_2Eindex @ V114x_27 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V115t_27 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ ty_2Enum_2Enum ) @ ( inj__ty_2Equote_2Eindex @ V113x ) ) @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V112vm ) ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V112vm ) ) @ ( inj__ty_2Equote_2Eindex @ V114x_27 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V115t_27 ) ) ) ) )
& ! [V116vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V116vm ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ! [V117vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V118x: tp__ty_2Equote_2Eindex,V119t: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V117vm ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Equote_2Eindex ) @ ( inj__ty_2Equote_2Eindex @ V118x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V119t ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V117vm ) ) @ ( inj__ty_2Equote_2Eindex @ V118x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V119t ) ) ) )
& ! [V120vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V121c: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V120vm ) ) @ ( inj__ty_2Enum_2Enum @ V121c ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) )
= V121c )
& ! [V122vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V123c: tp__ty_2Enum_2Enum,V124x: tp__ty_2Equote_2Eindex,V125t: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V122vm ) ) @ ( inj__ty_2Enum_2Enum @ V123c ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Equote_2Eindex ) @ ( inj__ty_2Equote_2Eindex @ V124x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V125t ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V123c ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ivl__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V122vm ) ) @ ( inj__ty_2Equote_2Eindex @ V124x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V125t ) ) ) ) )
& ! [V126vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V127a: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V126vm ) ) @ ( inj__ty_2Enum_2Enum @ V127a ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= V127a )
& ! [V128vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V129a: tp__ty_2Enum_2Enum,V130l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V131t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V128vm ) ) @ ( inj__ty_2Enum_2Enum @ V129a ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V130l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V131t ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V129a ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V128vm ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V128vm ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V130l ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V131t ) ) ) ) )
& ! [V132vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V133a: tp__ty_2Enum_2Enum,V134c: tp__ty_2Enum_2Enum,V135l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V136t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V132vm ) ) @ ( inj__ty_2Enum_2Enum @ V133a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V134c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V135l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V136t ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V133a ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V132vm ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V132vm ) ) @ ( inj__ty_2Enum_2Enum @ V134c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V135l ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V136t ) ) ) ) )
& ! [V137vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V137vm ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) )
= fo__c_2Enum_2E0 )
& ! [V138vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V139l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V140t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V138vm ) ) @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V139l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V140t ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V138vm ) ) @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__vl @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V138vm ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V139l ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V140t ) ) ) )
& ! [V141vm: tp__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum,V142c: tp__ty_2Enum_2Enum,V143l: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V144t: tp__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__cs @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V141vm ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V142c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V143l ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V144t ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__ics__aux @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V141vm ) ) @ ( ap @ ( ap @ ( ap @ c_2EnumRing_2Enum__interp__m @ ( inj__c_ty_2Equote_2Evarmap_ty_2Enum_2Enum @ V141vm ) ) @ ( inj__ty_2Enum_2Enum @ V142c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V143l ) ) ) @ ( inj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ V144t ) ) ) )
& ! [V145i: tp__ty_2Equote_2Eindex] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( ap @ ( c_2Ecanonical_2ESPvar @ ty_2Enum_2Enum ) @ ( inj__ty_2Equote_2Eindex @ V145i ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__varlist @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Equote_2Eindex ) @ ( inj__ty_2Equote_2Eindex @ V145i ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) ) )
& ! [V146c: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( ap @ ( c_2Ecanonical_2ESPconst @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V146c ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ecanonical_2ECons__monom @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V146c ) ) @ ( c_2Elist_2ENIL @ ty_2Equote_2Eindex ) ) @ ( c_2Ecanonical_2ENil__monom @ ty_2Enum_2Enum ) ) ) )
& ! [V147l: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,V148r: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( ap @ ( ap @ ( c_2Ecanonical_2ESPplus @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V147l ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V148r ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__merge @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V147l ) ) ) @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V148r ) ) ) ) )
& ! [V149l: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum,V150r: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( ap @ ( ap @ ( c_2Ecanonical_2ESPmult @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V149l ) ) @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V150r ) ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2EnumRing_2Enum__canonical__sum__prod @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V149l ) ) ) @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V150r ) ) ) ) )
& ! [V151x: tp__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum] :
( ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__spolynom__simplify @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V151x ) ) )
= ( surj__c_ty_2Ecanonical_2Ecanonical__sum_ty_2Enum_2Enum @ ( ap @ c_2EnumRing_2Enum__canonical__sum__simplify @ ( ap @ c_2EnumRing_2Enum__spolynom__normalize @ ( inj__c_ty_2Ecanonical_2Espolynom_ty_2Enum_2Enum @ V151x ) ) ) ) ) ) ).
thf(conj_thm_2EnumRing_2Enum__rewrites,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ! [V1n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= V1n )
& ! [V2n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= V2n )
& ! [V3n: tp__ty_2Enum_2Enum,V4m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V4m ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V4m ) ) ) ) ) )
& ! [V5n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) )
= fo__c_2Enum_2E0 )
& ! [V6n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V6n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= fo__c_2Enum_2E0 )
& ! [V7n: tp__ty_2Enum_2Enum,V8m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V7n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V8m ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V7n ) ) @ ( inj__ty_2Enum_2Enum @ V8m ) ) ) ) )
& ! [V9n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V9n ) ) )
= fo__c_2Enum_2E0 )
& ! [V10n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V10n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= V10n )
& ! [V11n: tp__ty_2Enum_2Enum,V12m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V11n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V12m ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V11n ) ) @ ( inj__ty_2Enum_2Enum @ V12m ) ) ) ) )
& ! [V13n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V13n ) ) ) ) )
= fo__c_2Enum_2E0 )
& ! [V14n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V14n ) ) ) ) )
= fo__c_2Enum_2E0 )
& ! [V15n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V15n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ! [V16n: tp__ty_2Enum_2Enum,V17m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V16n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V17m ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V16n ) ) @ ( inj__ty_2Enum_2Enum @ V17m ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ! [V18n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V18n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V18n ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= fo__c_2Enum_2E0 )
& ! [V19n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V19n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V19n ) ) ) ) )
& ! [V20n: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V20n ) ) )
= fo__c_2Enum_2E0 )
<=> ( V20n = fo__c_2Earithmetic_2EZERO ) )
& ! [V21n: tp__ty_2Enum_2Enum] :
( ( fo__c_2Enum_2E0
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V21n ) ) ) )
<=> ( V21n = fo__c_2Earithmetic_2EZERO ) )
& ! [V22n: tp__ty_2Enum_2Enum,V23m: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V22n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V23m ) ) ) )
<=> ( V22n = V23m ) )
& ! [V24n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V24n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $false )
& ! [V25n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V25n ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V25n ) ) ) )
& ! [V26n: tp__ty_2Enum_2Enum,V27m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V26n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V27m ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V26n ) ) @ ( inj__ty_2Enum_2Enum @ V27m ) ) ) )
& ! [V28n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V28n ) ) )
<=> $false )
& ! [V29n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V29n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V29n ) ) ) )
& ! [V30n: tp__ty_2Enum_2Enum,V31m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V30n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V31m ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V31m ) ) @ ( inj__ty_2Enum_2Enum @ V30n ) ) ) )
& ! [V32n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V32n ) ) )
<=> $true )
& ! [V33n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V33n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V33n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
& ! [V34n: tp__ty_2Enum_2Enum,V35m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V34n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V35m ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V34n ) ) @ ( inj__ty_2Enum_2Enum @ V35m ) ) ) )
& ! [V36n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V36n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $true )
& ! [V37n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V37n ) ) )
<=> ( V37n = fo__c_2Enum_2E0 ) )
& ! [V38n: tp__ty_2Enum_2Enum,V39m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V38n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V39m ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V39m ) ) @ ( inj__ty_2Enum_2Enum @ V38n ) ) ) )
& ! [V40n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V40n ) ) ) )
<=> ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V40n ) ) ) )
& ! [V41n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V41n ) ) ) )
<=> ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V41n ) ) ) )
& ~ ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V42n: tp__ty_2Enum_2Enum,V43m: tp__ty_2Enum_2Enum] :
( ( ( fo__c_2Earithmetic_2EZERO
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V42n ) ) ) )
<=> $false )
& ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V42n ) ) )
= fo__c_2Earithmetic_2EZERO )
<=> $false )
& ( ( fo__c_2Earithmetic_2EZERO
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V42n ) ) ) )
<=> $false )
& ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V42n ) ) )
= fo__c_2Earithmetic_2EZERO )
<=> $false )
& ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V42n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V43m ) ) ) )
<=> $false )
& ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V42n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V43m ) ) ) )
<=> $false )
& ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V42n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V43m ) ) ) )
<=> ( V42n = V43m ) )
& ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V42n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V43m ) ) ) )
<=> ( V42n = V43m ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
& ! [V44n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V44n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V44n ) ) ) )
& ! [V45n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V45n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V45n ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
& ! [V46n: tp__ty_2Enum_2Enum,V47m: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) )
= V46n )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
= V46n )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V46n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V46n ) ) @ ( inj__ty_2Enum_2Enum @ V47m ) ) ) ) ) ) )
& ! [V48n: tp__ty_2Enum_2Enum,V49m: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V48n ) ) )
= fo__c_2Earithmetic_2EZERO )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V48n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
= fo__c_2Earithmetic_2EZERO )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V48n ) ) ) @ ( inj__ty_2Enum_2Enum @ V49m ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V48n ) ) @ ( inj__ty_2Enum_2Enum @ V49m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V49m ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V48n ) ) ) @ ( inj__ty_2Enum_2Enum @ V49m ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V48n ) ) @ ( inj__ty_2Enum_2Enum @ V49m ) ) ) @ ( inj__ty_2Enum_2Enum @ V49m ) ) ) ) ) ) )
& ! [V50n: tp__ty_2Enum_2Enum] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V50n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V50n ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V50n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V50n ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
= fo__c_2Earithmetic_2EZERO ) )
& ( ( fo__c_2Earithmetic_2EZERO = fo__c_2Earithmetic_2EZERO )
<=> $true )
& ( ( fo__c_2Enum_2E0 = fo__c_2Enum_2E0 )
<=> $true ) ) ).
%------------------------------------------------------------------------------